idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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11,101 | Why should we care about rapid mixing in MCMC chains? | The ideal Monte Carlo algorithm uses independent successive random values. In MCMC, successive values are not independant, which makes the method converge slower than ideal Monte Carlo; however, the faster it mixes, the faster the dependence decays in successive iterations¹, and the faster it converges.
¹ I mean here t... | Why should we care about rapid mixing in MCMC chains? | The ideal Monte Carlo algorithm uses independent successive random values. In MCMC, successive values are not independant, which makes the method converge slower than ideal Monte Carlo; however, the f | Why should we care about rapid mixing in MCMC chains?
The ideal Monte Carlo algorithm uses independent successive random values. In MCMC, successive values are not independant, which makes the method converge slower than ideal Monte Carlo; however, the faster it mixes, the faster the dependence decays in successive ite... | Why should we care about rapid mixing in MCMC chains?
The ideal Monte Carlo algorithm uses independent successive random values. In MCMC, successive values are not independant, which makes the method converge slower than ideal Monte Carlo; however, the f |
11,102 | Why should we care about rapid mixing in MCMC chains? | In completion of both earlier answers, mixing is only one aspect of MCMC convergence. It is indeed directly connected with the speed of forgetting the initial value or distribution of the Markov chain $(X_n)$. For instance,the mathematical notion of $\alpha$-mixing is defined by the measure
$$
\alpha(n) = \sup_{A,B} \... | Why should we care about rapid mixing in MCMC chains? | In completion of both earlier answers, mixing is only one aspect of MCMC convergence. It is indeed directly connected with the speed of forgetting the initial value or distribution of the Markov chain | Why should we care about rapid mixing in MCMC chains?
In completion of both earlier answers, mixing is only one aspect of MCMC convergence. It is indeed directly connected with the speed of forgetting the initial value or distribution of the Markov chain $(X_n)$. For instance,the mathematical notion of $\alpha$-mixing ... | Why should we care about rapid mixing in MCMC chains?
In completion of both earlier answers, mixing is only one aspect of MCMC convergence. It is indeed directly connected with the speed of forgetting the initial value or distribution of the Markov chain |
11,103 | Why should we care about rapid mixing in MCMC chains? | The presumptions that motivate the desire for a rapidly mixing chain are that you care about computing time and that you want a representative sample from the posterior. The former will depend on the complexity of the problem: if you have a small/simple problem, it may not matter much whether your algorithm is efficie... | Why should we care about rapid mixing in MCMC chains? | The presumptions that motivate the desire for a rapidly mixing chain are that you care about computing time and that you want a representative sample from the posterior. The former will depend on the | Why should we care about rapid mixing in MCMC chains?
The presumptions that motivate the desire for a rapidly mixing chain are that you care about computing time and that you want a representative sample from the posterior. The former will depend on the complexity of the problem: if you have a small/simple problem, it... | Why should we care about rapid mixing in MCMC chains?
The presumptions that motivate the desire for a rapidly mixing chain are that you care about computing time and that you want a representative sample from the posterior. The former will depend on the |
11,104 | Is it possible to accumulate a set of statistics that describes a large number of samples such that I can then produce a boxplot? | For 'on the fly' boxplot, you will need 'on the fly' min/max (trivial) as well as 'on the fly' quartiles (0.25,0.5=median and 0.75).
A lot of work has been going on recently in the problem of online (or 'on the fly') algorithm for median computation.
A recent developements is binmedian. As a side-kick, it also enjoy ... | Is it possible to accumulate a set of statistics that describes a large number of samples such that | For 'on the fly' boxplot, you will need 'on the fly' min/max (trivial) as well as 'on the fly' quartiles (0.25,0.5=median and 0.75).
A lot of work has been going on recently in the problem of online ( | Is it possible to accumulate a set of statistics that describes a large number of samples such that I can then produce a boxplot?
For 'on the fly' boxplot, you will need 'on the fly' min/max (trivial) as well as 'on the fly' quartiles (0.25,0.5=median and 0.75).
A lot of work has been going on recently in the problem o... | Is it possible to accumulate a set of statistics that describes a large number of samples such that
For 'on the fly' boxplot, you will need 'on the fly' min/max (trivial) as well as 'on the fly' quartiles (0.25,0.5=median and 0.75).
A lot of work has been going on recently in the problem of online ( |
11,105 | Is it possible to accumulate a set of statistics that describes a large number of samples such that I can then produce a boxplot? | Instead of just finding the median, there is an algorithm that directly maintains an estimated histogram: "the P-Square Algorithm for Dynamic Calculation of Quantiles and Histograms Without Storing Observations". This will probably be much more efficient that repeated binning for every quantile you want. | Is it possible to accumulate a set of statistics that describes a large number of samples such that | Instead of just finding the median, there is an algorithm that directly maintains an estimated histogram: "the P-Square Algorithm for Dynamic Calculation of Quantiles and Histograms Without Storin | Is it possible to accumulate a set of statistics that describes a large number of samples such that I can then produce a boxplot?
Instead of just finding the median, there is an algorithm that directly maintains an estimated histogram: "the P-Square Algorithm for Dynamic Calculation of Quantiles and Histograms Witho... | Is it possible to accumulate a set of statistics that describes a large number of samples such that
Instead of just finding the median, there is an algorithm that directly maintains an estimated histogram: "the P-Square Algorithm for Dynamic Calculation of Quantiles and Histograms Without Storin |
11,106 | How bad is hyperparameter tuning outside cross-validation? | The effects of this bias can be very great. A good demonstration of this is given by the open machine learning competitions that feature in some machine learning conferences. These generally have a training set, a validation set and a test set. The competitors don't get to see the labels for either the validation se... | How bad is hyperparameter tuning outside cross-validation? | The effects of this bias can be very great. A good demonstration of this is given by the open machine learning competitions that feature in some machine learning conferences. These generally have a | How bad is hyperparameter tuning outside cross-validation?
The effects of this bias can be very great. A good demonstration of this is given by the open machine learning competitions that feature in some machine learning conferences. These generally have a training set, a validation set and a test set. The competito... | How bad is hyperparameter tuning outside cross-validation?
The effects of this bias can be very great. A good demonstration of this is given by the open machine learning competitions that feature in some machine learning conferences. These generally have a |
11,107 | How bad is hyperparameter tuning outside cross-validation? | The bias you are talking about is still mainly connected to overfitting.
You can keep the risk low by evaluating only very few models for fixing the regularization hyperparameter plus going for a low complexity within the plausible choice.
As @MarcClaesen points out, you have the learning curve working for you, which... | How bad is hyperparameter tuning outside cross-validation? | The bias you are talking about is still mainly connected to overfitting.
You can keep the risk low by evaluating only very few models for fixing the regularization hyperparameter plus going for a low | How bad is hyperparameter tuning outside cross-validation?
The bias you are talking about is still mainly connected to overfitting.
You can keep the risk low by evaluating only very few models for fixing the regularization hyperparameter plus going for a low complexity within the plausible choice.
As @MarcClaesen poi... | How bad is hyperparameter tuning outside cross-validation?
The bias you are talking about is still mainly connected to overfitting.
You can keep the risk low by evaluating only very few models for fixing the regularization hyperparameter plus going for a low |
11,108 | How bad is hyperparameter tuning outside cross-validation? | If you are only selecting the hyperparameter for the LASSO, there is no need for a nested CV. Hyper-parameter selection is done in a single/flat CV interaction.
Given that you have already decided to use LASSO and given that you have already decided which features to keep and give to the algorithm (the LASSO will like... | How bad is hyperparameter tuning outside cross-validation? | If you are only selecting the hyperparameter for the LASSO, there is no need for a nested CV. Hyper-parameter selection is done in a single/flat CV interaction.
Given that you have already decided to | How bad is hyperparameter tuning outside cross-validation?
If you are only selecting the hyperparameter for the LASSO, there is no need for a nested CV. Hyper-parameter selection is done in a single/flat CV interaction.
Given that you have already decided to use LASSO and given that you have already decided which feat... | How bad is hyperparameter tuning outside cross-validation?
If you are only selecting the hyperparameter for the LASSO, there is no need for a nested CV. Hyper-parameter selection is done in a single/flat CV interaction.
Given that you have already decided to |
11,109 | How bad is hyperparameter tuning outside cross-validation? | Any complex learning algorithm, like SVM, neural networks, random forest, ... can attain 100% training accuracy if you let them (for instance through weak/no regularization), with absolutely horrible generalization performance as a result.
For instance, lets use an SVM with RBF kernel $\kappa(\mathbf{x}_i,\mathbf{x}_j... | How bad is hyperparameter tuning outside cross-validation? | Any complex learning algorithm, like SVM, neural networks, random forest, ... can attain 100% training accuracy if you let them (for instance through weak/no regularization), with absolutely horrible | How bad is hyperparameter tuning outside cross-validation?
Any complex learning algorithm, like SVM, neural networks, random forest, ... can attain 100% training accuracy if you let them (for instance through weak/no regularization), with absolutely horrible generalization performance as a result.
For instance, lets u... | How bad is hyperparameter tuning outside cross-validation?
Any complex learning algorithm, like SVM, neural networks, random forest, ... can attain 100% training accuracy if you let them (for instance through weak/no regularization), with absolutely horrible |
11,110 | Why are random variables defined as functions? | If you are wondering why all this machinery is used when something much simpler could suffice--you are right, for most common situations. However, the measure-theoretic version of probability was developed by Kolmogorov for the purpose of establishing a theory of such generality that it could handle, in some cases, ve... | Why are random variables defined as functions? | If you are wondering why all this machinery is used when something much simpler could suffice--you are right, for most common situations. However, the measure-theoretic version of probability was dev | Why are random variables defined as functions?
If you are wondering why all this machinery is used when something much simpler could suffice--you are right, for most common situations. However, the measure-theoretic version of probability was developed by Kolmogorov for the purpose of establishing a theory of such gen... | Why are random variables defined as functions?
If you are wondering why all this machinery is used when something much simpler could suffice--you are right, for most common situations. However, the measure-theoretic version of probability was dev |
11,111 | Why are random variables defined as functions? | The issues regarding $\sigma$-algebras are mathematical subtleties, that do not really explain why or if we need a background space. Indeed, I would say that there is no compelling evidence that the background space is a necessity. For any probabilistic setup
$(E, \mathbb{E}, \mu)$ where $E$ is the sample space, $\mat... | Why are random variables defined as functions? | The issues regarding $\sigma$-algebras are mathematical subtleties, that do not really explain why or if we need a background space. Indeed, I would say that there is no compelling evidence that the b | Why are random variables defined as functions?
The issues regarding $\sigma$-algebras are mathematical subtleties, that do not really explain why or if we need a background space. Indeed, I would say that there is no compelling evidence that the background space is a necessity. For any probabilistic setup
$(E, \mathbb... | Why are random variables defined as functions?
The issues regarding $\sigma$-algebras are mathematical subtleties, that do not really explain why or if we need a background space. Indeed, I would say that there is no compelling evidence that the b |
11,112 | Why are random variables defined as functions? | I only recently stumbled over this new way to think about the Random Variable $X$ as well as about the background space $\Omega$. I am not sure whether this is the question you were looking for, as it is not a mathematical reason, but I think it provides a very neat way to think of RVs.
Imagine a situation in which we ... | Why are random variables defined as functions? | I only recently stumbled over this new way to think about the Random Variable $X$ as well as about the background space $\Omega$. I am not sure whether this is the question you were looking for, as it | Why are random variables defined as functions?
I only recently stumbled over this new way to think about the Random Variable $X$ as well as about the background space $\Omega$. I am not sure whether this is the question you were looking for, as it is not a mathematical reason, but I think it provides a very neat way to... | Why are random variables defined as functions?
I only recently stumbled over this new way to think about the Random Variable $X$ as well as about the background space $\Omega$. I am not sure whether this is the question you were looking for, as it |
11,113 | When are Shao's results on leave-one-out cross-validation applicable? | You need to specify the purpose of the model before you can say whether Shao's results are applicable. For example, if the purpose is prediction, then LOOCV makes good sense and the inconsistency of variable selection is not a problem. On the other hand, if the purpose is to identify the important variables and explain... | When are Shao's results on leave-one-out cross-validation applicable? | You need to specify the purpose of the model before you can say whether Shao's results are applicable. For example, if the purpose is prediction, then LOOCV makes good sense and the inconsistency of v | When are Shao's results on leave-one-out cross-validation applicable?
You need to specify the purpose of the model before you can say whether Shao's results are applicable. For example, if the purpose is prediction, then LOOCV makes good sense and the inconsistency of variable selection is not a problem. On the other h... | When are Shao's results on leave-one-out cross-validation applicable?
You need to specify the purpose of the model before you can say whether Shao's results are applicable. For example, if the purpose is prediction, then LOOCV makes good sense and the inconsistency of v |
11,114 | When are Shao's results on leave-one-out cross-validation applicable? | This paper is somewhat controversial, and somewhat ignored
Not really, it's well regarded where the theory of model selection is concerned, though it's certainly misinterpreted. The real issue is how relevant it is to the practice of modeling in the wild. Suppose you perform the simulations for the cases you propose... | When are Shao's results on leave-one-out cross-validation applicable? | This paper is somewhat controversial, and somewhat ignored
Not really, it's well regarded where the theory of model selection is concerned, though it's certainly misinterpreted. The real issue is ho | When are Shao's results on leave-one-out cross-validation applicable?
This paper is somewhat controversial, and somewhat ignored
Not really, it's well regarded where the theory of model selection is concerned, though it's certainly misinterpreted. The real issue is how relevant it is to the practice of modeling in th... | When are Shao's results on leave-one-out cross-validation applicable?
This paper is somewhat controversial, and somewhat ignored
Not really, it's well regarded where the theory of model selection is concerned, though it's certainly misinterpreted. The real issue is ho |
11,115 | When are Shao's results on leave-one-out cross-validation applicable? | I would say: everywhere, but I haven't seen a strict proof of it. The intuition behind is such that when doing CV one must hold a balance between train large enough to build sensible model and test large enough so it would be a sensible benchmark.
When dealing with thousands of pretty homogeneous objects, picking one i... | When are Shao's results on leave-one-out cross-validation applicable? | I would say: everywhere, but I haven't seen a strict proof of it. The intuition behind is such that when doing CV one must hold a balance between train large enough to build sensible model and test la | When are Shao's results on leave-one-out cross-validation applicable?
I would say: everywhere, but I haven't seen a strict proof of it. The intuition behind is such that when doing CV one must hold a balance between train large enough to build sensible model and test large enough so it would be a sensible benchmark.
Wh... | When are Shao's results on leave-one-out cross-validation applicable?
I would say: everywhere, but I haven't seen a strict proof of it. The intuition behind is such that when doing CV one must hold a balance between train large enough to build sensible model and test la |
11,116 | When are Shao's results on leave-one-out cross-validation applicable? | 1) The answer by @ars mentions Yang (2005), "Can The Strengths of AIC and BIC Be Shared?". Loosely speaking, it seems that you can't have a model-selection criterion achieve both consistency (tend to pick the correct model, if there is indeed a correct model and it is among the models being considered) and efficiency (... | When are Shao's results on leave-one-out cross-validation applicable? | 1) The answer by @ars mentions Yang (2005), "Can The Strengths of AIC and BIC Be Shared?". Loosely speaking, it seems that you can't have a model-selection criterion achieve both consistency (tend to | When are Shao's results on leave-one-out cross-validation applicable?
1) The answer by @ars mentions Yang (2005), "Can The Strengths of AIC and BIC Be Shared?". Loosely speaking, it seems that you can't have a model-selection criterion achieve both consistency (tend to pick the correct model, if there is indeed a corre... | When are Shao's results on leave-one-out cross-validation applicable?
1) The answer by @ars mentions Yang (2005), "Can The Strengths of AIC and BIC Be Shared?". Loosely speaking, it seems that you can't have a model-selection criterion achieve both consistency (tend to |
11,117 | When are Shao's results on leave-one-out cross-validation applicable? | I believe Shao's article applies most effectively to situations where a person is trying to eliminate predictors from a model (whether linear or non-linear, such as machine learning, etc.), and he recommends using Monte Carlo CV (MCCV) in this case.
On the other hand, if you are not worried about the size (number of ... | When are Shao's results on leave-one-out cross-validation applicable? | I believe Shao's article applies most effectively to situations where a person is trying to eliminate predictors from a model (whether linear or non-linear, such as machine learning, etc.), and he rec | When are Shao's results on leave-one-out cross-validation applicable?
I believe Shao's article applies most effectively to situations where a person is trying to eliminate predictors from a model (whether linear or non-linear, such as machine learning, etc.), and he recommends using Monte Carlo CV (MCCV) in this case. ... | When are Shao's results on leave-one-out cross-validation applicable?
I believe Shao's article applies most effectively to situations where a person is trying to eliminate predictors from a model (whether linear or non-linear, such as machine learning, etc.), and he rec |
11,118 | How does ACF & PACF identify the order of MA and AR terms? | The quotes are from the link in the OP:
Identification of an AR model is often best done with the PACF.
For an AR model, the theoretical PACF “shuts off” past the order of
the model. The phrase “shuts off” means that in theory the partial
autocorrelations are equal to $0$ beyond that point. Put another way,
the numb... | How does ACF & PACF identify the order of MA and AR terms? | The quotes are from the link in the OP:
Identification of an AR model is often best done with the PACF.
For an AR model, the theoretical PACF “shuts off” past the order of
the model. The phrase “shu | How does ACF & PACF identify the order of MA and AR terms?
The quotes are from the link in the OP:
Identification of an AR model is often best done with the PACF.
For an AR model, the theoretical PACF “shuts off” past the order of
the model. The phrase “shuts off” means that in theory the partial
autocorrelations are... | How does ACF & PACF identify the order of MA and AR terms?
The quotes are from the link in the OP:
Identification of an AR model is often best done with the PACF.
For an AR model, the theoretical PACF “shuts off” past the order of
the model. The phrase “shu |
11,119 | How does ACF & PACF identify the order of MA and AR terms? | Robert Nau from Duke's Fuqua School of Business gives a detailed and somewhat intuitive explanation of how ACF and PACF plots can be used to choose AR and MA orders here and here. I give a brief summary of his arguments below.
A simple explanation of why PACF identifies the AR order
The partial autocorrelations can be ... | How does ACF & PACF identify the order of MA and AR terms? | Robert Nau from Duke's Fuqua School of Business gives a detailed and somewhat intuitive explanation of how ACF and PACF plots can be used to choose AR and MA orders here and here. I give a brief summa | How does ACF & PACF identify the order of MA and AR terms?
Robert Nau from Duke's Fuqua School of Business gives a detailed and somewhat intuitive explanation of how ACF and PACF plots can be used to choose AR and MA orders here and here. I give a brief summary of his arguments below.
A simple explanation of why PACF i... | How does ACF & PACF identify the order of MA and AR terms?
Robert Nau from Duke's Fuqua School of Business gives a detailed and somewhat intuitive explanation of how ACF and PACF plots can be used to choose AR and MA orders here and here. I give a brief summa |
11,120 | How does ACF & PACF identify the order of MA and AR terms? | On a higher level, here is how to understand it. (If you need a more mathematical approach, I can gladly go after some of my notes on time series analysis)
ACF and PACF are theoretical statistical constructs just like an expected value or variance, but on different domains. The same way that Expected values come up whe... | How does ACF & PACF identify the order of MA and AR terms? | On a higher level, here is how to understand it. (If you need a more mathematical approach, I can gladly go after some of my notes on time series analysis)
ACF and PACF are theoretical statistical con | How does ACF & PACF identify the order of MA and AR terms?
On a higher level, here is how to understand it. (If you need a more mathematical approach, I can gladly go after some of my notes on time series analysis)
ACF and PACF are theoretical statistical constructs just like an expected value or variance, but on diffe... | How does ACF & PACF identify the order of MA and AR terms?
On a higher level, here is how to understand it. (If you need a more mathematical approach, I can gladly go after some of my notes on time series analysis)
ACF and PACF are theoretical statistical con |
11,121 | Distribution of an observation-level Mahalanobis distance | Check out Gaussian Mixture Modeling by Exploiting the Mahalanobis Distance
(alternative link). See page no 13, Second column. Authors also given some proof also for deriving the distribution. The distribution is scaled beta. Please let me know if this is not working for you. Otherwise I could check any hint in the S.S... | Distribution of an observation-level Mahalanobis distance | Check out Gaussian Mixture Modeling by Exploiting the Mahalanobis Distance
(alternative link). See page no 13, Second column. Authors also given some proof also for deriving the distribution. The dis | Distribution of an observation-level Mahalanobis distance
Check out Gaussian Mixture Modeling by Exploiting the Mahalanobis Distance
(alternative link). See page no 13, Second column. Authors also given some proof also for deriving the distribution. The distribution is scaled beta. Please let me know if this is not wo... | Distribution of an observation-level Mahalanobis distance
Check out Gaussian Mixture Modeling by Exploiting the Mahalanobis Distance
(alternative link). See page no 13, Second column. Authors also given some proof also for deriving the distribution. The dis |
11,122 | Distribution of an observation-level Mahalanobis distance | There are 3 relevant distributions. As noted, if the true population parameters are used then the distribution is chi-squared with $df=p$. This is also the asymptotic distribution with estimated parameters and large sample size.
Another answer gives the correct distribution for the most common situation, with estimated... | Distribution of an observation-level Mahalanobis distance | There are 3 relevant distributions. As noted, if the true population parameters are used then the distribution is chi-squared with $df=p$. This is also the asymptotic distribution with estimated param | Distribution of an observation-level Mahalanobis distance
There are 3 relevant distributions. As noted, if the true population parameters are used then the distribution is chi-squared with $df=p$. This is also the asymptotic distribution with estimated parameters and large sample size.
Another answer gives the correct ... | Distribution of an observation-level Mahalanobis distance
There are 3 relevant distributions. As noted, if the true population parameters are used then the distribution is chi-squared with $df=p$. This is also the asymptotic distribution with estimated param |
11,123 | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE? | Definitely not.
I agree that t-SNE is an amazing algorithm that works extremely well and that was a real breakthrough at the time. However:
it does have serious shortcomings;
some of the shortcomings must be solvable;
there already are algorithms that perform noticeably better in some cases;
many t-SNE's properties ar... | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE? | Definitely not.
I agree that t-SNE is an amazing algorithm that works extremely well and that was a real breakthrough at the time. However:
it does have serious shortcomings;
some of the shortcomings | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE?
Definitely not.
I agree that t-SNE is an amazing algorithm that works extremely well and that was a real breakthrough at the time. However:
it does have serious shortcomings;
some of the shortcomings must be solvable;
... | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE?
Definitely not.
I agree that t-SNE is an amazing algorithm that works extremely well and that was a real breakthrough at the time. However:
it does have serious shortcomings;
some of the shortcomings |
11,124 | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE? | I would still love to hear other comments but I'll post my own answer for now, as I see it. While I was looking for a more "practical" answer, there are two theoretical "dis-advantages" to t-sne which are worth mentioning; the first one is less problematic, and the second should definitely be considered:
t-sne cost fu... | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE? | I would still love to hear other comments but I'll post my own answer for now, as I see it. While I was looking for a more "practical" answer, there are two theoretical "dis-advantages" to t-sne which | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE?
I would still love to hear other comments but I'll post my own answer for now, as I see it. While I was looking for a more "practical" answer, there are two theoretical "dis-advantages" to t-sne which are worth mentioni... | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE?
I would still love to hear other comments but I'll post my own answer for now, as I see it. While I was looking for a more "practical" answer, there are two theoretical "dis-advantages" to t-sne which |
11,125 | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE? | Here's an excellent analysis of how varying the parameters when running t-SNE affects some very simple datasets: http://distill.pub/2016/misread-tsne/. In general, t-SNE seems to do well at recognizing high-dimensional structures (including relationships more complex than clusters), though this is subject to parameter ... | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE? | Here's an excellent analysis of how varying the parameters when running t-SNE affects some very simple datasets: http://distill.pub/2016/misread-tsne/. In general, t-SNE seems to do well at recognizin | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE?
Here's an excellent analysis of how varying the parameters when running t-SNE affects some very simple datasets: http://distill.pub/2016/misread-tsne/. In general, t-SNE seems to do well at recognizing high-dimensional ... | Should dimensionality reduction for visualization be considered a "closed" problem, solved by t-SNE?
Here's an excellent analysis of how varying the parameters when running t-SNE affects some very simple datasets: http://distill.pub/2016/misread-tsne/. In general, t-SNE seems to do well at recognizin |
11,126 | Modelling with more variables than data points | It's certainly possible to fit good models when there are more variables than data points, but this must be done with care.
When there are more variables than data points, the problem may not have a unique solution unless it's further constrained. That is, there may be multiple (perhaps infinitely many) solutions that ... | Modelling with more variables than data points | It's certainly possible to fit good models when there are more variables than data points, but this must be done with care.
When there are more variables than data points, the problem may not have a u | Modelling with more variables than data points
It's certainly possible to fit good models when there are more variables than data points, but this must be done with care.
When there are more variables than data points, the problem may not have a unique solution unless it's further constrained. That is, there may be mul... | Modelling with more variables than data points
It's certainly possible to fit good models when there are more variables than data points, but this must be done with care.
When there are more variables than data points, the problem may not have a u |
11,127 | Modelling with more variables than data points | There are many solutions this problem: find three terms whose sum is equal to $3$: $3=7-3-1$, $3=1234-23451+22220$, for instance. Here, the number of observations is one ($n=1$) and $p=3$.
In mathematics, a useful concept is that of overdetermined systems (and their converse, underdetermined systems). Key features from... | Modelling with more variables than data points | There are many solutions this problem: find three terms whose sum is equal to $3$: $3=7-3-1$, $3=1234-23451+22220$, for instance. Here, the number of observations is one ($n=1$) and $p=3$.
In mathemat | Modelling with more variables than data points
There are many solutions this problem: find three terms whose sum is equal to $3$: $3=7-3-1$, $3=1234-23451+22220$, for instance. Here, the number of observations is one ($n=1$) and $p=3$.
In mathematics, a useful concept is that of overdetermined systems (and their conver... | Modelling with more variables than data points
There are many solutions this problem: find three terms whose sum is equal to $3$: $3=7-3-1$, $3=1234-23451+22220$, for instance. Here, the number of observations is one ($n=1$) and $p=3$.
In mathemat |
11,128 | Why does the variance of a sample change if the observations are duplicated? | If you define variance as $s^2_{n}=$$\,\text{MSE}\,$$=\frac1n \sum_{i=1}^n (x_i-\bar{x})^2$ -- similar to population variance but with sample mean for $\mu$, then both your samples would have the same variance.
So the difference is purely because of Bessel's correction in the usual formula for the sample variance ($s^2... | Why does the variance of a sample change if the observations are duplicated? | If you define variance as $s^2_{n}=$$\,\text{MSE}\,$$=\frac1n \sum_{i=1}^n (x_i-\bar{x})^2$ -- similar to population variance but with sample mean for $\mu$, then both your samples would have the same | Why does the variance of a sample change if the observations are duplicated?
If you define variance as $s^2_{n}=$$\,\text{MSE}\,$$=\frac1n \sum_{i=1}^n (x_i-\bar{x})^2$ -- similar to population variance but with sample mean for $\mu$, then both your samples would have the same variance.
So the difference is purely beca... | Why does the variance of a sample change if the observations are duplicated?
If you define variance as $s^2_{n}=$$\,\text{MSE}\,$$=\frac1n \sum_{i=1}^n (x_i-\bar{x})^2$ -- similar to population variance but with sample mean for $\mu$, then both your samples would have the same |
11,129 | Why does the variance of a sample change if the observations are duplicated? | As some sort of mnemonic, $V\,X = E\,V\,X + V\,E\,X$. So the expected value of a sample's variance is too low, with the difference being the variance of the sample's mean.
The usual sample variance formula compensates for that, and the variance of the sample's mean scales inversely with sample size.
As an extreme exam... | Why does the variance of a sample change if the observations are duplicated? | As some sort of mnemonic, $V\,X = E\,V\,X + V\,E\,X$. So the expected value of a sample's variance is too low, with the difference being the variance of the sample's mean.
The usual sample variance f | Why does the variance of a sample change if the observations are duplicated?
As some sort of mnemonic, $V\,X = E\,V\,X + V\,E\,X$. So the expected value of a sample's variance is too low, with the difference being the variance of the sample's mean.
The usual sample variance formula compensates for that, and the varian... | Why does the variance of a sample change if the observations are duplicated?
As some sort of mnemonic, $V\,X = E\,V\,X + V\,E\,X$. So the expected value of a sample's variance is too low, with the difference being the variance of the sample's mean.
The usual sample variance f |
11,130 | The reference book for statistics with R – does it exist and what should it contain? | I personally thought that Modern Applied Statistics with S-Plus ticks all of the boxes you have outlined. Every example has R code, they give good references to other sources, and Venables and Ripley have a wonderfully terse and explanatory writing style which I really appreciated. I tend to re-read the book every so o... | The reference book for statistics with R – does it exist and what should it contain? | I personally thought that Modern Applied Statistics with S-Plus ticks all of the boxes you have outlined. Every example has R code, they give good references to other sources, and Venables and Ripley | The reference book for statistics with R – does it exist and what should it contain?
I personally thought that Modern Applied Statistics with S-Plus ticks all of the boxes you have outlined. Every example has R code, they give good references to other sources, and Venables and Ripley have a wonderfully terse and explan... | The reference book for statistics with R – does it exist and what should it contain?
I personally thought that Modern Applied Statistics with S-Plus ticks all of the boxes you have outlined. Every example has R code, they give good references to other sources, and Venables and Ripley |
11,131 | The reference book for statistics with R – does it exist and what should it contain? | I don't think a book like this exists. The book that I think comes closest is Gelman and Hill's Data Analysis Using Regression and Multilevel/Hierarchical Models.
Cons:
It's ~5 old and aimed at social scientists.
It does not have everything on your TOC list (nothing spatial, basically nothing on time series, etc.)
P... | The reference book for statistics with R – does it exist and what should it contain? | I don't think a book like this exists. The book that I think comes closest is Gelman and Hill's Data Analysis Using Regression and Multilevel/Hierarchical Models.
Cons:
It's ~5 old and aimed at soci | The reference book for statistics with R – does it exist and what should it contain?
I don't think a book like this exists. The book that I think comes closest is Gelman and Hill's Data Analysis Using Regression and Multilevel/Hierarchical Models.
Cons:
It's ~5 old and aimed at social scientists.
It does not have eve... | The reference book for statistics with R – does it exist and what should it contain?
I don't think a book like this exists. The book that I think comes closest is Gelman and Hill's Data Analysis Using Regression and Multilevel/Hierarchical Models.
Cons:
It's ~5 old and aimed at soci |
11,132 | The reference book for statistics with R – does it exist and what should it contain? | Thanks for such a good question, and especially compiling all of that information. Unfortunately, the book you're describing doesn't exist, and to be honest, it couldn't possibly exist. If what you primarily want is a reference book for statistics, I would start with a really good book on linear models. My recommend... | The reference book for statistics with R – does it exist and what should it contain? | Thanks for such a good question, and especially compiling all of that information. Unfortunately, the book you're describing doesn't exist, and to be honest, it couldn't possibly exist. If what you | The reference book for statistics with R – does it exist and what should it contain?
Thanks for such a good question, and especially compiling all of that information. Unfortunately, the book you're describing doesn't exist, and to be honest, it couldn't possibly exist. If what you primarily want is a reference book ... | The reference book for statistics with R – does it exist and what should it contain?
Thanks for such a good question, and especially compiling all of that information. Unfortunately, the book you're describing doesn't exist, and to be honest, it couldn't possibly exist. If what you |
11,133 | The reference book for statistics with R – does it exist and what should it contain? | I am working my way through Elements of Statistical Learning. This book covers an incredible range of techniques (so is 700+ pages) but each approach is explained clearly in a very practical, rather than highly theoretical way. It doesn't explicitly contain anything about R, however the plots and graphs are all clearly... | The reference book for statistics with R – does it exist and what should it contain? | I am working my way through Elements of Statistical Learning. This book covers an incredible range of techniques (so is 700+ pages) but each approach is explained clearly in a very practical, rather t | The reference book for statistics with R – does it exist and what should it contain?
I am working my way through Elements of Statistical Learning. This book covers an incredible range of techniques (so is 700+ pages) but each approach is explained clearly in a very practical, rather than highly theoretical way. It does... | The reference book for statistics with R – does it exist and what should it contain?
I am working my way through Elements of Statistical Learning. This book covers an incredible range of techniques (so is 700+ pages) but each approach is explained clearly in a very practical, rather t |
11,134 | The reference book for statistics with R – does it exist and what should it contain? | I agreed with the currently top-voted answer that MASS4 was a pretty good fit to the request and have the same experience as another respondent with difficulty meeting its requirement of a fairly high level of statistical sophistication. MASS3 was in fact my first "Rbook" and it served me fairly well in that capacity. ... | The reference book for statistics with R – does it exist and what should it contain? | I agreed with the currently top-voted answer that MASS4 was a pretty good fit to the request and have the same experience as another respondent with difficulty meeting its requirement of a fairly high | The reference book for statistics with R – does it exist and what should it contain?
I agreed with the currently top-voted answer that MASS4 was a pretty good fit to the request and have the same experience as another respondent with difficulty meeting its requirement of a fairly high level of statistical sophisticatio... | The reference book for statistics with R – does it exist and what should it contain?
I agreed with the currently top-voted answer that MASS4 was a pretty good fit to the request and have the same experience as another respondent with difficulty meeting its requirement of a fairly high |
11,135 | The reference book for statistics with R – does it exist and what should it contain? | If you want to translate... (this a companion book of a 4,900 page theoretical book):
Big R Book
This book (of which I am a co-author) is a compilation of 15 years of consulting experience and teaching at undergraduate and graduate level and show only examples of R stuff for whose the details of mathematics (proofs) ar... | The reference book for statistics with R – does it exist and what should it contain? | If you want to translate... (this a companion book of a 4,900 page theoretical book):
Big R Book
This book (of which I am a co-author) is a compilation of 15 years of consulting experience and teachin | The reference book for statistics with R – does it exist and what should it contain?
If you want to translate... (this a companion book of a 4,900 page theoretical book):
Big R Book
This book (of which I am a co-author) is a compilation of 15 years of consulting experience and teaching at undergraduate and graduate lev... | The reference book for statistics with R – does it exist and what should it contain?
If you want to translate... (this a companion book of a 4,900 page theoretical book):
Big R Book
This book (of which I am a co-author) is a compilation of 15 years of consulting experience and teachin |
11,136 | Are machine learning techniques "approximation algorithms"? | I think you're mixing multiple important concepts. Let me try to clarify a couple of things:
There are metaheuristic methods, which are methods that iteratively try to improve a candidate solution. Examples of this are tabu search, simulated annealing, genetic algorithms, etc. Observe that while there can be many case... | Are machine learning techniques "approximation algorithms"? | I think you're mixing multiple important concepts. Let me try to clarify a couple of things:
There are metaheuristic methods, which are methods that iteratively try to improve a candidate solution. E | Are machine learning techniques "approximation algorithms"?
I think you're mixing multiple important concepts. Let me try to clarify a couple of things:
There are metaheuristic methods, which are methods that iteratively try to improve a candidate solution. Examples of this are tabu search, simulated annealing, geneti... | Are machine learning techniques "approximation algorithms"?
I think you're mixing multiple important concepts. Let me try to clarify a couple of things:
There are metaheuristic methods, which are methods that iteratively try to improve a candidate solution. E |
11,137 | Are machine learning techniques "approximation algorithms"? | Machine learning often deals with optimization of a function which has many local minimas. Feedforward neural networks with hidden units is a good example. Whether these functions are discrete or continuous, there is no method which achieves a global minimum and stops. It is easy to prove that there is no general algor... | Are machine learning techniques "approximation algorithms"? | Machine learning often deals with optimization of a function which has many local minimas. Feedforward neural networks with hidden units is a good example. Whether these functions are discrete or cont | Are machine learning techniques "approximation algorithms"?
Machine learning often deals with optimization of a function which has many local minimas. Feedforward neural networks with hidden units is a good example. Whether these functions are discrete or continuous, there is no method which achieves a global minimum a... | Are machine learning techniques "approximation algorithms"?
Machine learning often deals with optimization of a function which has many local minimas. Feedforward neural networks with hidden units is a good example. Whether these functions are discrete or cont |
11,138 | What is the difference between learning and inference? | I agree with Neil G's answer, but perhaps this alternative phrasing also helps:
Consider the setting of a simple Gaussian mixture model. Here we can think of the model parameters as the set of Gaussian components of the mixture model (each of their means and variances, and each one's weight in the mixture).
Given a set... | What is the difference between learning and inference? | I agree with Neil G's answer, but perhaps this alternative phrasing also helps:
Consider the setting of a simple Gaussian mixture model. Here we can think of the model parameters as the set of Gaussia | What is the difference between learning and inference?
I agree with Neil G's answer, but perhaps this alternative phrasing also helps:
Consider the setting of a simple Gaussian mixture model. Here we can think of the model parameters as the set of Gaussian components of the mixture model (each of their means and varian... | What is the difference between learning and inference?
I agree with Neil G's answer, but perhaps this alternative phrasing also helps:
Consider the setting of a simple Gaussian mixture model. Here we can think of the model parameters as the set of Gaussia |
11,139 | What is the difference between learning and inference? | Inference is choosing a configuration based on a single input. Learning is choosing parameters based on some training examples.
In the energy-based model framework (a way of looking at nearly all machine learning architectures), inference chooses a configuration to minimize an energy function while holding the paramet... | What is the difference between learning and inference? | Inference is choosing a configuration based on a single input. Learning is choosing parameters based on some training examples.
In the energy-based model framework (a way of looking at nearly all mac | What is the difference between learning and inference?
Inference is choosing a configuration based on a single input. Learning is choosing parameters based on some training examples.
In the energy-based model framework (a way of looking at nearly all machine learning architectures), inference chooses a configuration t... | What is the difference between learning and inference?
Inference is choosing a configuration based on a single input. Learning is choosing parameters based on some training examples.
In the energy-based model framework (a way of looking at nearly all mac |
11,140 | What is the difference between learning and inference? | This looks like classic cross-discipline lingo confusion. The OP seems to be using neuroscience-like terminology where the two terms in question may have different connotations. But since Cross Validated generally deals with statistics and maching learning, I'll try answering the question based on the common usage of t... | What is the difference between learning and inference? | This looks like classic cross-discipline lingo confusion. The OP seems to be using neuroscience-like terminology where the two terms in question may have different connotations. But since Cross Valida | What is the difference between learning and inference?
This looks like classic cross-discipline lingo confusion. The OP seems to be using neuroscience-like terminology where the two terms in question may have different connotations. But since Cross Validated generally deals with statistics and maching learning, I'll tr... | What is the difference between learning and inference?
This looks like classic cross-discipline lingo confusion. The OP seems to be using neuroscience-like terminology where the two terms in question may have different connotations. But since Cross Valida |
11,141 | What is the difference between learning and inference? | It is strange no one else mentioned this, but you can have inference only in cases where you have a probability distribution. Here to quote Wiki, which quotes Oxford dictionary:
Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution (Oxford Dictionary ... | What is the difference between learning and inference? | It is strange no one else mentioned this, but you can have inference only in cases where you have a probability distribution. Here to quote Wiki, which quotes Oxford dictionary:
Statistical inference | What is the difference between learning and inference?
It is strange no one else mentioned this, but you can have inference only in cases where you have a probability distribution. Here to quote Wiki, which quotes Oxford dictionary:
Statistical inference is the process of using data analysis to deduce properties of an ... | What is the difference between learning and inference?
It is strange no one else mentioned this, but you can have inference only in cases where you have a probability distribution. Here to quote Wiki, which quotes Oxford dictionary:
Statistical inference |
11,142 | Why do the estimated values from a Best Linear Unbiased Predictor (BLUP) differ from a Best Linear Unbiased Estimator (BLUE)? | The values that you get from BLUPs aren't estimated in the same way as the BLUE estimates of fixed effects; by convention BLUPs are referred to as predictions. When you fit a mixed effects model, what are estimated initially are the mean and variance (and possibly the covariance) of the random effects. The random eff... | Why do the estimated values from a Best Linear Unbiased Predictor (BLUP) differ from a Best Linear U | The values that you get from BLUPs aren't estimated in the same way as the BLUE estimates of fixed effects; by convention BLUPs are referred to as predictions. When you fit a mixed effects model, wha | Why do the estimated values from a Best Linear Unbiased Predictor (BLUP) differ from a Best Linear Unbiased Estimator (BLUE)?
The values that you get from BLUPs aren't estimated in the same way as the BLUE estimates of fixed effects; by convention BLUPs are referred to as predictions. When you fit a mixed effects mode... | Why do the estimated values from a Best Linear Unbiased Predictor (BLUP) differ from a Best Linear U
The values that you get from BLUPs aren't estimated in the same way as the BLUE estimates of fixed effects; by convention BLUPs are referred to as predictions. When you fit a mixed effects model, wha |
11,143 | Why log-transforming the data before performing principal component analysis? | The iris data set is a fine example to learn PCA. That said, the first four columns describing length and width of sepals and petals are not an example of strongly skewed data. Therefore log-transforming the data does not change the results much, since the resulting rotation of the principal components is quite unchang... | Why log-transforming the data before performing principal component analysis? | The iris data set is a fine example to learn PCA. That said, the first four columns describing length and width of sepals and petals are not an example of strongly skewed data. Therefore log-transform | Why log-transforming the data before performing principal component analysis?
The iris data set is a fine example to learn PCA. That said, the first four columns describing length and width of sepals and petals are not an example of strongly skewed data. Therefore log-transforming the data does not change the results m... | Why log-transforming the data before performing principal component analysis?
The iris data set is a fine example to learn PCA. That said, the first four columns describing length and width of sepals and petals are not an example of strongly skewed data. Therefore log-transform |
11,144 | Why log-transforming the data before performing principal component analysis? | Well, the other answer gives an example, when the log-transform is used to reduce the influence of extreme values or outliers.
Another general argument occurs, when you try to analyze data which are multiplicatively composed instead of addititively - PCA and FA model by their math such additive compositions. Multiplica... | Why log-transforming the data before performing principal component analysis? | Well, the other answer gives an example, when the log-transform is used to reduce the influence of extreme values or outliers.
Another general argument occurs, when you try to analyze data which are m | Why log-transforming the data before performing principal component analysis?
Well, the other answer gives an example, when the log-transform is used to reduce the influence of extreme values or outliers.
Another general argument occurs, when you try to analyze data which are multiplicatively composed instead of additi... | Why log-transforming the data before performing principal component analysis?
Well, the other answer gives an example, when the log-transform is used to reduce the influence of extreme values or outliers.
Another general argument occurs, when you try to analyze data which are m |
11,145 | Difference between Factorization machines and Matrix Factorization? | Matrix factorization is a method to, well, factorize matrices. It does one job of decomposing a matrix into two matrices such that their product closely matches the original matrix.
But Factorization Machines are quite general in nature compared to
Matrix Factorization. The problem formulation itself is very
different... | Difference between Factorization machines and Matrix Factorization? | Matrix factorization is a method to, well, factorize matrices. It does one job of decomposing a matrix into two matrices such that their product closely matches the original matrix.
But Factorization | Difference between Factorization machines and Matrix Factorization?
Matrix factorization is a method to, well, factorize matrices. It does one job of decomposing a matrix into two matrices such that their product closely matches the original matrix.
But Factorization Machines are quite general in nature compared to
Ma... | Difference between Factorization machines and Matrix Factorization?
Matrix factorization is a method to, well, factorize matrices. It does one job of decomposing a matrix into two matrices such that their product closely matches the original matrix.
But Factorization |
11,146 | Difference between Factorization machines and Matrix Factorization? | Just some extension to Dileep's answer.
If the only features involved are two categorical variables (e.g., users and items), then the (nature of the interaction terms of) FM is equivalent to the matrix factorization model. But FM can be easily applied to more than two real-valued features. | Difference between Factorization machines and Matrix Factorization? | Just some extension to Dileep's answer.
If the only features involved are two categorical variables (e.g., users and items), then the (nature of the interaction terms of) FM is equivalent to the matri | Difference between Factorization machines and Matrix Factorization?
Just some extension to Dileep's answer.
If the only features involved are two categorical variables (e.g., users and items), then the (nature of the interaction terms of) FM is equivalent to the matrix factorization model. But FM can be easily applied ... | Difference between Factorization machines and Matrix Factorization?
Just some extension to Dileep's answer.
If the only features involved are two categorical variables (e.g., users and items), then the (nature of the interaction terms of) FM is equivalent to the matri |
11,147 | Difference between Factorization machines and Matrix Factorization? | Matrix factorization is a different factorization model.
From the article about FM:
There are many different factorization models like matrix
factorization, parallel factor analysis or specialized models like
SVD++, PITF or FPMC.
The drawback of these models is that they are not applicable for
general predicti... | Difference between Factorization machines and Matrix Factorization? | Matrix factorization is a different factorization model.
From the article about FM:
There are many different factorization models like matrix
factorization, parallel factor analysis or specialized | Difference between Factorization machines and Matrix Factorization?
Matrix factorization is a different factorization model.
From the article about FM:
There are many different factorization models like matrix
factorization, parallel factor analysis or specialized models like
SVD++, PITF or FPMC.
The drawback of... | Difference between Factorization machines and Matrix Factorization?
Matrix factorization is a different factorization model.
From the article about FM:
There are many different factorization models like matrix
factorization, parallel factor analysis or specialized |
11,148 | Difference between Factorization machines and Matrix Factorization? | Let me take a force-march through a simple item-user example below, where there are only two categorical variables for the user and item scenario, and hence both matrix factorization and factorization machines work(inspired by @dontloo's answer).
Let's say we have two users: $u_1$ and $u_2$, and two items: $i_1$ and $i... | Difference between Factorization machines and Matrix Factorization? | Let me take a force-march through a simple item-user example below, where there are only two categorical variables for the user and item scenario, and hence both matrix factorization and factorization | Difference between Factorization machines and Matrix Factorization?
Let me take a force-march through a simple item-user example below, where there are only two categorical variables for the user and item scenario, and hence both matrix factorization and factorization machines work(inspired by @dontloo's answer).
Let's... | Difference between Factorization machines and Matrix Factorization?
Let me take a force-march through a simple item-user example below, where there are only two categorical variables for the user and item scenario, and hence both matrix factorization and factorization |
11,149 | Caret and randomForest number of trees [duplicate] | In theory, the performance of a RF model should be a monotonic function of ntree that plateaus beyond a certain point once you have 'enough' trees. This makes ntree more of a performance parameter than a Goldilocks parameter that you would want to tune. Caret tends to focus on tuning parameters that perform poorly for ... | Caret and randomForest number of trees [duplicate] | In theory, the performance of a RF model should be a monotonic function of ntree that plateaus beyond a certain point once you have 'enough' trees. This makes ntree more of a performance parameter tha | Caret and randomForest number of trees [duplicate]
In theory, the performance of a RF model should be a monotonic function of ntree that plateaus beyond a certain point once you have 'enough' trees. This makes ntree more of a performance parameter than a Goldilocks parameter that you would want to tune. Caret tends to ... | Caret and randomForest number of trees [duplicate]
In theory, the performance of a RF model should be a monotonic function of ntree that plateaus beyond a certain point once you have 'enough' trees. This makes ntree more of a performance parameter tha |
11,150 | Caret and randomForest number of trees [duplicate] | Caret does let you tune the number of trees on its backend randomForest package. For instance, considering the latest version (4.6-12) as of now, you just pass the normal ntree parameter. caret will "repass" it to randomForest, e.g.:
train(formula,
data = mydata,
method = "rf",
ntree = 5,
trCont... | Caret and randomForest number of trees [duplicate] | Caret does let you tune the number of trees on its backend randomForest package. For instance, considering the latest version (4.6-12) as of now, you just pass the normal ntree parameter. caret will " | Caret and randomForest number of trees [duplicate]
Caret does let you tune the number of trees on its backend randomForest package. For instance, considering the latest version (4.6-12) as of now, you just pass the normal ntree parameter. caret will "repass" it to randomForest, e.g.:
train(formula,
data = mydata,... | Caret and randomForest number of trees [duplicate]
Caret does let you tune the number of trees on its backend randomForest package. For instance, considering the latest version (4.6-12) as of now, you just pass the normal ntree parameter. caret will " |
11,151 | Caret and randomForest number of trees [duplicate] | If you already have an idea about how many trees you want to use (Breiman recommends at least 1000) and have used randomForest::tuneRF to get an optimal mtry value (let's use 6 as an example), then:
ctrl <- trainControl(method = "none")
set.seed(2)
rforest <- train(response ~ ., data = data_set,
method ... | Caret and randomForest number of trees [duplicate] | If you already have an idea about how many trees you want to use (Breiman recommends at least 1000) and have used randomForest::tuneRF to get an optimal mtry value (let's use 6 as an example), then:
c | Caret and randomForest number of trees [duplicate]
If you already have an idea about how many trees you want to use (Breiman recommends at least 1000) and have used randomForest::tuneRF to get an optimal mtry value (let's use 6 as an example), then:
ctrl <- trainControl(method = "none")
set.seed(2)
rforest <- train(re... | Caret and randomForest number of trees [duplicate]
If you already have an idea about how many trees you want to use (Breiman recommends at least 1000) and have used randomForest::tuneRF to get an optimal mtry value (let's use 6 as an example), then:
c |
11,152 | Caret and randomForest number of trees [duplicate] | Though I agree the with the theoretical explanations posted here, in practice, having a too large number of trees is a waste of computational power and makes the model objects uncomfortably heavy for working with them (especially if you use to constantly save and load .RDS objects). Because of that, I think if we want ... | Caret and randomForest number of trees [duplicate] | Though I agree the with the theoretical explanations posted here, in practice, having a too large number of trees is a waste of computational power and makes the model objects uncomfortably heavy for | Caret and randomForest number of trees [duplicate]
Though I agree the with the theoretical explanations posted here, in practice, having a too large number of trees is a waste of computational power and makes the model objects uncomfortably heavy for working with them (especially if you use to constantly save and load ... | Caret and randomForest number of trees [duplicate]
Though I agree the with the theoretical explanations posted here, in practice, having a too large number of trees is a waste of computational power and makes the model objects uncomfortably heavy for |
11,153 | lme() and lmer() giving conflicting results | tl;dr if you change the optimizer to "nloptwrap" I think it will avoid these issues (probably).
Congratulations, you've found one of the simplest examples of multiple optima in a statistical estimation problem! The parameter that lme4 uses internally (thus convenient for illustration) is the scaled standard deviation o... | lme() and lmer() giving conflicting results | tl;dr if you change the optimizer to "nloptwrap" I think it will avoid these issues (probably).
Congratulations, you've found one of the simplest examples of multiple optima in a statistical estimatio | lme() and lmer() giving conflicting results
tl;dr if you change the optimizer to "nloptwrap" I think it will avoid these issues (probably).
Congratulations, you've found one of the simplest examples of multiple optima in a statistical estimation problem! The parameter that lme4 uses internally (thus convenient for illu... | lme() and lmer() giving conflicting results
tl;dr if you change the optimizer to "nloptwrap" I think it will avoid these issues (probably).
Congratulations, you've found one of the simplest examples of multiple optima in a statistical estimatio |
11,154 | What is meant by fine-tuning of neural network? | Finetuning means taking weights of a trained neural network and use it as initialization for a new model being trained on data from the same domain (often e.g. images). It is used to:
speed up the training
overcome small dataset size
There are various strategies, such as training the whole initialized network or "fre... | What is meant by fine-tuning of neural network? | Finetuning means taking weights of a trained neural network and use it as initialization for a new model being trained on data from the same domain (often e.g. images). It is used to:
speed up the tr | What is meant by fine-tuning of neural network?
Finetuning means taking weights of a trained neural network and use it as initialization for a new model being trained on data from the same domain (often e.g. images). It is used to:
speed up the training
overcome small dataset size
There are various strategies, such a... | What is meant by fine-tuning of neural network?
Finetuning means taking weights of a trained neural network and use it as initialization for a new model being trained on data from the same domain (often e.g. images). It is used to:
speed up the tr |
11,155 | Difference between statsmodel OLS and scikit linear regression | First in terms of usage. You can get the prediction in statsmodels in a very similar way as in scikit-learn, except that we use the results instance returned by fit
predictions = results.predict(X_test)
Given the predictions, we can calculate statistics that are based on the prediction error
prediction_error = y_test -... | Difference between statsmodel OLS and scikit linear regression | First in terms of usage. You can get the prediction in statsmodels in a very similar way as in scikit-learn, except that we use the results instance returned by fit
predictions = results.predict(X_tes | Difference between statsmodel OLS and scikit linear regression
First in terms of usage. You can get the prediction in statsmodels in a very similar way as in scikit-learn, except that we use the results instance returned by fit
predictions = results.predict(X_test)
Given the predictions, we can calculate statistics tha... | Difference between statsmodel OLS and scikit linear regression
First in terms of usage. You can get the prediction in statsmodels in a very similar way as in scikit-learn, except that we use the results instance returned by fit
predictions = results.predict(X_tes |
11,156 | Difference between statsmodel OLS and scikit linear regression | In the OLS model you are using the training data to fit and predict.
With the LinearRegression model you are using training data to fit and test data to predict, therefore different results in R2 scores.
If you would take test data in OLS model, you should have same results and lower value | Difference between statsmodel OLS and scikit linear regression | In the OLS model you are using the training data to fit and predict.
With the LinearRegression model you are using training data to fit and test data to predict, therefore different results in R2 scor | Difference between statsmodel OLS and scikit linear regression
In the OLS model you are using the training data to fit and predict.
With the LinearRegression model you are using training data to fit and test data to predict, therefore different results in R2 scores.
If you would take test data in OLS model, you should ... | Difference between statsmodel OLS and scikit linear regression
In the OLS model you are using the training data to fit and predict.
With the LinearRegression model you are using training data to fit and test data to predict, therefore different results in R2 scor |
11,157 | Difference between statsmodel OLS and scikit linear regression | I have encountered a similar issue where the OLS is giving different Rsquared and Adjusted Rsquared values compared to Sklearn LinearRegression model.
Reason for it: OLS does not consider, be default, the intercept coefficient and there builds the model without it and Sklearn considers it in building the model.
Solutio... | Difference between statsmodel OLS and scikit linear regression | I have encountered a similar issue where the OLS is giving different Rsquared and Adjusted Rsquared values compared to Sklearn LinearRegression model.
Reason for it: OLS does not consider, be default, | Difference between statsmodel OLS and scikit linear regression
I have encountered a similar issue where the OLS is giving different Rsquared and Adjusted Rsquared values compared to Sklearn LinearRegression model.
Reason for it: OLS does not consider, be default, the intercept coefficient and there builds the model wit... | Difference between statsmodel OLS and scikit linear regression
I have encountered a similar issue where the OLS is giving different Rsquared and Adjusted Rsquared values compared to Sklearn LinearRegression model.
Reason for it: OLS does not consider, be default, |
11,158 | Difference between statsmodel OLS and scikit linear regression | Let me make it crystal clear:
we know that multiple linear regression is represented as :
y = b0 + b1X1 + b2X2 + b3X3 +…..+ bnXn
but we can also, represent it as:
y = b0X0 + b1X1 + b2X2 + b3X3 +…..+ bnXn
where X0 = 1
We have to add one column with all the same values as 1 to represent b0X0.
Why we need to do that??
sta... | Difference between statsmodel OLS and scikit linear regression | Let me make it crystal clear:
we know that multiple linear regression is represented as :
y = b0 + b1X1 + b2X2 + b3X3 +…..+ bnXn
but we can also, represent it as:
y = b0X0 + b1X1 + b2X2 + b3X3 +…..+ b | Difference between statsmodel OLS and scikit linear regression
Let me make it crystal clear:
we know that multiple linear regression is represented as :
y = b0 + b1X1 + b2X2 + b3X3 +…..+ bnXn
but we can also, represent it as:
y = b0X0 + b1X1 + b2X2 + b3X3 +…..+ bnXn
where X0 = 1
We have to add one column with all the s... | Difference between statsmodel OLS and scikit linear regression
Let me make it crystal clear:
we know that multiple linear regression is represented as :
y = b0 + b1X1 + b2X2 + b3X3 +…..+ bnXn
but we can also, represent it as:
y = b0X0 + b1X1 + b2X2 + b3X3 +…..+ b |
11,159 | Allowed comparisons of mixed effects models (random effects primarily) | Using maximum likelihood, any of these can be compared with AIC; if the fixed effects are the same (m1 to m4), using either REML or ML is fine, with REML usually preferred, but if they are different, only ML can be used. However, interpretation is usually difficult when both fixed effects and random effects are changi... | Allowed comparisons of mixed effects models (random effects primarily) | Using maximum likelihood, any of these can be compared with AIC; if the fixed effects are the same (m1 to m4), using either REML or ML is fine, with REML usually preferred, but if they are different, | Allowed comparisons of mixed effects models (random effects primarily)
Using maximum likelihood, any of these can be compared with AIC; if the fixed effects are the same (m1 to m4), using either REML or ML is fine, with REML usually preferred, but if they are different, only ML can be used. However, interpretation is ... | Allowed comparisons of mixed effects models (random effects primarily)
Using maximum likelihood, any of these can be compared with AIC; if the fixed effects are the same (m1 to m4), using either REML or ML is fine, with REML usually preferred, but if they are different, |
11,160 | Allowed comparisons of mixed effects models (random effects primarily) | You have to be careful using likelihood-ratio tests when evaluating whether a variance component is 0 (m vs m-m4), because the typical chi-square approximation does not apply. The reason is that the null-hypothesis is $\sigma^2=0$, and it is on the boundary of the parameter space, so the classical results do not apply.... | Allowed comparisons of mixed effects models (random effects primarily) | You have to be careful using likelihood-ratio tests when evaluating whether a variance component is 0 (m vs m-m4), because the typical chi-square approximation does not apply. The reason is that the n | Allowed comparisons of mixed effects models (random effects primarily)
You have to be careful using likelihood-ratio tests when evaluating whether a variance component is 0 (m vs m-m4), because the typical chi-square approximation does not apply. The reason is that the null-hypothesis is $\sigma^2=0$, and it is on the ... | Allowed comparisons of mixed effects models (random effects primarily)
You have to be careful using likelihood-ratio tests when evaluating whether a variance component is 0 (m vs m-m4), because the typical chi-square approximation does not apply. The reason is that the n |
11,161 | What is the correct way to test for significant differences between coefficients? | The two approaches do differ.
Let the estimated standard errors of the two regressions be $s_1$ and $s_2$. Then, because the combined regression (with all coefficient-dummy interactions) fits the same coefficients, it has the same residuals, whence its standard error can be computed as
$$s = \sqrt{\frac{(n_1-p) s_1^2... | What is the correct way to test for significant differences between coefficients? | The two approaches do differ.
Let the estimated standard errors of the two regressions be $s_1$ and $s_2$. Then, because the combined regression (with all coefficient-dummy interactions) fits the sam | What is the correct way to test for significant differences between coefficients?
The two approaches do differ.
Let the estimated standard errors of the two regressions be $s_1$ and $s_2$. Then, because the combined regression (with all coefficient-dummy interactions) fits the same coefficients, it has the same residu... | What is the correct way to test for significant differences between coefficients?
The two approaches do differ.
Let the estimated standard errors of the two regressions be $s_1$ and $s_2$. Then, because the combined regression (with all coefficient-dummy interactions) fits the sam |
11,162 | What is the correct way to test for significant differences between coefficients? | The most direct way to test for a difference in the coefficient between two groups is to include an interaction term into your regression, which is almost what you describe in your question. The model you would run is the following:
$y_i = \alpha + \beta x_i + \gamma g_i + \delta (x_i \times g_i) + \varepsilon_i$
Note ... | What is the correct way to test for significant differences between coefficients? | The most direct way to test for a difference in the coefficient between two groups is to include an interaction term into your regression, which is almost what you describe in your question. The model | What is the correct way to test for significant differences between coefficients?
The most direct way to test for a difference in the coefficient between two groups is to include an interaction term into your regression, which is almost what you describe in your question. The model you would run is the following:
$y_i ... | What is the correct way to test for significant differences between coefficients?
The most direct way to test for a difference in the coefficient between two groups is to include an interaction term into your regression, which is almost what you describe in your question. The model |
11,163 | In genome-wide association studies, what are principal components? | In this particular context, PCA is mainly used to account for population-specific variations in alleles distribution on the SNPs (or other DNA markers, although I'm only familiar with the SNP case) under investigation. Such "population substructure" mainly arises as a consequence of varying frequencies of minor alleles... | In genome-wide association studies, what are principal components? | In this particular context, PCA is mainly used to account for population-specific variations in alleles distribution on the SNPs (or other DNA markers, although I'm only familiar with the SNP case) un | In genome-wide association studies, what are principal components?
In this particular context, PCA is mainly used to account for population-specific variations in alleles distribution on the SNPs (or other DNA markers, although I'm only familiar with the SNP case) under investigation. Such "population substructure" mai... | In genome-wide association studies, what are principal components?
In this particular context, PCA is mainly used to account for population-specific variations in alleles distribution on the SNPs (or other DNA markers, although I'm only familiar with the SNP case) un |
11,164 | Using regularization when doing statistical inference | There is a major difference between performing estimating using ridge type penalties and lasso-type penalties. Ridge type estimators tend to shrink all regression coefficients towards zero and are biased, but have an easy to derive asymptotic distribution because they do not shrink any variable to exactly zero. The bia... | Using regularization when doing statistical inference | There is a major difference between performing estimating using ridge type penalties and lasso-type penalties. Ridge type estimators tend to shrink all regression coefficients towards zero and are bia | Using regularization when doing statistical inference
There is a major difference between performing estimating using ridge type penalties and lasso-type penalties. Ridge type estimators tend to shrink all regression coefficients towards zero and are biased, but have an easy to derive asymptotic distribution because th... | Using regularization when doing statistical inference
There is a major difference between performing estimating using ridge type penalties and lasso-type penalties. Ridge type estimators tend to shrink all regression coefficients towards zero and are bia |
11,165 | Using regularization when doing statistical inference | The term "regularization" covers a very wide variety of methods. For the purpose of this answer, I am going to narrow in to mean "penalized optimization", i.e. adding an $L_1$ or $L_2$ penalty to your optimization problem.
If that's the case, then the answer is a definitive "Yes! Well kinda".
The reason for this is t... | Using regularization when doing statistical inference | The term "regularization" covers a very wide variety of methods. For the purpose of this answer, I am going to narrow in to mean "penalized optimization", i.e. adding an $L_1$ or $L_2$ penalty to your | Using regularization when doing statistical inference
The term "regularization" covers a very wide variety of methods. For the purpose of this answer, I am going to narrow in to mean "penalized optimization", i.e. adding an $L_1$ or $L_2$ penalty to your optimization problem.
If that's the case, then the answer is a d... | Using regularization when doing statistical inference
The term "regularization" covers a very wide variety of methods. For the purpose of this answer, I am going to narrow in to mean "penalized optimization", i.e. adding an $L_1$ or $L_2$ penalty to your |
11,166 | Using regularization when doing statistical inference | I would particularly recommend LASSO if you are attempting to use regression for inference based on "which predictors are statisically significant"--but not for the reason you might expect.
In practice, predictors in a model tend to be correlated. Even if there isn't substantial multicollinearity, regression's choice o... | Using regularization when doing statistical inference | I would particularly recommend LASSO if you are attempting to use regression for inference based on "which predictors are statisically significant"--but not for the reason you might expect.
In practic | Using regularization when doing statistical inference
I would particularly recommend LASSO if you are attempting to use regression for inference based on "which predictors are statisically significant"--but not for the reason you might expect.
In practice, predictors in a model tend to be correlated. Even if there isn'... | Using regularization when doing statistical inference
I would particularly recommend LASSO if you are attempting to use regression for inference based on "which predictors are statisically significant"--but not for the reason you might expect.
In practic |
11,167 | Does Dimensionality curse effect some models more than others? | In general, the curse of dimensionality makes the problem of searching through a space much more difficult, and effects the majority of algorithms that "learn" through partitioning their vector space. The higher the dimensionality of our optimization problem the more data we need to fill the space that we are optimizin... | Does Dimensionality curse effect some models more than others? | In general, the curse of dimensionality makes the problem of searching through a space much more difficult, and effects the majority of algorithms that "learn" through partitioning their vector space. | Does Dimensionality curse effect some models more than others?
In general, the curse of dimensionality makes the problem of searching through a space much more difficult, and effects the majority of algorithms that "learn" through partitioning their vector space. The higher the dimensionality of our optimization proble... | Does Dimensionality curse effect some models more than others?
In general, the curse of dimensionality makes the problem of searching through a space much more difficult, and effects the majority of algorithms that "learn" through partitioning their vector space. |
11,168 | How to determine the accuracy of regression? Which measure should be used? | You should ask yourself what were you trying to achieve with your modeling approach.
As you correctly said "how far from true solution am I" is a good starting point (notice this is also true for classification, we only get into specifics when we run into dichotomization, usually in more CS oriented machine learning, s... | How to determine the accuracy of regression? Which measure should be used? | You should ask yourself what were you trying to achieve with your modeling approach.
As you correctly said "how far from true solution am I" is a good starting point (notice this is also true for clas | How to determine the accuracy of regression? Which measure should be used?
You should ask yourself what were you trying to achieve with your modeling approach.
As you correctly said "how far from true solution am I" is a good starting point (notice this is also true for classification, we only get into specifics when w... | How to determine the accuracy of regression? Which measure should be used?
You should ask yourself what were you trying to achieve with your modeling approach.
As you correctly said "how far from true solution am I" is a good starting point (notice this is also true for clas |
11,169 | Restricted Boltzmann machines vs multilayer neural networks | First of all RBM's are certainly different from normal Neural Nets, and when used properly they achieve much better performance. Also, training a few layers of a RBM, and then using the found weights as a starting point for a Mulitlayer NN often yields better results than simply using a Multilayer NN.
The best pointer ... | Restricted Boltzmann machines vs multilayer neural networks | First of all RBM's are certainly different from normal Neural Nets, and when used properly they achieve much better performance. Also, training a few layers of a RBM, and then using the found weights | Restricted Boltzmann machines vs multilayer neural networks
First of all RBM's are certainly different from normal Neural Nets, and when used properly they achieve much better performance. Also, training a few layers of a RBM, and then using the found weights as a starting point for a Mulitlayer NN often yields better ... | Restricted Boltzmann machines vs multilayer neural networks
First of all RBM's are certainly different from normal Neural Nets, and when used properly they achieve much better performance. Also, training a few layers of a RBM, and then using the found weights |
11,170 | Restricted Boltzmann machines vs multilayer neural networks | In R you can use neuralnet and RSNNS (which provides an interface to the Stuttgart Neural Network Simulator) to fit standard multilayer neural networks, but there are differences to RBM.
Regarding implementing deep neural nets in R, I think the only worthwhile strategy would be to interface existing FOSS implementatio... | Restricted Boltzmann machines vs multilayer neural networks | In R you can use neuralnet and RSNNS (which provides an interface to the Stuttgart Neural Network Simulator) to fit standard multilayer neural networks, but there are differences to RBM.
Regarding im | Restricted Boltzmann machines vs multilayer neural networks
In R you can use neuralnet and RSNNS (which provides an interface to the Stuttgart Neural Network Simulator) to fit standard multilayer neural networks, but there are differences to RBM.
Regarding implementing deep neural nets in R, I think the only worthwhil... | Restricted Boltzmann machines vs multilayer neural networks
In R you can use neuralnet and RSNNS (which provides an interface to the Stuttgart Neural Network Simulator) to fit standard multilayer neural networks, but there are differences to RBM.
Regarding im |
11,171 | Efficient calculation of matrix inverse in R | Have you tried what cardinal suggested and explored some of the alternative methods for computing the inverse? Let's consider a specific example:
library(MASS)
k <- 2000
rho <- .3
S <- matrix(rep(rho, k*k), nrow=k)
diag(S) <- 1
dat <- mvrnorm(10000, mu=rep(0,k), Sigma=S) ### be patient!
R <- cor(dat)
syste... | Efficient calculation of matrix inverse in R | Have you tried what cardinal suggested and explored some of the alternative methods for computing the inverse? Let's consider a specific example:
library(MASS)
k <- 2000
rho <- .3
S <- matri | Efficient calculation of matrix inverse in R
Have you tried what cardinal suggested and explored some of the alternative methods for computing the inverse? Let's consider a specific example:
library(MASS)
k <- 2000
rho <- .3
S <- matrix(rep(rho, k*k), nrow=k)
diag(S) <- 1
dat <- mvrnorm(10000, mu=rep(0,k), S... | Efficient calculation of matrix inverse in R
Have you tried what cardinal suggested and explored some of the alternative methods for computing the inverse? Let's consider a specific example:
library(MASS)
k <- 2000
rho <- .3
S <- matri |
11,172 | Efficient calculation of matrix inverse in R | If you are working with covariance matrix or any positive definite matrix you can use pd.solve is faster.
Following the Wolfgang example:
library(MASS)
library(mnormt)
k <- 2000
rho <- .3
S <- matrix(rep(rho, k*k), nrow=k)
diag(S) <- 1
dat <- mvrnorm(10000, mu=rep(0,k), Sigma=S) ### be patient!
R <- cor(dat... | Efficient calculation of matrix inverse in R | If you are working with covariance matrix or any positive definite matrix you can use pd.solve is faster.
Following the Wolfgang example:
library(MASS)
library(mnormt)
k <- 2000
rho <- .3
S | Efficient calculation of matrix inverse in R
If you are working with covariance matrix or any positive definite matrix you can use pd.solve is faster.
Following the Wolfgang example:
library(MASS)
library(mnormt)
k <- 2000
rho <- .3
S <- matrix(rep(rho, k*k), nrow=k)
diag(S) <- 1
dat <- mvrnorm(10000, mu=rep... | Efficient calculation of matrix inverse in R
If you are working with covariance matrix or any positive definite matrix you can use pd.solve is faster.
Following the Wolfgang example:
library(MASS)
library(mnormt)
k <- 2000
rho <- .3
S |
11,173 | Top five classifiers to try first | Random Forest
Fast, robust, good accuracy, in most cases nothing to tune, requires no normalization, immune to collinearity, generates quite good error approximation and useful importance ranking as a side effect of training, trivially parallel, predicts in a blink of an eye.
Drawbacks: slower than trivial methods like... | Top five classifiers to try first | Random Forest
Fast, robust, good accuracy, in most cases nothing to tune, requires no normalization, immune to collinearity, generates quite good error approximation and useful importance ranking as a | Top five classifiers to try first
Random Forest
Fast, robust, good accuracy, in most cases nothing to tune, requires no normalization, immune to collinearity, generates quite good error approximation and useful importance ranking as a side effect of training, trivially parallel, predicts in a blink of an eye.
Drawbacks... | Top five classifiers to try first
Random Forest
Fast, robust, good accuracy, in most cases nothing to tune, requires no normalization, immune to collinearity, generates quite good error approximation and useful importance ranking as a |
11,174 | Top five classifiers to try first | Gaussian process classifier (not using the Laplace approximation), preferably with marginalisation rather than optimisation of the hyper-parameters. Why?
because they give a probabilistic classification
you can use a kernel function that allows you to operate directly on non-vectorial data and/or incorporate expert k... | Top five classifiers to try first | Gaussian process classifier (not using the Laplace approximation), preferably with marginalisation rather than optimisation of the hyper-parameters. Why?
because they give a probabilistic classifica | Top five classifiers to try first
Gaussian process classifier (not using the Laplace approximation), preferably with marginalisation rather than optimisation of the hyper-parameters. Why?
because they give a probabilistic classification
you can use a kernel function that allows you to operate directly on non-vectoria... | Top five classifiers to try first
Gaussian process classifier (not using the Laplace approximation), preferably with marginalisation rather than optimisation of the hyper-parameters. Why?
because they give a probabilistic classifica |
11,175 | Top five classifiers to try first | By myself when you are approaching to a new data set you should start to watch to the whole problem. First of all get a distribution for categorical features and mean and standard deviations for each continuous feature. Then:
Delete features with more than X% missing values;
Delete categorical features when a particul... | Top five classifiers to try first | By myself when you are approaching to a new data set you should start to watch to the whole problem. First of all get a distribution for categorical features and mean and standard deviations for each | Top five classifiers to try first
By myself when you are approaching to a new data set you should start to watch to the whole problem. First of all get a distribution for categorical features and mean and standard deviations for each continuous feature. Then:
Delete features with more than X% missing values;
Delete ca... | Top five classifiers to try first
By myself when you are approaching to a new data set you should start to watch to the whole problem. First of all get a distribution for categorical features and mean and standard deviations for each |
11,176 | Is the second parameter for the normal distribution the variance or std deviation? | There's a choice of parameterizations of the normal distribution, and none is inherently more correct. Sometimes one or another is more convenient, and arguably one or another is more conventional in a given situation.
From what I've seen, when statisticians* are writing algebraic formulas, the most common convention i... | Is the second parameter for the normal distribution the variance or std deviation? | There's a choice of parameterizations of the normal distribution, and none is inherently more correct. Sometimes one or another is more convenient, and arguably one or another is more conventional in | Is the second parameter for the normal distribution the variance or std deviation?
There's a choice of parameterizations of the normal distribution, and none is inherently more correct. Sometimes one or another is more convenient, and arguably one or another is more conventional in a given situation.
From what I've see... | Is the second parameter for the normal distribution the variance or std deviation?
There's a choice of parameterizations of the normal distribution, and none is inherently more correct. Sometimes one or another is more convenient, and arguably one or another is more conventional in |
11,177 | Is the second parameter for the normal distribution the variance or std deviation? | From an earlier answer 7 years ago: ".... there are at least
three different conventions for interpreting $X \sim N(a,b)$ as
a normal random variable. Usually, $a$ is the mean $\mu_X$
but $b$ can have different meanings.
$X \sim N(a,b)$ means that the standard deviation of $X$ is $b$.
$X \sim N(a,b)$ means that th... | Is the second parameter for the normal distribution the variance or std deviation? | From an earlier answer 7 years ago: ".... there are at least
three different conventions for interpreting $X \sim N(a,b)$ as
a normal random variable. Usually, $a$ is the mean $\mu_X$
but $b$ can h | Is the second parameter for the normal distribution the variance or std deviation?
From an earlier answer 7 years ago: ".... there are at least
three different conventions for interpreting $X \sim N(a,b)$ as
a normal random variable. Usually, $a$ is the mean $\mu_X$
but $b$ can have different meanings.
$X \sim N(a... | Is the second parameter for the normal distribution the variance or std deviation?
From an earlier answer 7 years ago: ".... there are at least
three different conventions for interpreting $X \sim N(a,b)$ as
a normal random variable. Usually, $a$ is the mean $\mu_X$
but $b$ can h |
11,178 | Which Theories of Causality Should I know? | Strictly speaking, "Granger causality" is not at all about causality. It's about predictive ability/time precedence, you want to check whether one time series is useful to predict another time series---it's suited for claims like "usually A happens before B happens" or "knowing A helps me predict B will happen, but not... | Which Theories of Causality Should I know? | Strictly speaking, "Granger causality" is not at all about causality. It's about predictive ability/time precedence, you want to check whether one time series is useful to predict another time series- | Which Theories of Causality Should I know?
Strictly speaking, "Granger causality" is not at all about causality. It's about predictive ability/time precedence, you want to check whether one time series is useful to predict another time series---it's suited for claims like "usually A happens before B happens" or "knowin... | Which Theories of Causality Should I know?
Strictly speaking, "Granger causality" is not at all about causality. It's about predictive ability/time precedence, you want to check whether one time series is useful to predict another time series- |
11,179 | Why is ROC AUC equivalent to the probability that two randomly-selected samples are correctly ranked? [duplicate] | It's easy to see once you obtained a closed-form formula for AUC.
Since we have finite number of samples $\{(x_i, y_i)\}_{i=1}^N$, we'll have finite number of points on the ROC curve. We do linear interpolation in between.
First, some definitions. Suppose we'd like to evaluate an algorithm $A(x)$ that outputs a probabi... | Why is ROC AUC equivalent to the probability that two randomly-selected samples are correctly ranked | It's easy to see once you obtained a closed-form formula for AUC.
Since we have finite number of samples $\{(x_i, y_i)\}_{i=1}^N$, we'll have finite number of points on the ROC curve. We do linear int | Why is ROC AUC equivalent to the probability that two randomly-selected samples are correctly ranked? [duplicate]
It's easy to see once you obtained a closed-form formula for AUC.
Since we have finite number of samples $\{(x_i, y_i)\}_{i=1}^N$, we'll have finite number of points on the ROC curve. We do linear interpola... | Why is ROC AUC equivalent to the probability that two randomly-selected samples are correctly ranked
It's easy to see once you obtained a closed-form formula for AUC.
Since we have finite number of samples $\{(x_i, y_i)\}_{i=1}^N$, we'll have finite number of points on the ROC curve. We do linear int |
11,180 | How do I calculate the variance of the OLS estimator $\beta_0$, conditional on $x_1, \ldots , x_n$? | This is a self-study question, so I provide hints that will hopefully help to find the solution, and I'll edit the answer based on your feedbacks/progress.
The parameter estimates that minimize the sum of squares are
\begin{align}
\hat{\beta}_0 &= \bar{y} - \hat{\beta}_1 \bar{x} , \\
\hat{\beta}_1 &= \frac{ \sum_{i... | How do I calculate the variance of the OLS estimator $\beta_0$, conditional on $x_1, \ldots , x_n$? | This is a self-study question, so I provide hints that will hopefully help to find the solution, and I'll edit the answer based on your feedbacks/progress.
The parameter estimates that minimize the su | How do I calculate the variance of the OLS estimator $\beta_0$, conditional on $x_1, \ldots , x_n$?
This is a self-study question, so I provide hints that will hopefully help to find the solution, and I'll edit the answer based on your feedbacks/progress.
The parameter estimates that minimize the sum of squares are
\be... | How do I calculate the variance of the OLS estimator $\beta_0$, conditional on $x_1, \ldots , x_n$?
This is a self-study question, so I provide hints that will hopefully help to find the solution, and I'll edit the answer based on your feedbacks/progress.
The parameter estimates that minimize the su |
11,181 | How do I calculate the variance of the OLS estimator $\beta_0$, conditional on $x_1, \ldots , x_n$? | I got it! Well, with help. I found the part of the book that gives steps to work through when proving the $Var \left( \hat{\beta}_0 \right)$ formula (thankfully it doesn't actually work them out, otherwise I'd be tempted to not actually do the proof). I proved each separate step, and I think it worked.
I'm using the b... | How do I calculate the variance of the OLS estimator $\beta_0$, conditional on $x_1, \ldots , x_n$? | I got it! Well, with help. I found the part of the book that gives steps to work through when proving the $Var \left( \hat{\beta}_0 \right)$ formula (thankfully it doesn't actually work them out, othe | How do I calculate the variance of the OLS estimator $\beta_0$, conditional on $x_1, \ldots , x_n$?
I got it! Well, with help. I found the part of the book that gives steps to work through when proving the $Var \left( \hat{\beta}_0 \right)$ formula (thankfully it doesn't actually work them out, otherwise I'd be tempted... | How do I calculate the variance of the OLS estimator $\beta_0$, conditional on $x_1, \ldots , x_n$?
I got it! Well, with help. I found the part of the book that gives steps to work through when proving the $Var \left( \hat{\beta}_0 \right)$ formula (thankfully it doesn't actually work them out, othe |
11,182 | use of weights in svyglm vs glm | There are lots of different sorts of weights and they get kind of confusing. You have to be pretty careful when you're using different functions or software that you're using the kind of weights you think you're using.
The svyglm function uses survey weights - these weight the importance of each case to make them repr... | use of weights in svyglm vs glm | There are lots of different sorts of weights and they get kind of confusing. You have to be pretty careful when you're using different functions or software that you're using the kind of weights you | use of weights in svyglm vs glm
There are lots of different sorts of weights and they get kind of confusing. You have to be pretty careful when you're using different functions or software that you're using the kind of weights you think you're using.
The svyglm function uses survey weights - these weight the importanc... | use of weights in svyglm vs glm
There are lots of different sorts of weights and they get kind of confusing. You have to be pretty careful when you're using different functions or software that you're using the kind of weights you |
11,183 | use of weights in svyglm vs glm | survey computes the standard errors with consideration of the loss of precision introduced by sampling weights. Weights in glm simply adjust the weight given to the errors in the least squares estimation, so the standard errors aren't correct. Here's a selection from Lumley (2010):
In a model-based analysis it would b... | use of weights in svyglm vs glm | survey computes the standard errors with consideration of the loss of precision introduced by sampling weights. Weights in glm simply adjust the weight given to the errors in the least squares estimat | use of weights in svyglm vs glm
survey computes the standard errors with consideration of the loss of precision introduced by sampling weights. Weights in glm simply adjust the weight given to the errors in the least squares estimation, so the standard errors aren't correct. Here's a selection from Lumley (2010):
In a... | use of weights in svyglm vs glm
survey computes the standard errors with consideration of the loss of precision introduced by sampling weights. Weights in glm simply adjust the weight given to the errors in the least squares estimat |
11,184 | Proper scoring rule when there is a decision to make (e.g. spam vs ham email) | I guess I'm one of the "among others", so I'll chime in.
The short version: I'm afraid your example is a bit of a straw man, and I don't think we can learn a lot from it.
In the first case, yes, you can threshold your predictions at 0.50 to get a perfect classification. True. But we also see that your model is actually... | Proper scoring rule when there is a decision to make (e.g. spam vs ham email) | I guess I'm one of the "among others", so I'll chime in.
The short version: I'm afraid your example is a bit of a straw man, and I don't think we can learn a lot from it.
In the first case, yes, you c | Proper scoring rule when there is a decision to make (e.g. spam vs ham email)
I guess I'm one of the "among others", so I'll chime in.
The short version: I'm afraid your example is a bit of a straw man, and I don't think we can learn a lot from it.
In the first case, yes, you can threshold your predictions at 0.50 to g... | Proper scoring rule when there is a decision to make (e.g. spam vs ham email)
I guess I'm one of the "among others", so I'll chime in.
The short version: I'm afraid your example is a bit of a straw man, and I don't think we can learn a lot from it.
In the first case, yes, you c |
11,185 | Proper scoring rule when there is a decision to make (e.g. spam vs ham email) | I think it is worth making the distinction between performance evaluation and model selection criteria.
In performance evaluation you want to know how well your system is likely to perform in operation, based on the data you have available now. When evaluating performance, you need to use the metric that is appropriat... | Proper scoring rule when there is a decision to make (e.g. spam vs ham email) | I think it is worth making the distinction between performance evaluation and model selection criteria.
In performance evaluation you want to know how well your system is likely to perform in operatio | Proper scoring rule when there is a decision to make (e.g. spam vs ham email)
I think it is worth making the distinction between performance evaluation and model selection criteria.
In performance evaluation you want to know how well your system is likely to perform in operation, based on the data you have available no... | Proper scoring rule when there is a decision to make (e.g. spam vs ham email)
I think it is worth making the distinction between performance evaluation and model selection criteria.
In performance evaluation you want to know how well your system is likely to perform in operatio |
11,186 | Statistical tables in old books purposefully wrong? | The Wikipedia article "Fictitious entry", which is on the more general subject of "deliberately incorrect entries in reference works", cites one example of something close to this:
By including a trivial piece of false information in a larger work, it is easier to demonstrate subsequent plagiarism if the fictitious en... | Statistical tables in old books purposefully wrong? | The Wikipedia article "Fictitious entry", which is on the more general subject of "deliberately incorrect entries in reference works", cites one example of something close to this:
By including a tri | Statistical tables in old books purposefully wrong?
The Wikipedia article "Fictitious entry", which is on the more general subject of "deliberately incorrect entries in reference works", cites one example of something close to this:
By including a trivial piece of false information in a larger work, it is easier to de... | Statistical tables in old books purposefully wrong?
The Wikipedia article "Fictitious entry", which is on the more general subject of "deliberately incorrect entries in reference works", cites one example of something close to this:
By including a tri |
11,187 | Distribution of the largest fragment of a broken stick (spacings) | With the information given by @Glen_b I could find the answer. Using the same notations as the question
$$
P(Z_k \leq x) = \sum_{j=0}^{k+1} { k+1 \choose j } (-1)^j (1-jx)_+^k,
$$
where $a_+ = a$ if $a > 0$ and $0$ otherwise. I also give the expectation and the asymptotic convergence to the Gumbel (NB: not Beta) distri... | Distribution of the largest fragment of a broken stick (spacings) | With the information given by @Glen_b I could find the answer. Using the same notations as the question
$$
P(Z_k \leq x) = \sum_{j=0}^{k+1} { k+1 \choose j } (-1)^j (1-jx)_+^k,
$$
where $a_+ = a$ if $ | Distribution of the largest fragment of a broken stick (spacings)
With the information given by @Glen_b I could find the answer. Using the same notations as the question
$$
P(Z_k \leq x) = \sum_{j=0}^{k+1} { k+1 \choose j } (-1)^j (1-jx)_+^k,
$$
where $a_+ = a$ if $a > 0$ and $0$ otherwise. I also give the expectation ... | Distribution of the largest fragment of a broken stick (spacings)
With the information given by @Glen_b I could find the answer. Using the same notations as the question
$$
P(Z_k \leq x) = \sum_{j=0}^{k+1} { k+1 \choose j } (-1)^j (1-jx)_+^k,
$$
where $a_+ = a$ if $ |
11,188 | Distribution of the largest fragment of a broken stick (spacings) | This is not a complete answer, but I did some quick simulations, and this is what I obtained:
This looks remarkably beta-ish, and this makes a bit of sense, since the order statistics of i.i.d. uniform distributions are beta wiki.
This might give some starting point to derive the resulting p.d.f..
I'll update if I get... | Distribution of the largest fragment of a broken stick (spacings) | This is not a complete answer, but I did some quick simulations, and this is what I obtained:
This looks remarkably beta-ish, and this makes a bit of sense, since the order statistics of i.i.d. unifo | Distribution of the largest fragment of a broken stick (spacings)
This is not a complete answer, but I did some quick simulations, and this is what I obtained:
This looks remarkably beta-ish, and this makes a bit of sense, since the order statistics of i.i.d. uniform distributions are beta wiki.
This might give some s... | Distribution of the largest fragment of a broken stick (spacings)
This is not a complete answer, but I did some quick simulations, and this is what I obtained:
This looks remarkably beta-ish, and this makes a bit of sense, since the order statistics of i.i.d. unifo |
11,189 | Distribution of the largest fragment of a broken stick (spacings) | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
I produced the answer for a conference in Siena (Italy... | Distribution of the largest fragment of a broken stick (spacings) | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Distribution of the largest fragment of a broken stick (spacings)
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | Distribution of the largest fragment of a broken stick (spacings)
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
11,190 | Analogy of Pearson correlation for 3 variables | It is indeed something. To find out, we need to examine what we know about correlation itself.
The correlation matrix of a vector-valued random variable $\mathbf{X}=(X_1,X_2,\ldots,X_p)$ is the variance-covariance matrix, or simply "variance," of the standardized version of $\mathbf{X}$. That is, each $X_i$ is repla... | Analogy of Pearson correlation for 3 variables | It is indeed something. To find out, we need to examine what we know about correlation itself.
The correlation matrix of a vector-valued random variable $\mathbf{X}=(X_1,X_2,\ldots,X_p)$ is the vari | Analogy of Pearson correlation for 3 variables
It is indeed something. To find out, we need to examine what we know about correlation itself.
The correlation matrix of a vector-valued random variable $\mathbf{X}=(X_1,X_2,\ldots,X_p)$ is the variance-covariance matrix, or simply "variance," of the standardized version... | Analogy of Pearson correlation for 3 variables
It is indeed something. To find out, we need to examine what we know about correlation itself.
The correlation matrix of a vector-valued random variable $\mathbf{X}=(X_1,X_2,\ldots,X_p)$ is the vari |
11,191 | Analogy of Pearson correlation for 3 variables | Hmmm. If we run...
a <- rnorm(100);
b <- rnorm(100);
c <- rnorm(100)
mean((a-mean(a))*(b-mean(b))*(c-mean(c)))/
(sd(a) * sd(b) * sd(c))
it does seem to center on 0 (I haven't done a real simulation), but as @ttnphns alludes, running this (all variables the same)
a <- rnorm(100)
mean((a-mean(a))*(a-mean(a))*(a-mean(a... | Analogy of Pearson correlation for 3 variables | Hmmm. If we run...
a <- rnorm(100);
b <- rnorm(100);
c <- rnorm(100)
mean((a-mean(a))*(b-mean(b))*(c-mean(c)))/
(sd(a) * sd(b) * sd(c))
it does seem to center on 0 (I haven't done a real simulation | Analogy of Pearson correlation for 3 variables
Hmmm. If we run...
a <- rnorm(100);
b <- rnorm(100);
c <- rnorm(100)
mean((a-mean(a))*(b-mean(b))*(c-mean(c)))/
(sd(a) * sd(b) * sd(c))
it does seem to center on 0 (I haven't done a real simulation), but as @ttnphns alludes, running this (all variables the same)
a <- rn... | Analogy of Pearson correlation for 3 variables
Hmmm. If we run...
a <- rnorm(100);
b <- rnorm(100);
c <- rnorm(100)
mean((a-mean(a))*(b-mean(b))*(c-mean(c)))/
(sd(a) * sd(b) * sd(c))
it does seem to center on 0 (I haven't done a real simulation |
11,192 | Analogy of Pearson correlation for 3 variables | If You need to calculate "correlation" between three or more variables, you could not use Pearson, as in this case it will be different for different order of variables have a look here.
If you are interesting in linear dependency, or how well they are fitted by 3D line, you may use PCA, obtain explained variance for f... | Analogy of Pearson correlation for 3 variables | If You need to calculate "correlation" between three or more variables, you could not use Pearson, as in this case it will be different for different order of variables have a look here.
If you are in | Analogy of Pearson correlation for 3 variables
If You need to calculate "correlation" between three or more variables, you could not use Pearson, as in this case it will be different for different order of variables have a look here.
If you are interesting in linear dependency, or how well they are fitted by 3D line, y... | Analogy of Pearson correlation for 3 variables
If You need to calculate "correlation" between three or more variables, you could not use Pearson, as in this case it will be different for different order of variables have a look here.
If you are in |
11,193 | How do betting houses determine betting odds for sports? | How odds are set is a really interesting subject that I have done some research into, and in a similar way sports analytics.
The first paper I would refer to covers the NFL specifically "Why are Gambling Markets organised so differently from Financial Markets", Steven.D.Levitt (The Economic Journal 2004). This illustra... | How do betting houses determine betting odds for sports? | How odds are set is a really interesting subject that I have done some research into, and in a similar way sports analytics.
The first paper I would refer to covers the NFL specifically "Why are Gambl | How do betting houses determine betting odds for sports?
How odds are set is a really interesting subject that I have done some research into, and in a similar way sports analytics.
The first paper I would refer to covers the NFL specifically "Why are Gambling Markets organised so differently from Financial Markets", S... | How do betting houses determine betting odds for sports?
How odds are set is a really interesting subject that I have done some research into, and in a similar way sports analytics.
The first paper I would refer to covers the NFL specifically "Why are Gambl |
11,194 | How do betting houses determine betting odds for sports? | The following is for entertainment purposes only. Sports betting is a very interesting academic topic, and I recommend you keep it an academic topic. You incur your own financial (and legal, in some jurisdictions) risks by acting upon anything I say :)
The process is more complicated than many people make it out to b... | How do betting houses determine betting odds for sports? | The following is for entertainment purposes only. Sports betting is a very interesting academic topic, and I recommend you keep it an academic topic. You incur your own financial (and legal, in some | How do betting houses determine betting odds for sports?
The following is for entertainment purposes only. Sports betting is a very interesting academic topic, and I recommend you keep it an academic topic. You incur your own financial (and legal, in some jurisdictions) risks by acting upon anything I say :)
The proc... | How do betting houses determine betting odds for sports?
The following is for entertainment purposes only. Sports betting is a very interesting academic topic, and I recommend you keep it an academic topic. You incur your own financial (and legal, in some |
11,195 | Building a linear model for a ratio vs. percentage? | I've never seen a regression model for ratios before, but regression for a percentage (or more commonly, a fraction) is quite common. The reason may be that it's easy to write down a likelihood (probability of the data given your parameter) in terms of a fraction or probability: each element has a probability $p$ of b... | Building a linear model for a ratio vs. percentage? | I've never seen a regression model for ratios before, but regression for a percentage (or more commonly, a fraction) is quite common. The reason may be that it's easy to write down a likelihood (prob | Building a linear model for a ratio vs. percentage?
I've never seen a regression model for ratios before, but regression for a percentage (or more commonly, a fraction) is quite common. The reason may be that it's easy to write down a likelihood (probability of the data given your parameter) in terms of a fraction or ... | Building a linear model for a ratio vs. percentage?
I've never seen a regression model for ratios before, but regression for a percentage (or more commonly, a fraction) is quite common. The reason may be that it's easy to write down a likelihood (prob |
11,196 | Building a linear model for a ratio vs. percentage? | Echoing the first answer. Don't bother to convert - just model the counts and covariates directly.
If you do that and fit a Binomial (or equivalently logistic) regression model to the boy girl counts you will, if you choose the usual link function for such models, implicitly already be fitting a (covariate smoothed lo... | Building a linear model for a ratio vs. percentage? | Echoing the first answer. Don't bother to convert - just model the counts and covariates directly.
If you do that and fit a Binomial (or equivalently logistic) regression model to the boy girl counts | Building a linear model for a ratio vs. percentage?
Echoing the first answer. Don't bother to convert - just model the counts and covariates directly.
If you do that and fit a Binomial (or equivalently logistic) regression model to the boy girl counts you will, if you choose the usual link function for such models, im... | Building a linear model for a ratio vs. percentage?
Echoing the first answer. Don't bother to convert - just model the counts and covariates directly.
If you do that and fit a Binomial (or equivalently logistic) regression model to the boy girl counts |
11,197 | Meaning of 'number of parameters' in AIC | As mugen mentioned, $k$ represents the number of parameters estimated. In other words, it's the number of additional quantities you need to know in order to fully specify the model. In the simple linear regression model
$$y=ax+b$$
you can estimate $a$, $b$, or both. Whichever quantities you don't estimate you must fix... | Meaning of 'number of parameters' in AIC | As mugen mentioned, $k$ represents the number of parameters estimated. In other words, it's the number of additional quantities you need to know in order to fully specify the model. In the simple line | Meaning of 'number of parameters' in AIC
As mugen mentioned, $k$ represents the number of parameters estimated. In other words, it's the number of additional quantities you need to know in order to fully specify the model. In the simple linear regression model
$$y=ax+b$$
you can estimate $a$, $b$, or both. Whichever q... | Meaning of 'number of parameters' in AIC
As mugen mentioned, $k$ represents the number of parameters estimated. In other words, it's the number of additional quantities you need to know in order to fully specify the model. In the simple line |
11,198 | Meaning of 'number of parameters' in AIC | For any statistical model, the AIC value is $\mathit{AIC} = 2k - 2\ln(L)$
where k is the number of parameters in the model, and L is the maximized value of the likelihood function for the model.
(see here)
As you may see, $k$ represents the number of parameters estimated in each model. If you model includes an inter... | Meaning of 'number of parameters' in AIC | For any statistical model, the AIC value is $\mathit{AIC} = 2k - 2\ln(L)$
where k is the number of parameters in the model, and L is the maximized value of the likelihood function for the model.
(s | Meaning of 'number of parameters' in AIC
For any statistical model, the AIC value is $\mathit{AIC} = 2k - 2\ln(L)$
where k is the number of parameters in the model, and L is the maximized value of the likelihood function for the model.
(see here)
As you may see, $k$ represents the number of parameters estimated in e... | Meaning of 'number of parameters' in AIC
For any statistical model, the AIC value is $\mathit{AIC} = 2k - 2\ln(L)$
where k is the number of parameters in the model, and L is the maximized value of the likelihood function for the model.
(s |
11,199 | Meaning of 'number of parameters' in AIC | First, to those who may not be familiar with AIC: the Akaike Information Criterion (AIC) is a simple metric designed to compare the "goodness" of models.
According to AIC, when trying to choose between two different models applying to the same input and response variables, i.e. models designed to solve the same problem... | Meaning of 'number of parameters' in AIC | First, to those who may not be familiar with AIC: the Akaike Information Criterion (AIC) is a simple metric designed to compare the "goodness" of models.
According to AIC, when trying to choose betwee | Meaning of 'number of parameters' in AIC
First, to those who may not be familiar with AIC: the Akaike Information Criterion (AIC) is a simple metric designed to compare the "goodness" of models.
According to AIC, when trying to choose between two different models applying to the same input and response variables, i.e. ... | Meaning of 'number of parameters' in AIC
First, to those who may not be familiar with AIC: the Akaike Information Criterion (AIC) is a simple metric designed to compare the "goodness" of models.
According to AIC, when trying to choose betwee |
11,200 | Equations in the news: Translating a multi-level model to a general audience | Here's one possibility.
Assessing teacher performance has traditionally been difficult. One part of this difficulty is that different students have different levels of interest in a given subject. If a given student gets an A, this doesn't necessarily mean that teaching was excellent -- rather, it may mean that a very ... | Equations in the news: Translating a multi-level model to a general audience | Here's one possibility.
Assessing teacher performance has traditionally been difficult. One part of this difficulty is that different students have different levels of interest in a given subject. If | Equations in the news: Translating a multi-level model to a general audience
Here's one possibility.
Assessing teacher performance has traditionally been difficult. One part of this difficulty is that different students have different levels of interest in a given subject. If a given student gets an A, this doesn't nec... | Equations in the news: Translating a multi-level model to a general audience
Here's one possibility.
Assessing teacher performance has traditionally been difficult. One part of this difficulty is that different students have different levels of interest in a given subject. If |
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