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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6,301 | Feature map for the Gaussian kernel | You can obtain the explicit equation of $\phi$ for the Gaussian kernel via the Tailor series expansion of $e^x$. For notational simplicity, assume $x\in \mathbb{R}^1$:
$$\phi(x) = e^{-x^2/2\sigma^2} \Big[ 1, \sqrt{\frac{1}{1!\sigma^2}}x,\sqrt{\frac{1}{2!\sigma^4}}x^2,\sqrt{\frac{1}{3!\sigma^6}}x^3,\ldots\Big]^T$$
This ... | Feature map for the Gaussian kernel | You can obtain the explicit equation of $\phi$ for the Gaussian kernel via the Tailor series expansion of $e^x$. For notational simplicity, assume $x\in \mathbb{R}^1$:
$$\phi(x) = e^{-x^2/2\sigma^2} \ | Feature map for the Gaussian kernel
You can obtain the explicit equation of $\phi$ for the Gaussian kernel via the Tailor series expansion of $e^x$. For notational simplicity, assume $x\in \mathbb{R}^1$:
$$\phi(x) = e^{-x^2/2\sigma^2} \Big[ 1, \sqrt{\frac{1}{1!\sigma^2}}x,\sqrt{\frac{1}{2!\sigma^4}}x^2,\sqrt{\frac{1}{3... | Feature map for the Gaussian kernel
You can obtain the explicit equation of $\phi$ for the Gaussian kernel via the Tailor series expansion of $e^x$. For notational simplicity, assume $x\in \mathbb{R}^1$:
$$\phi(x) = e^{-x^2/2\sigma^2} \ |
6,302 | Feature map for the Gaussian kernel | For any valid psd kernel $k : \mathcal X \times \mathcal X \to \mathbb R$, there exists a feature map $\varphi : \mathcal X \to \mathcal H$ such that $k(x, y) = \langle \varphi(x), \varphi(y) \rangle_{\mathcal H}$. The space $\mathcal H$ and embedding $\varphi$ in fact need not be unique, but there is an important uniq... | Feature map for the Gaussian kernel | For any valid psd kernel $k : \mathcal X \times \mathcal X \to \mathbb R$, there exists a feature map $\varphi : \mathcal X \to \mathcal H$ such that $k(x, y) = \langle \varphi(x), \varphi(y) \rangle_ | Feature map for the Gaussian kernel
For any valid psd kernel $k : \mathcal X \times \mathcal X \to \mathbb R$, there exists a feature map $\varphi : \mathcal X \to \mathcal H$ such that $k(x, y) = \langle \varphi(x), \varphi(y) \rangle_{\mathcal H}$. The space $\mathcal H$ and embedding $\varphi$ in fact need not be un... | Feature map for the Gaussian kernel
For any valid psd kernel $k : \mathcal X \times \mathcal X \to \mathbb R$, there exists a feature map $\varphi : \mathcal X \to \mathcal H$ such that $k(x, y) = \langle \varphi(x), \varphi(y) \rangle_ |
6,303 | Feature map for the Gaussian kernel | It seems to me that your second equation will only be true if $\phi$ is a linear mapping (and hence $K$ is a linear kernel). As the Gaussian kernel is non-linear, the equality will not hold (except perhaps in the limit as $\sigma$ goes to zero). | Feature map for the Gaussian kernel | It seems to me that your second equation will only be true if $\phi$ is a linear mapping (and hence $K$ is a linear kernel). As the Gaussian kernel is non-linear, the equality will not hold (except p | Feature map for the Gaussian kernel
It seems to me that your second equation will only be true if $\phi$ is a linear mapping (and hence $K$ is a linear kernel). As the Gaussian kernel is non-linear, the equality will not hold (except perhaps in the limit as $\sigma$ goes to zero). | Feature map for the Gaussian kernel
It seems to me that your second equation will only be true if $\phi$ is a linear mapping (and hence $K$ is a linear kernel). As the Gaussian kernel is non-linear, the equality will not hold (except p |
6,304 | Feature map for the Gaussian kernel | EXPLICIT EXPRESSION AND DERIVATION VIA DIRECT PROOF
The explicit expression for $\phi$ you are asking for is the following:
Lemma:
Given the Gaussian RBF Kernel $K_\sigma$ between two $n$-dimensional vectors ($x$ and another), for each $j$ from 0 to infinity and for every combination of $n$ indices (labeled as $k$) th... | Feature map for the Gaussian kernel | EXPLICIT EXPRESSION AND DERIVATION VIA DIRECT PROOF
The explicit expression for $\phi$ you are asking for is the following:
Lemma:
Given the Gaussian RBF Kernel $K_\sigma$ between two $n$-dimensional | Feature map for the Gaussian kernel
EXPLICIT EXPRESSION AND DERIVATION VIA DIRECT PROOF
The explicit expression for $\phi$ you are asking for is the following:
Lemma:
Given the Gaussian RBF Kernel $K_\sigma$ between two $n$-dimensional vectors ($x$ and another), for each $j$ from 0 to infinity and for every combinatio... | Feature map for the Gaussian kernel
EXPLICIT EXPRESSION AND DERIVATION VIA DIRECT PROOF
The explicit expression for $\phi$ you are asking for is the following:
Lemma:
Given the Gaussian RBF Kernel $K_\sigma$ between two $n$-dimensional |
6,305 | What exactly is the difference between a parametric and non-parametric model? | In a parametric model, the number of parameters is fixed with respect to the sample size. In a nonparametric model, the (effective) number of parameters can grow with the sample size.
In an OLS regression, the number of parameters will always be the length of $\beta$, plus one for the variance.
A neural net with f... | What exactly is the difference between a parametric and non-parametric model? | In a parametric model, the number of parameters is fixed with respect to the sample size. In a nonparametric model, the (effective) number of parameters can grow with the sample size.
In an OLS reg | What exactly is the difference between a parametric and non-parametric model?
In a parametric model, the number of parameters is fixed with respect to the sample size. In a nonparametric model, the (effective) number of parameters can grow with the sample size.
In an OLS regression, the number of parameters will alw... | What exactly is the difference between a parametric and non-parametric model?
In a parametric model, the number of parameters is fixed with respect to the sample size. In a nonparametric model, the (effective) number of parameters can grow with the sample size.
In an OLS reg |
6,306 | What exactly is the difference between a parametric and non-parametric model? | I think that the word "effective" in the accepted answer should be deleted. Because due to the different number of effective parameters, as Aksakal pointed out, the accepted answer implies that Ridge and Lasso are non-parametric, but it doesn't seem to be true. Effective parameters (effective degrees of freedom) are ch... | What exactly is the difference between a parametric and non-parametric model? | I think that the word "effective" in the accepted answer should be deleted. Because due to the different number of effective parameters, as Aksakal pointed out, the accepted answer implies that Ridge | What exactly is the difference between a parametric and non-parametric model?
I think that the word "effective" in the accepted answer should be deleted. Because due to the different number of effective parameters, as Aksakal pointed out, the accepted answer implies that Ridge and Lasso are non-parametric, but it doesn... | What exactly is the difference between a parametric and non-parametric model?
I think that the word "effective" in the accepted answer should be deleted. Because due to the different number of effective parameters, as Aksakal pointed out, the accepted answer implies that Ridge |
6,307 | What exactly is the difference between a parametric and non-parametric model? | I think if the model is defined as a set of equations (can be a system of concurrent equations or a single one), and we learn its parameters, then is parametric. That includes differential equations, and even Navier-Stokes' equation. Models defined descriptively, regardless of how they are solved, fall into the catego... | What exactly is the difference between a parametric and non-parametric model? | I think if the model is defined as a set of equations (can be a system of concurrent equations or a single one), and we learn its parameters, then is parametric. That includes differential equations, | What exactly is the difference between a parametric and non-parametric model?
I think if the model is defined as a set of equations (can be a system of concurrent equations or a single one), and we learn its parameters, then is parametric. That includes differential equations, and even Navier-Stokes' equation. Models ... | What exactly is the difference between a parametric and non-parametric model?
I think if the model is defined as a set of equations (can be a system of concurrent equations or a single one), and we learn its parameters, then is parametric. That includes differential equations, |
6,308 | What exactly is the difference between a parametric and non-parametric model? | Parametric model: assumes that the population can be adequately modeled by a probability distribution that has a fixed set of parameters.
Non-parametric model: makes no assumptions about some probability distribution when modeling the data. | What exactly is the difference between a parametric and non-parametric model? | Parametric model: assumes that the population can be adequately modeled by a probability distribution that has a fixed set of parameters.
Non-parametric model: makes no assumptions about some probabil | What exactly is the difference between a parametric and non-parametric model?
Parametric model: assumes that the population can be adequately modeled by a probability distribution that has a fixed set of parameters.
Non-parametric model: makes no assumptions about some probability distribution when modeling the data. | What exactly is the difference between a parametric and non-parametric model?
Parametric model: assumes that the population can be adequately modeled by a probability distribution that has a fixed set of parameters.
Non-parametric model: makes no assumptions about some probabil |
6,309 | Random number-Set.seed(N) in R [duplicate] | The seed number you choose is the starting point used in the generation of a sequence of random numbers, which is why (provided you use the same pseudo-random number generator) you'll obtain the same results given the same seed number. As far as your second question is concerned, this short snippet from the description... | Random number-Set.seed(N) in R [duplicate] | The seed number you choose is the starting point used in the generation of a sequence of random numbers, which is why (provided you use the same pseudo-random number generator) you'll obtain the same | Random number-Set.seed(N) in R [duplicate]
The seed number you choose is the starting point used in the generation of a sequence of random numbers, which is why (provided you use the same pseudo-random number generator) you'll obtain the same results given the same seed number. As far as your second question is concern... | Random number-Set.seed(N) in R [duplicate]
The seed number you choose is the starting point used in the generation of a sequence of random numbers, which is why (provided you use the same pseudo-random number generator) you'll obtain the same |
6,310 | Random number-Set.seed(N) in R [duplicate] | In short, the numbers themselves don't really mean anything! If you are looking at someone else's code (like in the two examples you gave above), the numbers don't alter the functionality of the function; neither are there "good" numbers for specific functions. It's just down to the authors' choice.
Further, if you ar... | Random number-Set.seed(N) in R [duplicate] | In short, the numbers themselves don't really mean anything! If you are looking at someone else's code (like in the two examples you gave above), the numbers don't alter the functionality of the funct | Random number-Set.seed(N) in R [duplicate]
In short, the numbers themselves don't really mean anything! If you are looking at someone else's code (like in the two examples you gave above), the numbers don't alter the functionality of the function; neither are there "good" numbers for specific functions. It's just down ... | Random number-Set.seed(N) in R [duplicate]
In short, the numbers themselves don't really mean anything! If you are looking at someone else's code (like in the two examples you gave above), the numbers don't alter the functionality of the funct |
6,311 | Random number-Set.seed(N) in R [duplicate] | The set.seed()function in R takes an (arbitrary) integer argument. So we can take any argument, say, 1 or 123 or 300 or 12345 to get the reproducible random numbers.
Also, in theTeachingDemos package, the char2seed function allows user to set the seed based on a character string. | Random number-Set.seed(N) in R [duplicate] | The set.seed()function in R takes an (arbitrary) integer argument. So we can take any argument, say, 1 or 123 or 300 or 12345 to get the reproducible random numbers.
Also, in theTeachingDemos package | Random number-Set.seed(N) in R [duplicate]
The set.seed()function in R takes an (arbitrary) integer argument. So we can take any argument, say, 1 or 123 or 300 or 12345 to get the reproducible random numbers.
Also, in theTeachingDemos package, the char2seed function allows user to set the seed based on a character str... | Random number-Set.seed(N) in R [duplicate]
The set.seed()function in R takes an (arbitrary) integer argument. So we can take any argument, say, 1 or 123 or 300 or 12345 to get the reproducible random numbers.
Also, in theTeachingDemos package |
6,312 | What are the advantages of stacking multiple LSTMs? | I think that you are referring to vertically stacked LSTM layers (assuming the horizontal axes is the time axis.
In that case the main reason for stacking LSTM is to allow for greater model complexity. In case of a simple feedforward net we stack layers to create a hierarchical feature representation of the input data... | What are the advantages of stacking multiple LSTMs? | I think that you are referring to vertically stacked LSTM layers (assuming the horizontal axes is the time axis.
In that case the main reason for stacking LSTM is to allow for greater model complexit | What are the advantages of stacking multiple LSTMs?
I think that you are referring to vertically stacked LSTM layers (assuming the horizontal axes is the time axis.
In that case the main reason for stacking LSTM is to allow for greater model complexity. In case of a simple feedforward net we stack layers to create a h... | What are the advantages of stacking multiple LSTMs?
I think that you are referring to vertically stacked LSTM layers (assuming the horizontal axes is the time axis.
In that case the main reason for stacking LSTM is to allow for greater model complexit |
6,313 | What are the advantages of stacking multiple LSTMs? | From {1}:
While it is not theoretically clear what is the additional power gained by the deeper
architecture, it was observed empirically that deep RNNs work better than shallower ones
on some tasks. In particular, Sutskever et al (2014) report that a 4-layers deep architecture
was crucial in achieving good mach... | What are the advantages of stacking multiple LSTMs? | From {1}:
While it is not theoretically clear what is the additional power gained by the deeper
architecture, it was observed empirically that deep RNNs work better than shallower ones
on some ta | What are the advantages of stacking multiple LSTMs?
From {1}:
While it is not theoretically clear what is the additional power gained by the deeper
architecture, it was observed empirically that deep RNNs work better than shallower ones
on some tasks. In particular, Sutskever et al (2014) report that a 4-layers de... | What are the advantages of stacking multiple LSTMs?
From {1}:
While it is not theoretically clear what is the additional power gained by the deeper
architecture, it was observed empirically that deep RNNs work better than shallower ones
on some ta |
6,314 | What are the advantages of stacking multiple LSTMs? | From playing around with LSTM for sequence classification it had the same effect as increasing model capacity in CNNs (if you're familiar with them). So you definitely get gains especially if you are underfitting your data.
Of course double edged as you can also over fit and get worse performance.
In my case I went fr... | What are the advantages of stacking multiple LSTMs? | From playing around with LSTM for sequence classification it had the same effect as increasing model capacity in CNNs (if you're familiar with them). So you definitely get gains especially if you are | What are the advantages of stacking multiple LSTMs?
From playing around with LSTM for sequence classification it had the same effect as increasing model capacity in CNNs (if you're familiar with them). So you definitely get gains especially if you are underfitting your data.
Of course double edged as you can also over ... | What are the advantages of stacking multiple LSTMs?
From playing around with LSTM for sequence classification it had the same effect as increasing model capacity in CNNs (if you're familiar with them). So you definitely get gains especially if you are |
6,315 | What are the advantages of stacking multiple LSTMs? | In my experience, stacking LSTM layers (beyond 3) seems to offer worse performance.
The purple has 2 layers, pink has 3 and green has 6. Everything else is held constant. It does, I'm sure, depend on task. My task is a sequence-to-sequence of fixed length input and output. | What are the advantages of stacking multiple LSTMs? | In my experience, stacking LSTM layers (beyond 3) seems to offer worse performance.
The purple has 2 layers, pink has 3 and green has 6. Everything else is held constant. It does, I'm sure, depend on | What are the advantages of stacking multiple LSTMs?
In my experience, stacking LSTM layers (beyond 3) seems to offer worse performance.
The purple has 2 layers, pink has 3 and green has 6. Everything else is held constant. It does, I'm sure, depend on task. My task is a sequence-to-sequence of fixed length input and ... | What are the advantages of stacking multiple LSTMs?
In my experience, stacking LSTM layers (beyond 3) seems to offer worse performance.
The purple has 2 layers, pink has 3 and green has 6. Everything else is held constant. It does, I'm sure, depend on |
6,316 | Evidence for man-made global warming hits 'gold standard': how did they do this? | It is not always about statistical testing. It can also be about information theory.
The term 5σ is what it says it is: a ratio of "signal" to "noise." In hypothesis testing we have an estimate of a distribution parameter, and standard error of the estimate. The first is a "signal," the second is "noise," and the ratio... | Evidence for man-made global warming hits 'gold standard': how did they do this? | It is not always about statistical testing. It can also be about information theory.
The term 5σ is what it says it is: a ratio of "signal" to "noise." In hypothesis testing we have an estimate of a d | Evidence for man-made global warming hits 'gold standard': how did they do this?
It is not always about statistical testing. It can also be about information theory.
The term 5σ is what it says it is: a ratio of "signal" to "noise." In hypothesis testing we have an estimate of a distribution parameter, and standard err... | Evidence for man-made global warming hits 'gold standard': how did they do this?
It is not always about statistical testing. It can also be about information theory.
The term 5σ is what it says it is: a ratio of "signal" to "noise." In hypothesis testing we have an estimate of a d |
6,317 | Evidence for man-made global warming hits 'gold standard': how did they do this? | Caveat: I am NOT an expert on climatology, this is not my field. Please bear this in mind. Corrections welcome.
The figure that you are referring to comes from a recent paper Santer et al. 2019, Celebrating the anniversary of three key events in climate change science from Nature Climate Change. It is not a research ... | Evidence for man-made global warming hits 'gold standard': how did they do this? | Caveat: I am NOT an expert on climatology, this is not my field. Please bear this in mind. Corrections welcome.
The figure that you are referring to comes from a recent paper Santer et al. 2019, Cel | Evidence for man-made global warming hits 'gold standard': how did they do this?
Caveat: I am NOT an expert on climatology, this is not my field. Please bear this in mind. Corrections welcome.
The figure that you are referring to comes from a recent paper Santer et al. 2019, Celebrating the anniversary of three key e... | Evidence for man-made global warming hits 'gold standard': how did they do this?
Caveat: I am NOT an expert on climatology, this is not my field. Please bear this in mind. Corrections welcome.
The figure that you are referring to comes from a recent paper Santer et al. 2019, Cel |
6,318 | Error "system is computationally singular" when running a glm | It means your design matrix is not invertible and therefore can't be used to develop a regression model. This results from linearly dependent columns, i.e. strongly correlated variables. Examine the pairwise covariance (or correlation) of your variables to investigate if there are any variables that can potentially be ... | Error "system is computationally singular" when running a glm | It means your design matrix is not invertible and therefore can't be used to develop a regression model. This results from linearly dependent columns, i.e. strongly correlated variables. Examine the p | Error "system is computationally singular" when running a glm
It means your design matrix is not invertible and therefore can't be used to develop a regression model. This results from linearly dependent columns, i.e. strongly correlated variables. Examine the pairwise covariance (or correlation) of your variables to i... | Error "system is computationally singular" when running a glm
It means your design matrix is not invertible and therefore can't be used to develop a regression model. This results from linearly dependent columns, i.e. strongly correlated variables. Examine the p |
6,319 | Error "system is computationally singular" when running a glm | I've dealt with the exact same problem. My teacher told me that this is because one of my variables is much bigger than the others. (In my case, the trading volume was much bigger than the returns in two different moments.) The problem is because of limitations in floating-point computations and precision, not anything... | Error "system is computationally singular" when running a glm | I've dealt with the exact same problem. My teacher told me that this is because one of my variables is much bigger than the others. (In my case, the trading volume was much bigger than the returns in | Error "system is computationally singular" when running a glm
I've dealt with the exact same problem. My teacher told me that this is because one of my variables is much bigger than the others. (In my case, the trading volume was much bigger than the returns in two different moments.) The problem is because of limitati... | Error "system is computationally singular" when running a glm
I've dealt with the exact same problem. My teacher told me that this is because one of my variables is much bigger than the others. (In my case, the trading volume was much bigger than the returns in |
6,320 | Creating a "certainty score" from the votes in random forests? | It makes perfect sense, and all implementations of random forests I've worked with (such as MATLAB's) provide probabilistic outputs as well to do just that.
I've not worked with the R implementation, but I'd be shocked if there wasn't a simple way to obtain soft outputs from the votes as well as the hard decision.
Edit... | Creating a "certainty score" from the votes in random forests? | It makes perfect sense, and all implementations of random forests I've worked with (such as MATLAB's) provide probabilistic outputs as well to do just that.
I've not worked with the R implementation, | Creating a "certainty score" from the votes in random forests?
It makes perfect sense, and all implementations of random forests I've worked with (such as MATLAB's) provide probabilistic outputs as well to do just that.
I've not worked with the R implementation, but I'd be shocked if there wasn't a simple way to obtain... | Creating a "certainty score" from the votes in random forests?
It makes perfect sense, and all implementations of random forests I've worked with (such as MATLAB's) provide probabilistic outputs as well to do just that.
I've not worked with the R implementation, |
6,321 | Creating a "certainty score" from the votes in random forests? | If you are using R, the caret package will save you from re-inventing the wheel. For example, the following code uses cross-validation to choose the tuning parameters for a random forest model, and then outputs the mean and standard deviation of accuracy for each cross-validation fold. Finally, it calculates class pr... | Creating a "certainty score" from the votes in random forests? | If you are using R, the caret package will save you from re-inventing the wheel. For example, the following code uses cross-validation to choose the tuning parameters for a random forest model, and t | Creating a "certainty score" from the votes in random forests?
If you are using R, the caret package will save you from re-inventing the wheel. For example, the following code uses cross-validation to choose the tuning parameters for a random forest model, and then outputs the mean and standard deviation of accuracy f... | Creating a "certainty score" from the votes in random forests?
If you are using R, the caret package will save you from re-inventing the wheel. For example, the following code uses cross-validation to choose the tuning parameters for a random forest model, and t |
6,322 | Creating a "certainty score" from the votes in random forests? | The randomForest package in R is a pretty decent package for getting into greater details about your analysis. It provides you with the votes (either as a fraction or raw counts) and it offers built in capacity for tuning and cross validation and can even give you more information about your features as well (if you wa... | Creating a "certainty score" from the votes in random forests? | The randomForest package in R is a pretty decent package for getting into greater details about your analysis. It provides you with the votes (either as a fraction or raw counts) and it offers built i | Creating a "certainty score" from the votes in random forests?
The randomForest package in R is a pretty decent package for getting into greater details about your analysis. It provides you with the votes (either as a fraction or raw counts) and it offers built in capacity for tuning and cross validation and can even g... | Creating a "certainty score" from the votes in random forests?
The randomForest package in R is a pretty decent package for getting into greater details about your analysis. It provides you with the votes (either as a fraction or raw counts) and it offers built i |
6,323 | Is Kolmogorov-Smirnov test valid with discrete distributions? | It does not apply to discrete distributions. See http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm for example.
Is there any reason you can't use a chi-square goodness of fit test?
see http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm for more info. | Is Kolmogorov-Smirnov test valid with discrete distributions? | It does not apply to discrete distributions. See http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm for example.
Is there any reason you can't use a chi-square goodness of fit test?
see h | Is Kolmogorov-Smirnov test valid with discrete distributions?
It does not apply to discrete distributions. See http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm for example.
Is there any reason you can't use a chi-square goodness of fit test?
see http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f... | Is Kolmogorov-Smirnov test valid with discrete distributions?
It does not apply to discrete distributions. See http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm for example.
Is there any reason you can't use a chi-square goodness of fit test?
see h |
6,324 | Is Kolmogorov-Smirnov test valid with discrete distributions? | As is often the case in statistics, it depends on what you mean.
If you mean "I calculate my test statistic on a sample drawn from a discrete distribution and then look up the standard tables" then you'll get a true type I error rate lower than the one you chose (possibly a lot lower).
How much depends on "how discret... | Is Kolmogorov-Smirnov test valid with discrete distributions? | As is often the case in statistics, it depends on what you mean.
If you mean "I calculate my test statistic on a sample drawn from a discrete distribution and then look up the standard tables" then y | Is Kolmogorov-Smirnov test valid with discrete distributions?
As is often the case in statistics, it depends on what you mean.
If you mean "I calculate my test statistic on a sample drawn from a discrete distribution and then look up the standard tables" then you'll get a true type I error rate lower than the one you ... | Is Kolmogorov-Smirnov test valid with discrete distributions?
As is often the case in statistics, it depends on what you mean.
If you mean "I calculate my test statistic on a sample drawn from a discrete distribution and then look up the standard tables" then y |
6,325 | Is Kolmogorov-Smirnov test valid with discrete distributions? | I believe the K-S test uses the fact that if $X$ is a random variable with CDF $F$ then $F(X)$ is a uniform random variable. This is not the case if $X$ is not continuous. For example, if $X$ is Bernoulli then $F(X)=X$, not a uniform. | Is Kolmogorov-Smirnov test valid with discrete distributions? | I believe the K-S test uses the fact that if $X$ is a random variable with CDF $F$ then $F(X)$ is a uniform random variable. This is not the case if $X$ is not continuous. For example, if $X$ is Be | Is Kolmogorov-Smirnov test valid with discrete distributions?
I believe the K-S test uses the fact that if $X$ is a random variable with CDF $F$ then $F(X)$ is a uniform random variable. This is not the case if $X$ is not continuous. For example, if $X$ is Bernoulli then $F(X)=X$, not a uniform. | Is Kolmogorov-Smirnov test valid with discrete distributions?
I believe the K-S test uses the fact that if $X$ is a random variable with CDF $F$ then $F(X)$ is a uniform random variable. This is not the case if $X$ is not continuous. For example, if $X$ is Be |
6,326 | Training loss increases with time [duplicate] | I had such a similar behavior when training a CNN, it was because I used the gradient descent with decaying learning rate for the error calculation. Have you significantly increased the number of iterations and checked if this behavior comes much later with the new low learning rate? | Training loss increases with time [duplicate] | I had such a similar behavior when training a CNN, it was because I used the gradient descent with decaying learning rate for the error calculation. Have you significantly increased the number of iter | Training loss increases with time [duplicate]
I had such a similar behavior when training a CNN, it was because I used the gradient descent with decaying learning rate for the error calculation. Have you significantly increased the number of iterations and checked if this behavior comes much later with the new low lear... | Training loss increases with time [duplicate]
I had such a similar behavior when training a CNN, it was because I used the gradient descent with decaying learning rate for the error calculation. Have you significantly increased the number of iter |
6,327 | Training loss increases with time [duplicate] | With higher learning rates you are moving too much in the direction opposite to the gradient and may move away from the local minima which can increase the loss. Learning rate scheduling and gradient clipping can help. | Training loss increases with time [duplicate] | With higher learning rates you are moving too much in the direction opposite to the gradient and may move away from the local minima which can increase the loss. Learning rate scheduling and gradient | Training loss increases with time [duplicate]
With higher learning rates you are moving too much in the direction opposite to the gradient and may move away from the local minima which can increase the loss. Learning rate scheduling and gradient clipping can help. | Training loss increases with time [duplicate]
With higher learning rates you are moving too much in the direction opposite to the gradient and may move away from the local minima which can increase the loss. Learning rate scheduling and gradient |
6,328 | Training loss increases with time [duplicate] | Because as learning rate is too big, it will diverge and fail to find the minimum of the loss function. Using a scheduler to decrease learning rate after certain epochs will help solve the problem | Training loss increases with time [duplicate] | Because as learning rate is too big, it will diverge and fail to find the minimum of the loss function. Using a scheduler to decrease learning rate after certain epochs will help solve the problem | Training loss increases with time [duplicate]
Because as learning rate is too big, it will diverge and fail to find the minimum of the loss function. Using a scheduler to decrease learning rate after certain epochs will help solve the problem | Training loss increases with time [duplicate]
Because as learning rate is too big, it will diverge and fail to find the minimum of the loss function. Using a scheduler to decrease learning rate after certain epochs will help solve the problem |
6,329 | Difference between a SVM and a perceptron | It sounds right to me. People sometimes also use the word "Perceptron" to refer to the training algorithm together with the classifier. For example, someone explained this to me in the answer to this question. Also, there is nothing to stop you from using a kernel with the perceptron, and this is often a better classif... | Difference between a SVM and a perceptron | It sounds right to me. People sometimes also use the word "Perceptron" to refer to the training algorithm together with the classifier. For example, someone explained this to me in the answer to this | Difference between a SVM and a perceptron
It sounds right to me. People sometimes also use the word "Perceptron" to refer to the training algorithm together with the classifier. For example, someone explained this to me in the answer to this question. Also, there is nothing to stop you from using a kernel with the perc... | Difference between a SVM and a perceptron
It sounds right to me. People sometimes also use the word "Perceptron" to refer to the training algorithm together with the classifier. For example, someone explained this to me in the answer to this |
6,330 | Difference between a SVM and a perceptron | SVM:
$$\min \|w\|_2 + C\sum_{i = 1}^{n}(1 - y_i(wx_i + w_0))_+ $$
Perceptron
$$\min \sum_{i = 1}^{n}(- y_i(wx_i + w_0))_+ $$
We can see that SVM has almost the same goal as L2-regularized perceptron.
Since the objective is different, we also have different optimization schemes for these two algorithms, from the $\|w\|_... | Difference between a SVM and a perceptron | SVM:
$$\min \|w\|_2 + C\sum_{i = 1}^{n}(1 - y_i(wx_i + w_0))_+ $$
Perceptron
$$\min \sum_{i = 1}^{n}(- y_i(wx_i + w_0))_+ $$
We can see that SVM has almost the same goal as L2-regularized perceptron.
| Difference between a SVM and a perceptron
SVM:
$$\min \|w\|_2 + C\sum_{i = 1}^{n}(1 - y_i(wx_i + w_0))_+ $$
Perceptron
$$\min \sum_{i = 1}^{n}(- y_i(wx_i + w_0))_+ $$
We can see that SVM has almost the same goal as L2-regularized perceptron.
Since the objective is different, we also have different optimization schemes ... | Difference between a SVM and a perceptron
SVM:
$$\min \|w\|_2 + C\sum_{i = 1}^{n}(1 - y_i(wx_i + w_0))_+ $$
Perceptron
$$\min \sum_{i = 1}^{n}(- y_i(wx_i + w_0))_+ $$
We can see that SVM has almost the same goal as L2-regularized perceptron.
|
6,331 | Difference between a SVM and a perceptron | Perceptron is the generalization of SVM where SVM is the perceptron with optimal stability. So you are correct when you say perceptron does not try to optimize the separation distance. | Difference between a SVM and a perceptron | Perceptron is the generalization of SVM where SVM is the perceptron with optimal stability. So you are correct when you say perceptron does not try to optimize the separation distance. | Difference between a SVM and a perceptron
Perceptron is the generalization of SVM where SVM is the perceptron with optimal stability. So you are correct when you say perceptron does not try to optimize the separation distance. | Difference between a SVM and a perceptron
Perceptron is the generalization of SVM where SVM is the perceptron with optimal stability. So you are correct when you say perceptron does not try to optimize the separation distance. |
6,332 | Detecting Outliers in Time Series (LS/AO/TC) using tsoutliers package in R. How to represent outliers in equation format? | The temporary change, TC, is a general type of outlier. The equation given in the documentation of the package and that you wrote is the equation that describes the dynamics of this type of outlier. You can generate it by means of the function filter as shown below. It is illuminating to display it for several values o... | Detecting Outliers in Time Series (LS/AO/TC) using tsoutliers package in R. How to represent outlier | The temporary change, TC, is a general type of outlier. The equation given in the documentation of the package and that you wrote is the equation that describes the dynamics of this type of outlier. Y | Detecting Outliers in Time Series (LS/AO/TC) using tsoutliers package in R. How to represent outliers in equation format?
The temporary change, TC, is a general type of outlier. The equation given in the documentation of the package and that you wrote is the equation that describes the dynamics of this type of outlier.... | Detecting Outliers in Time Series (LS/AO/TC) using tsoutliers package in R. How to represent outlier
The temporary change, TC, is a general type of outlier. The equation given in the documentation of the package and that you wrote is the equation that describes the dynamics of this type of outlier. Y |
6,333 | How to determine significant principal components using bootstrapping or Monte Carlo approach? | I am going to try and advance the dialogue here a bit even though this is my question. It's been 6 months since I asked this and unfortunately no complete answers have been given I will try and summarize what I have gathered thus far and see if anyone can elaborate on remaining issues. Please excuse the lengthy answer,... | How to determine significant principal components using bootstrapping or Monte Carlo approach? | I am going to try and advance the dialogue here a bit even though this is my question. It's been 6 months since I asked this and unfortunately no complete answers have been given I will try and summar | How to determine significant principal components using bootstrapping or Monte Carlo approach?
I am going to try and advance the dialogue here a bit even though this is my question. It's been 6 months since I asked this and unfortunately no complete answers have been given I will try and summarize what I have gathered ... | How to determine significant principal components using bootstrapping or Monte Carlo approach?
I am going to try and advance the dialogue here a bit even though this is my question. It's been 6 months since I asked this and unfortunately no complete answers have been given I will try and summar |
6,334 | When is nested cross-validation really needed and can make a practical difference? | I would suggest that the bias depends on the variance of the model selection criterion, the higher the variance, the larger the bias is likely to be. The variance of the model selection criterion has two principal sources, the size of the dataset on which it is evaluated (so if you have a small dataset, the larger the... | When is nested cross-validation really needed and can make a practical difference? | I would suggest that the bias depends on the variance of the model selection criterion, the higher the variance, the larger the bias is likely to be. The variance of the model selection criterion has | When is nested cross-validation really needed and can make a practical difference?
I would suggest that the bias depends on the variance of the model selection criterion, the higher the variance, the larger the bias is likely to be. The variance of the model selection criterion has two principal sources, the size of t... | When is nested cross-validation really needed and can make a practical difference?
I would suggest that the bias depends on the variance of the model selection criterion, the higher the variance, the larger the bias is likely to be. The variance of the model selection criterion has |
6,335 | Why is 600 out of 1000 more convincing than 6 out of 10? | I would like to list another intuitive example.
Suppose I tell you I can predict the outcome of any coin flip. You do not believe and want to test my ability.
You tested 5 times, and I got all of them right. Do you believe I have the special ability? Maybe not. Because I can get all of them right by chance. (Specifical... | Why is 600 out of 1000 more convincing than 6 out of 10? | I would like to list another intuitive example.
Suppose I tell you I can predict the outcome of any coin flip. You do not believe and want to test my ability.
You tested 5 times, and I got all of them | Why is 600 out of 1000 more convincing than 6 out of 10?
I would like to list another intuitive example.
Suppose I tell you I can predict the outcome of any coin flip. You do not believe and want to test my ability.
You tested 5 times, and I got all of them right. Do you believe I have the special ability? Maybe not. B... | Why is 600 out of 1000 more convincing than 6 out of 10?
I would like to list another intuitive example.
Suppose I tell you I can predict the outcome of any coin flip. You do not believe and want to test my ability.
You tested 5 times, and I got all of them |
6,336 | Why is 600 out of 1000 more convincing than 6 out of 10? | Think about it in terms of proportions. Let's say that preferring an orange is a success, while preferring an apple is a failure. So your mean success rate is $\mu = \frac{\text{# of sucesses}}{n}$ or in this case .6
The standard error of this quantity is estimated to be $\sqrt{\frac{\mu(1-\mu)}{n}}$. For a small sampl... | Why is 600 out of 1000 more convincing than 6 out of 10? | Think about it in terms of proportions. Let's say that preferring an orange is a success, while preferring an apple is a failure. So your mean success rate is $\mu = \frac{\text{# of sucesses}}{n}$ or | Why is 600 out of 1000 more convincing than 6 out of 10?
Think about it in terms of proportions. Let's say that preferring an orange is a success, while preferring an apple is a failure. So your mean success rate is $\mu = \frac{\text{# of sucesses}}{n}$ or in this case .6
The standard error of this quantity is estimat... | Why is 600 out of 1000 more convincing than 6 out of 10?
Think about it in terms of proportions. Let's say that preferring an orange is a success, while preferring an apple is a failure. So your mean success rate is $\mu = \frac{\text{# of sucesses}}{n}$ or |
6,337 | Why is 600 out of 1000 more convincing than 6 out of 10? | This concept is a consequence of the law of large numbers. From Wikipedia,
According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.
Results from a small sample may be farther from the ... | Why is 600 out of 1000 more convincing than 6 out of 10? | This concept is a consequence of the law of large numbers. From Wikipedia,
According to the law, the average of the results obtained from a large number of trials should be close to the expected val | Why is 600 out of 1000 more convincing than 6 out of 10?
This concept is a consequence of the law of large numbers. From Wikipedia,
According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed... | Why is 600 out of 1000 more convincing than 6 out of 10?
This concept is a consequence of the law of large numbers. From Wikipedia,
According to the law, the average of the results obtained from a large number of trials should be close to the expected val |
6,338 | Why is 600 out of 1000 more convincing than 6 out of 10? | We're in the situation of estimating some population quantity by some sample quantity. In this case, we're using sample proportions to estimate population proportions, but the principle is considerably more general.
If you think of all the observations in your sample taking the value $1$ when they have the characteris... | Why is 600 out of 1000 more convincing than 6 out of 10? | We're in the situation of estimating some population quantity by some sample quantity. In this case, we're using sample proportions to estimate population proportions, but the principle is considerabl | Why is 600 out of 1000 more convincing than 6 out of 10?
We're in the situation of estimating some population quantity by some sample quantity. In this case, we're using sample proportions to estimate population proportions, but the principle is considerably more general.
If you think of all the observations in your s... | Why is 600 out of 1000 more convincing than 6 out of 10?
We're in the situation of estimating some population quantity by some sample quantity. In this case, we're using sample proportions to estimate population proportions, but the principle is considerabl |
6,339 | Why is 600 out of 1000 more convincing than 6 out of 10? | A rule of thumb for "counting" statistics, like counting the number of people that like oranges, or counting the number of "clicks" in a Geiger counter due to radioactive decay, is that the margin of error for the count is roughly the square-root of the expected count value. Counting statistics are known are Poisson st... | Why is 600 out of 1000 more convincing than 6 out of 10? | A rule of thumb for "counting" statistics, like counting the number of people that like oranges, or counting the number of "clicks" in a Geiger counter due to radioactive decay, is that the margin of | Why is 600 out of 1000 more convincing than 6 out of 10?
A rule of thumb for "counting" statistics, like counting the number of people that like oranges, or counting the number of "clicks" in a Geiger counter due to radioactive decay, is that the margin of error for the count is roughly the square-root of the expected ... | Why is 600 out of 1000 more convincing than 6 out of 10?
A rule of thumb for "counting" statistics, like counting the number of people that like oranges, or counting the number of "clicks" in a Geiger counter due to radioactive decay, is that the margin of |
6,340 | Why is 600 out of 1000 more convincing than 6 out of 10? | I don't have the name you're looking for, but the issue isn't statistical. Psychologically, the way humans process numbers in our brains give greater weight (authority) to larger numbers than it does to smaller numbers because the magnitude (physical size) is visually as important as the representative value. Thus, 6... | Why is 600 out of 1000 more convincing than 6 out of 10? | I don't have the name you're looking for, but the issue isn't statistical. Psychologically, the way humans process numbers in our brains give greater weight (authority) to larger numbers than it does | Why is 600 out of 1000 more convincing than 6 out of 10?
I don't have the name you're looking for, but the issue isn't statistical. Psychologically, the way humans process numbers in our brains give greater weight (authority) to larger numbers than it does to smaller numbers because the magnitude (physical size) is vi... | Why is 600 out of 1000 more convincing than 6 out of 10?
I don't have the name you're looking for, but the issue isn't statistical. Psychologically, the way humans process numbers in our brains give greater weight (authority) to larger numbers than it does |
6,341 | Why is 600 out of 1000 more convincing than 6 out of 10? | While the actual margin of error is important, the reason it sounds more convincing is because of a more heuristic (rule of thumb) experience with people. The actual margin of error confirms this heuristic has merit.
If the sample is 6 for, and 4 against, this could be 50/50 if a single person changes their vote, or a ... | Why is 600 out of 1000 more convincing than 6 out of 10? | While the actual margin of error is important, the reason it sounds more convincing is because of a more heuristic (rule of thumb) experience with people. The actual margin of error confirms this heur | Why is 600 out of 1000 more convincing than 6 out of 10?
While the actual margin of error is important, the reason it sounds more convincing is because of a more heuristic (rule of thumb) experience with people. The actual margin of error confirms this heuristic has merit.
If the sample is 6 for, and 4 against, this co... | Why is 600 out of 1000 more convincing than 6 out of 10?
While the actual margin of error is important, the reason it sounds more convincing is because of a more heuristic (rule of thumb) experience with people. The actual margin of error confirms this heur |
6,342 | Why is 600 out of 1000 more convincing than 6 out of 10? | The short answer:
Basically it's more convincing to have 600 out of 1000 than six out of 10 because, given equal preferences it's far more likely for 6 out of 10 to occur by random chance.
Let's make an assumption - that the proportion who preferred oranges and apples are actually equal (so, 50% each). Call this a null... | Why is 600 out of 1000 more convincing than 6 out of 10? | The short answer:
Basically it's more convincing to have 600 out of 1000 than six out of 10 because, given equal preferences it's far more likely for 6 out of 10 to occur by random chance.
Let's make | Why is 600 out of 1000 more convincing than 6 out of 10?
The short answer:
Basically it's more convincing to have 600 out of 1000 than six out of 10 because, given equal preferences it's far more likely for 6 out of 10 to occur by random chance.
Let's make an assumption - that the proportion who preferred oranges and a... | Why is 600 out of 1000 more convincing than 6 out of 10?
The short answer:
Basically it's more convincing to have 600 out of 1000 than six out of 10 because, given equal preferences it's far more likely for 6 out of 10 to occur by random chance.
Let's make |
6,343 | Why is 600 out of 1000 more convincing than 6 out of 10? | Something that has not been mentioned is to look at the problem from a Bayesian point of view.
In a Bayesian setting, a natural approach to this problem would be to use a Beta-Binomial distribution.
You can assume that the probability of someone preferring oranges over apples is $p$, which Beta distributed, and that t... | Why is 600 out of 1000 more convincing than 6 out of 10? | Something that has not been mentioned is to look at the problem from a Bayesian point of view.
In a Bayesian setting, a natural approach to this problem would be to use a Beta-Binomial distribution.
| Why is 600 out of 1000 more convincing than 6 out of 10?
Something that has not been mentioned is to look at the problem from a Bayesian point of view.
In a Bayesian setting, a natural approach to this problem would be to use a Beta-Binomial distribution.
You can assume that the probability of someone preferring orang... | Why is 600 out of 1000 more convincing than 6 out of 10?
Something that has not been mentioned is to look at the problem from a Bayesian point of view.
In a Bayesian setting, a natural approach to this problem would be to use a Beta-Binomial distribution.
|
6,344 | Why is 600 out of 1000 more convincing than 6 out of 10? | This is because higher number ensures greater accuracy. For ex, if u would pick up 1000 random people from anywhere on the planet and 599 of them are male against 10 random people with 6 male, the former would be more accurate. Similarly, if you assume a population of 7 billion and calculate the number of males, you wo... | Why is 600 out of 1000 more convincing than 6 out of 10? | This is because higher number ensures greater accuracy. For ex, if u would pick up 1000 random people from anywhere on the planet and 599 of them are male against 10 random people with 6 male, the for | Why is 600 out of 1000 more convincing than 6 out of 10?
This is because higher number ensures greater accuracy. For ex, if u would pick up 1000 random people from anywhere on the planet and 599 of them are male against 10 random people with 6 male, the former would be more accurate. Similarly, if you assume a populati... | Why is 600 out of 1000 more convincing than 6 out of 10?
This is because higher number ensures greater accuracy. For ex, if u would pick up 1000 random people from anywhere on the planet and 599 of them are male against 10 random people with 6 male, the for |
6,345 | The Monty Hall Problem - where does our intuition fail us? | Consider two simple variations of the problem:
No doors are opened for the contestant. The host offers no help in picking a door. In this case it is obvious that the odds of picking the correct door are 1/3.
Before the contestant is asked to venture a guess, the host opens a door and reveals a goat. After the host re... | The Monty Hall Problem - where does our intuition fail us? | Consider two simple variations of the problem:
No doors are opened for the contestant. The host offers no help in picking a door. In this case it is obvious that the odds of picking the correct door | The Monty Hall Problem - where does our intuition fail us?
Consider two simple variations of the problem:
No doors are opened for the contestant. The host offers no help in picking a door. In this case it is obvious that the odds of picking the correct door are 1/3.
Before the contestant is asked to venture a guess, ... | The Monty Hall Problem - where does our intuition fail us?
Consider two simple variations of the problem:
No doors are opened for the contestant. The host offers no help in picking a door. In this case it is obvious that the odds of picking the correct door |
6,346 | The Monty Hall Problem - where does our intuition fail us? | To answer the original question: Our intuition fails because of the narrative. By relating the story in the same order as the tv script, we get confused. It gets much easier if we think about what is going to happen in advance. The quiz-master will reveal a goat, so our best chance is to select a door with a goat an... | The Monty Hall Problem - where does our intuition fail us? | To answer the original question: Our intuition fails because of the narrative. By relating the story in the same order as the tv script, we get confused. It gets much easier if we think about what i | The Monty Hall Problem - where does our intuition fail us?
To answer the original question: Our intuition fails because of the narrative. By relating the story in the same order as the tv script, we get confused. It gets much easier if we think about what is going to happen in advance. The quiz-master will reveal a ... | The Monty Hall Problem - where does our intuition fail us?
To answer the original question: Our intuition fails because of the narrative. By relating the story in the same order as the tv script, we get confused. It gets much easier if we think about what i |
6,347 | The Monty Hall Problem - where does our intuition fail us? | I find that people find the solution more intuitive if you change it to 100 doors, close first, second, to 98 doors. Similarly for 50 doors, etc. | The Monty Hall Problem - where does our intuition fail us? | I find that people find the solution more intuitive if you change it to 100 doors, close first, second, to 98 doors. Similarly for 50 doors, etc. | The Monty Hall Problem - where does our intuition fail us?
I find that people find the solution more intuitive if you change it to 100 doors, close first, second, to 98 doors. Similarly for 50 doors, etc. | The Monty Hall Problem - where does our intuition fail us?
I find that people find the solution more intuitive if you change it to 100 doors, close first, second, to 98 doors. Similarly for 50 doors, etc. |
6,348 | The Monty Hall Problem - where does our intuition fail us? | The answer is not, "of course YES!" The correct answer is, "I don't know, can you be more specific?"
The only reason why you think it is correct, is because Marliyn vos Savant said so. Her original answer to the question (although the question was widely know before her) appeared in Parade magazine on September 9, 1990... | The Monty Hall Problem - where does our intuition fail us? | The answer is not, "of course YES!" The correct answer is, "I don't know, can you be more specific?"
The only reason why you think it is correct, is because Marliyn vos Savant said so. Her original an | The Monty Hall Problem - where does our intuition fail us?
The answer is not, "of course YES!" The correct answer is, "I don't know, can you be more specific?"
The only reason why you think it is correct, is because Marliyn vos Savant said so. Her original answer to the question (although the question was widely know b... | The Monty Hall Problem - where does our intuition fail us?
The answer is not, "of course YES!" The correct answer is, "I don't know, can you be more specific?"
The only reason why you think it is correct, is because Marliyn vos Savant said so. Her original an |
6,349 | The Monty Hall Problem - where does our intuition fail us? | I'd modify what Graham Cookson said slightly. I think the really crucial thing that people overlook is not their first choice, but the host's choice, and the assumption that the host made sure not to reveal the car.
In fact, when I discuss this problem in a class, I present it in part as a case study in being clear ... | The Monty Hall Problem - where does our intuition fail us? | I'd modify what Graham Cookson said slightly. I think the really crucial thing that people overlook is not their first choice, but the host's choice, and the assumption that the host made sure not to | The Monty Hall Problem - where does our intuition fail us?
I'd modify what Graham Cookson said slightly. I think the really crucial thing that people overlook is not their first choice, but the host's choice, and the assumption that the host made sure not to reveal the car.
In fact, when I discuss this problem in a ... | The Monty Hall Problem - where does our intuition fail us?
I'd modify what Graham Cookson said slightly. I think the really crucial thing that people overlook is not their first choice, but the host's choice, and the assumption that the host made sure not to |
6,350 | The Monty Hall Problem - where does our intuition fail us? | I agree that students find this problem very difficult. The typical response I get is that after you've been shown a goat there's a 50:50 chance of getting the car so why does it matter? Students seem to divorce their first choice from the decision they're now being asked to make i.e. they view these two actions as ind... | The Monty Hall Problem - where does our intuition fail us? | I agree that students find this problem very difficult. The typical response I get is that after you've been shown a goat there's a 50:50 chance of getting the car so why does it matter? Students seem | The Monty Hall Problem - where does our intuition fail us?
I agree that students find this problem very difficult. The typical response I get is that after you've been shown a goat there's a 50:50 chance of getting the car so why does it matter? Students seem to divorce their first choice from the decision they're now ... | The Monty Hall Problem - where does our intuition fail us?
I agree that students find this problem very difficult. The typical response I get is that after you've been shown a goat there's a 50:50 chance of getting the car so why does it matter? Students seem |
6,351 | The Monty Hall Problem - where does our intuition fail us? | I believe that it's more a question of logic than a difficulty with probability that makes the Monty Hall solution surprising. Consider the following description of the problem.
You decide at home, before going to the TV show, if you are going to switch doors or stick with your first choice, whatever happens during the... | The Monty Hall Problem - where does our intuition fail us? | I believe that it's more a question of logic than a difficulty with probability that makes the Monty Hall solution surprising. Consider the following description of the problem.
You decide at home, be | The Monty Hall Problem - where does our intuition fail us?
I believe that it's more a question of logic than a difficulty with probability that makes the Monty Hall solution surprising. Consider the following description of the problem.
You decide at home, before going to the TV show, if you are going to switch doors o... | The Monty Hall Problem - where does our intuition fail us?
I believe that it's more a question of logic than a difficulty with probability that makes the Monty Hall solution surprising. Consider the following description of the problem.
You decide at home, be |
6,352 | The Monty Hall Problem - where does our intuition fail us? | One does not need to know about conditional probability or Bayes Theorem to figure out that it is best to switch your answer.
Suppose you initially pick Door 1. Then the probability of Door 1 being a winner is 1/3 and the probability of Doors 2 or 3 being a winner is 2/3. If Door 2 is shown to be a loser by the hos... | The Monty Hall Problem - where does our intuition fail us? | One does not need to know about conditional probability or Bayes Theorem to figure out that it is best to switch your answer.
Suppose you initially pick Door 1. Then the probability of Door 1 being | The Monty Hall Problem - where does our intuition fail us?
One does not need to know about conditional probability or Bayes Theorem to figure out that it is best to switch your answer.
Suppose you initially pick Door 1. Then the probability of Door 1 being a winner is 1/3 and the probability of Doors 2 or 3 being a w... | The Monty Hall Problem - where does our intuition fail us?
One does not need to know about conditional probability or Bayes Theorem to figure out that it is best to switch your answer.
Suppose you initially pick Door 1. Then the probability of Door 1 being |
6,353 | The Monty Hall Problem - where does our intuition fail us? | The lesson? Reformulate the question, and search for a strategy instead of looking at the situation. Turn the thing on its head, work backwards...
People are generally bad at working with chance. Animals typically fare better, once they discover that either A or B gives a higher payout on average; they stick to the ... | The Monty Hall Problem - where does our intuition fail us? | The lesson? Reformulate the question, and search for a strategy instead of looking at the situation. Turn the thing on its head, work backwards...
People are generally bad at working with chance. A | The Monty Hall Problem - where does our intuition fail us?
The lesson? Reformulate the question, and search for a strategy instead of looking at the situation. Turn the thing on its head, work backwards...
People are generally bad at working with chance. Animals typically fare better, once they discover that either ... | The Monty Hall Problem - where does our intuition fail us?
The lesson? Reformulate the question, and search for a strategy instead of looking at the situation. Turn the thing on its head, work backwards...
People are generally bad at working with chance. A |
6,354 | The Monty Hall Problem - where does our intuition fail us? | I think there are several things going on.
For one, the setup implies more information then the solution takes into account. That it is a game show, and the host is asking us if we want to switch.
If you assume the host does not want the show to spend extra money (which is reasonable), then you would assume he would tr... | The Monty Hall Problem - where does our intuition fail us? | I think there are several things going on.
For one, the setup implies more information then the solution takes into account. That it is a game show, and the host is asking us if we want to switch.
If | The Monty Hall Problem - where does our intuition fail us?
I think there are several things going on.
For one, the setup implies more information then the solution takes into account. That it is a game show, and the host is asking us if we want to switch.
If you assume the host does not want the show to spend extra mon... | The Monty Hall Problem - where does our intuition fail us?
I think there are several things going on.
For one, the setup implies more information then the solution takes into account. That it is a game show, and the host is asking us if we want to switch.
If |
6,355 | The Monty Hall Problem - where does our intuition fail us? | I'll quote this great article on lesswrong:
The possible hypotheses are Car in Door 1, Car in Door 2, and Car in
Door 3; before the game starts, there is no reason to believe any of
the three doors is more likely than the others to contain the car, and
so each of these hypotheses has prior probability 1/3.
The g... | The Monty Hall Problem - where does our intuition fail us? | I'll quote this great article on lesswrong:
The possible hypotheses are Car in Door 1, Car in Door 2, and Car in
Door 3; before the game starts, there is no reason to believe any of
the three doo | The Monty Hall Problem - where does our intuition fail us?
I'll quote this great article on lesswrong:
The possible hypotheses are Car in Door 1, Car in Door 2, and Car in
Door 3; before the game starts, there is no reason to believe any of
the three doors is more likely than the others to contain the car, and
s... | The Monty Hall Problem - where does our intuition fail us?
I'll quote this great article on lesswrong:
The possible hypotheses are Car in Door 1, Car in Door 2, and Car in
Door 3; before the game starts, there is no reason to believe any of
the three doo |
6,356 | The Monty Hall Problem - where does our intuition fail us? | In my experience, it is the fact that people do not automatically leap from words to math. Normally, when I first present it, people get it wrong. However, I then bring out a deck of 52 cards and have them choose one. I then reveal fifty cards and ask them if they want to switch. Most people then get it. They intu... | The Monty Hall Problem - where does our intuition fail us? | In my experience, it is the fact that people do not automatically leap from words to math. Normally, when I first present it, people get it wrong. However, I then bring out a deck of 52 cards and ha | The Monty Hall Problem - where does our intuition fail us?
In my experience, it is the fact that people do not automatically leap from words to math. Normally, when I first present it, people get it wrong. However, I then bring out a deck of 52 cards and have them choose one. I then reveal fifty cards and ask them i... | The Monty Hall Problem - where does our intuition fail us?
In my experience, it is the fact that people do not automatically leap from words to math. Normally, when I first present it, people get it wrong. However, I then bring out a deck of 52 cards and ha |
6,357 | The Monty Hall Problem - where does our intuition fail us? | Haha! Funny coincidence, I was just reading the Curious incident of the Dog in the Nighttime to have stopped at the chapter where the speaker was explaining what the Monty Hall problem was. Here's a nice image about the scenario case.
The intuitive mathematical way how I came to understand the problem: to win after swi... | The Monty Hall Problem - where does our intuition fail us? | Haha! Funny coincidence, I was just reading the Curious incident of the Dog in the Nighttime to have stopped at the chapter where the speaker was explaining what the Monty Hall problem was. Here's a n | The Monty Hall Problem - where does our intuition fail us?
Haha! Funny coincidence, I was just reading the Curious incident of the Dog in the Nighttime to have stopped at the chapter where the speaker was explaining what the Monty Hall problem was. Here's a nice image about the scenario case.
The intuitive mathematical... | The Monty Hall Problem - where does our intuition fail us?
Haha! Funny coincidence, I was just reading the Curious incident of the Dog in the Nighttime to have stopped at the chapter where the speaker was explaining what the Monty Hall problem was. Here's a n |
6,358 | The Monty Hall Problem - where does our intuition fail us? | What misunderstanding do most people have about probability that leads to us scratching our heads?
It is not the misunderstanding, it is the reluctance (or inability) to calculate probabilities.
What general rule can we take away from this puzzle to better train our intuition in the future?
Such puzzles are puzzles ... | The Monty Hall Problem - where does our intuition fail us? | What misunderstanding do most people have about probability that leads to us scratching our heads?
It is not the misunderstanding, it is the reluctance (or inability) to calculate probabilities.
Wha | The Monty Hall Problem - where does our intuition fail us?
What misunderstanding do most people have about probability that leads to us scratching our heads?
It is not the misunderstanding, it is the reluctance (or inability) to calculate probabilities.
What general rule can we take away from this puzzle to better tr... | The Monty Hall Problem - where does our intuition fail us?
What misunderstanding do most people have about probability that leads to us scratching our heads?
It is not the misunderstanding, it is the reluctance (or inability) to calculate probabilities.
Wha |
6,359 | The Monty Hall Problem - where does our intuition fail us? | We can understand this problem in a very easy way (indeed, it becomes trivial!) if, instead of 3 doors, we consider 1000 doors. Thus, you choose one door, and out of the remaining 999 doors, the host opens 998 of them. After that, you should change your door, obviously. The host didn't choose that very specific door ou... | The Monty Hall Problem - where does our intuition fail us? | We can understand this problem in a very easy way (indeed, it becomes trivial!) if, instead of 3 doors, we consider 1000 doors. Thus, you choose one door, and out of the remaining 999 doors, the host | The Monty Hall Problem - where does our intuition fail us?
We can understand this problem in a very easy way (indeed, it becomes trivial!) if, instead of 3 doors, we consider 1000 doors. Thus, you choose one door, and out of the remaining 999 doors, the host opens 998 of them. After that, you should change your door, o... | The Monty Hall Problem - where does our intuition fail us?
We can understand this problem in a very easy way (indeed, it becomes trivial!) if, instead of 3 doors, we consider 1000 doors. Thus, you choose one door, and out of the remaining 999 doors, the host |
6,360 | For plotting with R, should I learn ggplot2 or ggvis? | Start with ggplot2. It creates static plots.
Apart from static plots, ggvis can be used for creating interactive plots as well. Once you have learned the syntax of ggplot2, then the syntax for adding interactivity to create ggivs plots will follow naturally. | For plotting with R, should I learn ggplot2 or ggvis? | Start with ggplot2. It creates static plots.
Apart from static plots, ggvis can be used for creating interactive plots as well. Once you have learned the syntax of ggplot2, then the syntax for adding | For plotting with R, should I learn ggplot2 or ggvis?
Start with ggplot2. It creates static plots.
Apart from static plots, ggvis can be used for creating interactive plots as well. Once you have learned the syntax of ggplot2, then the syntax for adding interactivity to create ggivs plots will follow naturally. | For plotting with R, should I learn ggplot2 or ggvis?
Start with ggplot2. It creates static plots.
Apart from static plots, ggvis can be used for creating interactive plots as well. Once you have learned the syntax of ggplot2, then the syntax for adding |
6,361 | For plotting with R, should I learn ggplot2 or ggvis? | I want to expand a bit on Dianne Cook's answer. As she said, ggplot2 is for creating static plots, ggvis is for interactive plots. There are a bunch of implications to that:
File Type ggvis output is HTML including CSS and javascript files. ggvis does not naturally output ordinary image files. ggplot2 outputs ordi... | For plotting with R, should I learn ggplot2 or ggvis? | I want to expand a bit on Dianne Cook's answer. As she said, ggplot2 is for creating static plots, ggvis is for interactive plots. There are a bunch of implications to that:
File Type ggvis output | For plotting with R, should I learn ggplot2 or ggvis?
I want to expand a bit on Dianne Cook's answer. As she said, ggplot2 is for creating static plots, ggvis is for interactive plots. There are a bunch of implications to that:
File Type ggvis output is HTML including CSS and javascript files. ggvis does not natura... | For plotting with R, should I learn ggplot2 or ggvis?
I want to expand a bit on Dianne Cook's answer. As she said, ggplot2 is for creating static plots, ggvis is for interactive plots. There are a bunch of implications to that:
File Type ggvis output |
6,362 | For plotting with R, should I learn ggplot2 or ggvis? | I think the message appearing after library(ggvis) is self explanatory:
The ggvis API is currently rapidly evolving. We strongly recommend
that you do not rely on this for production, but feel free to explore.
If you encounter a clear bug, please file a minimal reproducible
example at https://github.com/rstudio/... | For plotting with R, should I learn ggplot2 or ggvis? | I think the message appearing after library(ggvis) is self explanatory:
The ggvis API is currently rapidly evolving. We strongly recommend
that you do not rely on this for production, but feel free | For plotting with R, should I learn ggplot2 or ggvis?
I think the message appearing after library(ggvis) is self explanatory:
The ggvis API is currently rapidly evolving. We strongly recommend
that you do not rely on this for production, but feel free to explore.
If you encounter a clear bug, please file a minimal... | For plotting with R, should I learn ggplot2 or ggvis?
I think the message appearing after library(ggvis) is self explanatory:
The ggvis API is currently rapidly evolving. We strongly recommend
that you do not rely on this for production, but feel free |
6,363 | For plotting with R, should I learn ggplot2 or ggvis? | The R community keeps coming up with new (and often overlapping) packages for a variety of reasons:
1) Someone wants to change something or add something that isn't available in an existing package, but much of it overlaps (hence, many packages that do regression)
2) Someone writes a package as an assignment
3) Writing... | For plotting with R, should I learn ggplot2 or ggvis? | The R community keeps coming up with new (and often overlapping) packages for a variety of reasons:
1) Someone wants to change something or add something that isn't available in an existing package, b | For plotting with R, should I learn ggplot2 or ggvis?
The R community keeps coming up with new (and often overlapping) packages for a variety of reasons:
1) Someone wants to change something or add something that isn't available in an existing package, but much of it overlaps (hence, many packages that do regression)
2... | For plotting with R, should I learn ggplot2 or ggvis?
The R community keeps coming up with new (and often overlapping) packages for a variety of reasons:
1) Someone wants to change something or add something that isn't available in an existing package, b |
6,364 | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution? | What the paradox is
There is a mixture of wine and water. Let $x$ be the amount of wine divided by the amount of water. Suppose we know that $x$ is between $1/3$ and $3$ but nothing else about $x$. We want the probability that $x \le 2$.
Without a sample space or probability model, we have no way to calculate probabili... | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution? | What the paradox is
There is a mixture of wine and water. Let $x$ be the amount of wine divided by the amount of water. Suppose we know that $x$ is between $1/3$ and $3$ but nothing else about $x$. We | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution?
What the paradox is
There is a mixture of wine and water. Let $x$ be the amount of wine divided by the amount of water. Suppose we know that $x$ is between $1/3$ and $3$ but nothing else about $x$. We want the probability that $x \le 2$.... | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution?
What the paradox is
There is a mixture of wine and water. Let $x$ be the amount of wine divided by the amount of water. Suppose we know that $x$ is between $1/3$ and $3$ but nothing else about $x$. We |
6,365 | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution? | In the context of modern understandings of Bayesian analysis, it is really quite generous to still call this a "paradox". It is nothing more than a demonstration that uniform distributions are not invariant to nonlinear reparameterisations of their referents, such that you have to be careful when forming a "non-inform... | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution? | In the context of modern understandings of Bayesian analysis, it is really quite generous to still call this a "paradox". It is nothing more than a demonstration that uniform distributions are not in | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution?
In the context of modern understandings of Bayesian analysis, it is really quite generous to still call this a "paradox". It is nothing more than a demonstration that uniform distributions are not invariant to nonlinear reparameterisati... | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution?
In the context of modern understandings of Bayesian analysis, it is really quite generous to still call this a "paradox". It is nothing more than a demonstration that uniform distributions are not in |
6,366 | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution? | I believe it to be an apparent paradox and highly instructive of a common and dangerous issue in all branches of statistics, how to handle ratios. Being conscious of a possible paradox will make you cautious as a researcher. I will give you a reason to believe that it is not a paradox.
The problem has no solution, of... | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution? | I believe it to be an apparent paradox and highly instructive of a common and dangerous issue in all branches of statistics, how to handle ratios. Being conscious of a possible paradox will make you | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution?
I believe it to be an apparent paradox and highly instructive of a common and dangerous issue in all branches of statistics, how to handle ratios. Being conscious of a possible paradox will make you cautious as a researcher. I will giv... | What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution?
I believe it to be an apparent paradox and highly instructive of a common and dangerous issue in all branches of statistics, how to handle ratios. Being conscious of a possible paradox will make you |
6,367 | How to take derivative of multivariate normal density? | In chapter 2 of the Matrix Cookbook there is a nice review of matrix calculus stuff that gives a lot of useful identities that help with problems one would encounter doing probability and statistics, including rules to help differentiate the multivariate Gaussian likelihood.
If you have a random vector ${\boldsymbol y... | How to take derivative of multivariate normal density? | In chapter 2 of the Matrix Cookbook there is a nice review of matrix calculus stuff that gives a lot of useful identities that help with problems one would encounter doing probability and statistics, | How to take derivative of multivariate normal density?
In chapter 2 of the Matrix Cookbook there is a nice review of matrix calculus stuff that gives a lot of useful identities that help with problems one would encounter doing probability and statistics, including rules to help differentiate the multivariate Gaussian l... | How to take derivative of multivariate normal density?
In chapter 2 of the Matrix Cookbook there is a nice review of matrix calculus stuff that gives a lot of useful identities that help with problems one would encounter doing probability and statistics, |
6,368 | How to take derivative of multivariate normal density? | Expression for log of normal density
We consider the log of the normal density
\begin{align}
\log p(y|\mu,\Sigma)=-\frac{D}{2}\log{|2\pi|}-\frac{1}{2}\log{|\Sigma|}-\frac{1}{2}(y-\mu)^\top\Sigma^{-1}(y-\mu)\quad\quad(1)
\end{align}
where $D$ denotes the dimension of $y$ and $\mu$.
Derivative w.r.t. mean
We have
\b... | How to take derivative of multivariate normal density? | Expression for log of normal density
We consider the log of the normal density
\begin{align}
\log p(y|\mu,\Sigma)=-\frac{D}{2}\log{|2\pi|}-\frac{1}{2}\log{|\Sigma|}-\frac{1}{2}(y-\mu)^\top\Sigma^ | How to take derivative of multivariate normal density?
Expression for log of normal density
We consider the log of the normal density
\begin{align}
\log p(y|\mu,\Sigma)=-\frac{D}{2}\log{|2\pi|}-\frac{1}{2}\log{|\Sigma|}-\frac{1}{2}(y-\mu)^\top\Sigma^{-1}(y-\mu)\quad\quad(1)
\end{align}
where $D$ denotes the dimens... | How to take derivative of multivariate normal density?
Expression for log of normal density
We consider the log of the normal density
\begin{align}
\log p(y|\mu,\Sigma)=-\frac{D}{2}\log{|2\pi|}-\frac{1}{2}\log{|\Sigma|}-\frac{1}{2}(y-\mu)^\top\Sigma^ |
6,369 | How to take derivative of multivariate normal density? | I tried to computationally verify @Macro's answer but found what appears to be a minor error in the covariance solution. He obtained
$$
\begin{align}
\frac{ \partial {\bf L} }{ \partial {\boldsymbol \Sigma}}
&= -\frac{1}{2} \left( {\boldsymbol \Sigma}^{-1} -
{\boldsymbol \Sigma}^{-1}
\left( {\boldsymbol y} - {\boldsy... | How to take derivative of multivariate normal density? | I tried to computationally verify @Macro's answer but found what appears to be a minor error in the covariance solution. He obtained
$$
\begin{align}
\frac{ \partial {\bf L} }{ \partial {\boldsymbol \ | How to take derivative of multivariate normal density?
I tried to computationally verify @Macro's answer but found what appears to be a minor error in the covariance solution. He obtained
$$
\begin{align}
\frac{ \partial {\bf L} }{ \partial {\boldsymbol \Sigma}}
&= -\frac{1}{2} \left( {\boldsymbol \Sigma}^{-1} -
{\bol... | How to take derivative of multivariate normal density?
I tried to computationally verify @Macro's answer but found what appears to be a minor error in the covariance solution. He obtained
$$
\begin{align}
\frac{ \partial {\bf L} }{ \partial {\boldsymbol \ |
6,370 | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate] | Both are done.
Least squares is easier, and the fact that for independent random variables "variances add" means that it's considerably more convenient; for examples, the ability to partition variances is particularly handy for comparing nested models. It's somewhat more efficient at the normal (least squares is maximu... | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate] | Both are done.
Least squares is easier, and the fact that for independent random variables "variances add" means that it's considerably more convenient; for examples, the ability to partition variance | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate]
Both are done.
Least squares is easier, and the fact that for independent random variables "variances add" means that it's considerably more convenient; for examples, the ability to partition variances is particularly handy for comparing... | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate]
Both are done.
Least squares is easier, and the fact that for independent random variables "variances add" means that it's considerably more convenient; for examples, the ability to partition variance |
6,371 | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate] | I can't help quoting from Huber, Robust Statistics, p.10 on this (sorry the quote is too long to fit in a comment):
Two time-honored measures of scatter are the mean absolute deviation
$$d_n=\frac{1}{n}\sum|x_i-\bar{x}|$$
and the mean square deviation
$$s_n=\left[\frac{1}{n}\sum(x_i-\bar{x})^2\right]^{1/2}$$
There was... | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate] | I can't help quoting from Huber, Robust Statistics, p.10 on this (sorry the quote is too long to fit in a comment):
Two time-honored measures of scatter are the mean absolute deviation
$$d_n=\frac{1} | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate]
I can't help quoting from Huber, Robust Statistics, p.10 on this (sorry the quote is too long to fit in a comment):
Two time-honored measures of scatter are the mean absolute deviation
$$d_n=\frac{1}{n}\sum|x_i-\bar{x}|$$
and the mean s... | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate]
I can't help quoting from Huber, Robust Statistics, p.10 on this (sorry the quote is too long to fit in a comment):
Two time-honored measures of scatter are the mean absolute deviation
$$d_n=\frac{1} |
6,372 | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate] | One thing that has not been mentioned yet is uniqueness. The least squares approach always produces a single "best" answer if the matrix of explanatory variables is full rank. When minimizing the sum of the absolute value of the residuals it is possible that there may be an infinite number of lines that all have the ... | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate] | One thing that has not been mentioned yet is uniqueness. The least squares approach always produces a single "best" answer if the matrix of explanatory variables is full rank. When minimizing the su | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate]
One thing that has not been mentioned yet is uniqueness. The least squares approach always produces a single "best" answer if the matrix of explanatory variables is full rank. When minimizing the sum of the absolute value of the residu... | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate]
One thing that has not been mentioned yet is uniqueness. The least squares approach always produces a single "best" answer if the matrix of explanatory variables is full rank. When minimizing the su |
6,373 | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate] | When the problem is expressed stochastically: $Y=aX+b+\epsilon$, where $\epsilon$ is normally distributed, the maximum likelihood estimate is the OLS estimate - not the minimum absolute deviation (MAD) estimate. So that's nice.
Furthermore, there is a strong link between OLS estimation and linear algebra. $\hat{Y}$ is ... | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate] | When the problem is expressed stochastically: $Y=aX+b+\epsilon$, where $\epsilon$ is normally distributed, the maximum likelihood estimate is the OLS estimate - not the minimum absolute deviation (MAD | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate]
When the problem is expressed stochastically: $Y=aX+b+\epsilon$, where $\epsilon$ is normally distributed, the maximum likelihood estimate is the OLS estimate - not the minimum absolute deviation (MAD) estimate. So that's nice.
Furthermo... | Why squared residuals instead of absolute residuals in OLS estimation? [duplicate]
When the problem is expressed stochastically: $Y=aX+b+\epsilon$, where $\epsilon$ is normally distributed, the maximum likelihood estimate is the OLS estimate - not the minimum absolute deviation (MAD |
6,374 | Interpretation of plot (glm.model) | R does not have a distinct plot.glm() method. When you fit a model with glm() and run plot(), it calls ?plot.lm, which is appropriate for linear models (i.e., with a normally distributed error term).
In general, the meaning of these plots (at least for linear models) can be learned in various existing threads on CV ... | Interpretation of plot (glm.model) | R does not have a distinct plot.glm() method. When you fit a model with glm() and run plot(), it calls ?plot.lm, which is appropriate for linear models (i.e., with a normally distributed error term). | Interpretation of plot (glm.model)
R does not have a distinct plot.glm() method. When you fit a model with glm() and run plot(), it calls ?plot.lm, which is appropriate for linear models (i.e., with a normally distributed error term).
In general, the meaning of these plots (at least for linear models) can be learned... | Interpretation of plot (glm.model)
R does not have a distinct plot.glm() method. When you fit a model with glm() and run plot(), it calls ?plot.lm, which is appropriate for linear models (i.e., with a normally distributed error term). |
6,375 | Interpretation of plot (glm.model) | Residuals vs fitted - there should be no strong patterns (mild patterns are not a problem, see @gung's answer) and no outliers, residuals should be randomly distributed around zero.
Normal Q-Q - residuals should go around the diagonal line, i.e. should be normally distributed (see wiki for Q-Q plot). This plot helps ch... | Interpretation of plot (glm.model) | Residuals vs fitted - there should be no strong patterns (mild patterns are not a problem, see @gung's answer) and no outliers, residuals should be randomly distributed around zero.
Normal Q-Q - resid | Interpretation of plot (glm.model)
Residuals vs fitted - there should be no strong patterns (mild patterns are not a problem, see @gung's answer) and no outliers, residuals should be randomly distributed around zero.
Normal Q-Q - residuals should go around the diagonal line, i.e. should be normally distributed (see wik... | Interpretation of plot (glm.model)
Residuals vs fitted - there should be no strong patterns (mild patterns are not a problem, see @gung's answer) and no outliers, residuals should be randomly distributed around zero.
Normal Q-Q - resid |
6,376 | Are there any good popular science book about statistics or machine learning? | I suspect The Lady Tasting Tea, by David Salsberg is exactly what you want. It's very much written in a narrative style, almost like a novel, with essentially no math (as I recall), so it would be accessible to anyone. I read it long ago and really enjoyed it. It reads very fast, and could give people a sense of wha... | Are there any good popular science book about statistics or machine learning? | I suspect The Lady Tasting Tea, by David Salsberg is exactly what you want. It's very much written in a narrative style, almost like a novel, with essentially no math (as I recall), so it would be ac | Are there any good popular science book about statistics or machine learning?
I suspect The Lady Tasting Tea, by David Salsberg is exactly what you want. It's very much written in a narrative style, almost like a novel, with essentially no math (as I recall), so it would be accessible to anyone. I read it long ago an... | Are there any good popular science book about statistics or machine learning?
I suspect The Lady Tasting Tea, by David Salsberg is exactly what you want. It's very much written in a narrative style, almost like a novel, with essentially no math (as I recall), so it would be ac |
6,377 | Are there any good popular science book about statistics or machine learning? | Nate Silver's new book The Signal and the Noise: Why Most Predictions Fail – But Some Don't fits your description quite well. It is also an introduction into Bayesian thinking for laypeople. It got some attention lately and a review of the book can be found here.
Also worth checking out are Levitt & Dubner's Freakonomi... | Are there any good popular science book about statistics or machine learning? | Nate Silver's new book The Signal and the Noise: Why Most Predictions Fail – But Some Don't fits your description quite well. It is also an introduction into Bayesian thinking for laypeople. It got so | Are there any good popular science book about statistics or machine learning?
Nate Silver's new book The Signal and the Noise: Why Most Predictions Fail – But Some Don't fits your description quite well. It is also an introduction into Bayesian thinking for laypeople. It got some attention lately and a review of the bo... | Are there any good popular science book about statistics or machine learning?
Nate Silver's new book The Signal and the Noise: Why Most Predictions Fail – But Some Don't fits your description quite well. It is also an introduction into Bayesian thinking for laypeople. It got so |
6,378 | Are there any good popular science book about statistics or machine learning? | More good reads:
The Flaw of Averages by Sam L. Savage
Fooled By Randomness by Nassim Taleb
Both are somewhat cautionary books about being careful towards how to interpret probability and statistics in our everyday lives. For example, in financial markets, one might misuse an everyday gaussian distribution as a risk me... | Are there any good popular science book about statistics or machine learning? | More good reads:
The Flaw of Averages by Sam L. Savage
Fooled By Randomness by Nassim Taleb
Both are somewhat cautionary books about being careful towards how to interpret probability and statistics i | Are there any good popular science book about statistics or machine learning?
More good reads:
The Flaw of Averages by Sam L. Savage
Fooled By Randomness by Nassim Taleb
Both are somewhat cautionary books about being careful towards how to interpret probability and statistics in our everyday lives. For example, in fina... | Are there any good popular science book about statistics or machine learning?
More good reads:
The Flaw of Averages by Sam L. Savage
Fooled By Randomness by Nassim Taleb
Both are somewhat cautionary books about being careful towards how to interpret probability and statistics i |
6,379 | Are there any good popular science book about statistics or machine learning? | "The Theory That Would Not Die" by Sharon Bertsch McGrayne is a very readable book on the history of Bayesian statistics and the general idea behind it without getting too bogged down in the math.
I am also a fan of "The Cartoon Guide to Statistics" by Gonnick and Smith as a nice introduction to the general concept of ... | Are there any good popular science book about statistics or machine learning? | "The Theory That Would Not Die" by Sharon Bertsch McGrayne is a very readable book on the history of Bayesian statistics and the general idea behind it without getting too bogged down in the math.
I a | Are there any good popular science book about statistics or machine learning?
"The Theory That Would Not Die" by Sharon Bertsch McGrayne is a very readable book on the history of Bayesian statistics and the general idea behind it without getting too bogged down in the math.
I am also a fan of "The Cartoon Guide to Stat... | Are there any good popular science book about statistics or machine learning?
"The Theory That Would Not Die" by Sharon Bertsch McGrayne is a very readable book on the history of Bayesian statistics and the general idea behind it without getting too bogged down in the math.
I a |
6,380 | Are there any good popular science book about statistics or machine learning? | I would suggest the following books, though neither is ideal, you should check out:
The (Mis)Behaviour of Markets by (the great) B. Mandelbrot
Struck By Lightning by Jefferey Rosenthal
with the former more focused on finance, but still statsy, and the latter is a introduction to all the interesting probability subjec... | Are there any good popular science book about statistics or machine learning? | I would suggest the following books, though neither is ideal, you should check out:
The (Mis)Behaviour of Markets by (the great) B. Mandelbrot
Struck By Lightning by Jefferey Rosenthal
with the form | Are there any good popular science book about statistics or machine learning?
I would suggest the following books, though neither is ideal, you should check out:
The (Mis)Behaviour of Markets by (the great) B. Mandelbrot
Struck By Lightning by Jefferey Rosenthal
with the former more focused on finance, but still stat... | Are there any good popular science book about statistics or machine learning?
I would suggest the following books, though neither is ideal, you should check out:
The (Mis)Behaviour of Markets by (the great) B. Mandelbrot
Struck By Lightning by Jefferey Rosenthal
with the form |
6,381 | Are there any good popular science book about statistics or machine learning? | A very good book for aiding basic statistical literacy and statistical reasoning - and for making the case for these as important - is The Tiger That Isn't by Andrew Dilnot, the former presenter of a popular radio show about applied statistics for the BBC.
I often recommend it as the statistics equivalent of the popu... | Are there any good popular science book about statistics or machine learning? | A very good book for aiding basic statistical literacy and statistical reasoning - and for making the case for these as important - is The Tiger That Isn't by Andrew Dilnot, the former presenter of | Are there any good popular science book about statistics or machine learning?
A very good book for aiding basic statistical literacy and statistical reasoning - and for making the case for these as important - is The Tiger That Isn't by Andrew Dilnot, the former presenter of a popular radio show about applied statist... | Are there any good popular science book about statistics or machine learning?
A very good book for aiding basic statistical literacy and statistical reasoning - and for making the case for these as important - is The Tiger That Isn't by Andrew Dilnot, the former presenter of |
6,382 | Are there any good popular science book about statistics or machine learning? | Ian Ayres is author of the book "Super Crunchers: Why Thinking-by-Numbers Is the New Way to Be Smart" which discusses several examples of data mining. | Are there any good popular science book about statistics or machine learning? | Ian Ayres is author of the book "Super Crunchers: Why Thinking-by-Numbers Is the New Way to Be Smart" which discusses several examples of data mining. | Are there any good popular science book about statistics or machine learning?
Ian Ayres is author of the book "Super Crunchers: Why Thinking-by-Numbers Is the New Way to Be Smart" which discusses several examples of data mining. | Are there any good popular science book about statistics or machine learning?
Ian Ayres is author of the book "Super Crunchers: Why Thinking-by-Numbers Is the New Way to Be Smart" which discusses several examples of data mining. |
6,383 | Are there any good popular science book about statistics or machine learning? | The Drunkard's Walk by Leonard Mlodinow is an easy to read introduction to basic stats and probability. The content is aimed at an audience with no statistical or mathematical training, and there are no equations. I found it a little too dumbed down. There are lots of anecdotes relating various applications of bad stat... | Are there any good popular science book about statistics or machine learning? | The Drunkard's Walk by Leonard Mlodinow is an easy to read introduction to basic stats and probability. The content is aimed at an audience with no statistical or mathematical training, and there are | Are there any good popular science book about statistics or machine learning?
The Drunkard's Walk by Leonard Mlodinow is an easy to read introduction to basic stats and probability. The content is aimed at an audience with no statistical or mathematical training, and there are no equations. I found it a little too dumb... | Are there any good popular science book about statistics or machine learning?
The Drunkard's Walk by Leonard Mlodinow is an easy to read introduction to basic stats and probability. The content is aimed at an audience with no statistical or mathematical training, and there are |
6,384 | Are there any good popular science book about statistics or machine learning? | I figured I'd fill in a gap here by pointing out a few good mass market-style books on fuzzy sets, information theory, entropy and statistical reasoning that I've read and highly recommend.
• For all things fuzzy, a good informal starting point is McNeill, Dan, 1993, Fuzzy Logic. Simon & Schuster: New York.
• For a go... | Are there any good popular science book about statistics or machine learning? | I figured I'd fill in a gap here by pointing out a few good mass market-style books on fuzzy sets, information theory, entropy and statistical reasoning that I've read and highly recommend.
• For all | Are there any good popular science book about statistics or machine learning?
I figured I'd fill in a gap here by pointing out a few good mass market-style books on fuzzy sets, information theory, entropy and statistical reasoning that I've read and highly recommend.
• For all things fuzzy, a good informal starting po... | Are there any good popular science book about statistics or machine learning?
I figured I'd fill in a gap here by pointing out a few good mass market-style books on fuzzy sets, information theory, entropy and statistical reasoning that I've read and highly recommend.
• For all |
6,385 | Are there any good popular science book about statistics or machine learning? | The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World is a book by Pedro Domingos released in 2015. Domingos wrote the book in order to generate interest from people outside the field.
The book outlines five tribes of machine learning: inductive
reasoning, connectionism, evoluti... | Are there any good popular science book about statistics or machine learning? | The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World is a book by Pedro Domingos released in 2015. Domingos wrote the book in order to generate interest from peo | Are there any good popular science book about statistics or machine learning?
The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World is a book by Pedro Domingos released in 2015. Domingos wrote the book in order to generate interest from people outside the field.
The book outlines ... | Are there any good popular science book about statistics or machine learning?
The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World is a book by Pedro Domingos released in 2015. Domingos wrote the book in order to generate interest from peo |
6,386 | Are there any good popular science book about statistics or machine learning? | Numbers Rule your World, by Kaiser Fung, describes the importance of statistics in a lot of systems that are fundamental to modern society, like insurance markets.
Number Sense, also by Kaiser Fung, talks about "big data" more specifically. | Are there any good popular science book about statistics or machine learning? | Numbers Rule your World, by Kaiser Fung, describes the importance of statistics in a lot of systems that are fundamental to modern society, like insurance markets.
Number Sense, also by Kaiser Fung, t | Are there any good popular science book about statistics or machine learning?
Numbers Rule your World, by Kaiser Fung, describes the importance of statistics in a lot of systems that are fundamental to modern society, like insurance markets.
Number Sense, also by Kaiser Fung, talks about "big data" more specifically. | Are there any good popular science book about statistics or machine learning?
Numbers Rule your World, by Kaiser Fung, describes the importance of statistics in a lot of systems that are fundamental to modern society, like insurance markets.
Number Sense, also by Kaiser Fung, t |
6,387 | Least-angle regression vs. lasso | The "no free lunch" theorems suggest that there are no a-priori distinctions between statistical inference algorithms, i.e. whether LARS or LASSO works best depends on the nature of the particular dataset. In practice then, it is best to try both and use some reliable estimator of generalisation performance to decide ... | Least-angle regression vs. lasso | The "no free lunch" theorems suggest that there are no a-priori distinctions between statistical inference algorithms, i.e. whether LARS or LASSO works best depends on the nature of the particular dat | Least-angle regression vs. lasso
The "no free lunch" theorems suggest that there are no a-priori distinctions between statistical inference algorithms, i.e. whether LARS or LASSO works best depends on the nature of the particular dataset. In practice then, it is best to try both and use some reliable estimator of gene... | Least-angle regression vs. lasso
The "no free lunch" theorems suggest that there are no a-priori distinctions between statistical inference algorithms, i.e. whether LARS or LASSO works best depends on the nature of the particular dat |
6,388 | Least-angle regression vs. lasso | When used in stage-wise mode, the LARS algorithm is a greedy method that does not yield a provably consistent estimator (in other words, it does not converge to a stable result when you increase the number of samples).
Conversely, the LASSO (and thus the LARS algorithm when used in LASSO mode) solves a convex data fit... | Least-angle regression vs. lasso | When used in stage-wise mode, the LARS algorithm is a greedy method that does not yield a provably consistent estimator (in other words, it does not converge to a stable result when you increase the n | Least-angle regression vs. lasso
When used in stage-wise mode, the LARS algorithm is a greedy method that does not yield a provably consistent estimator (in other words, it does not converge to a stable result when you increase the number of samples).
Conversely, the LASSO (and thus the LARS algorithm when used in LAS... | Least-angle regression vs. lasso
When used in stage-wise mode, the LARS algorithm is a greedy method that does not yield a provably consistent estimator (in other words, it does not converge to a stable result when you increase the n |
6,389 | Least-angle regression vs. lasso | As mentioned before, LARS is a particular method to solve the Lasso problem, i.e. the $l_1$-regularized least squares problem. Its success stems from the fact that it requires an asymptotic effort comparable to standard least-squares regression, and thus a highly superior performance than required by the solution of a ... | Least-angle regression vs. lasso | As mentioned before, LARS is a particular method to solve the Lasso problem, i.e. the $l_1$-regularized least squares problem. Its success stems from the fact that it requires an asymptotic effort com | Least-angle regression vs. lasso
As mentioned before, LARS is a particular method to solve the Lasso problem, i.e. the $l_1$-regularized least squares problem. Its success stems from the fact that it requires an asymptotic effort comparable to standard least-squares regression, and thus a highly superior performance th... | Least-angle regression vs. lasso
As mentioned before, LARS is a particular method to solve the Lasso problem, i.e. the $l_1$-regularized least squares problem. Its success stems from the fact that it requires an asymptotic effort com |
6,390 | Least-angle regression vs. lasso | LASSO is not an algorithm per se, but an operator.
There are many different ways to derive efficient algorithms for $\ell_1$ regularized problems. For instance, one can use quadratic programming to them tackle directly. I guess this is what you refer to as LASSO.
Another one is LARS, very popular because of its simpl... | Least-angle regression vs. lasso | LASSO is not an algorithm per se, but an operator.
There are many different ways to derive efficient algorithms for $\ell_1$ regularized problems. For instance, one can use quadratic programming to t | Least-angle regression vs. lasso
LASSO is not an algorithm per se, but an operator.
There are many different ways to derive efficient algorithms for $\ell_1$ regularized problems. For instance, one can use quadratic programming to them tackle directly. I guess this is what you refer to as LASSO.
Another one is LARS, ... | Least-angle regression vs. lasso
LASSO is not an algorithm per se, but an operator.
There are many different ways to derive efficient algorithms for $\ell_1$ regularized problems. For instance, one can use quadratic programming to t |
6,391 | Least-angle regression vs. lasso | The computation of the lasso solutions is a quadratic programming problem, and can be tackled by standard numerical analysis algorithms. But the least angle regression procedure is a better approach. This algorithm exploits the special structure of the lasso problem, and provides an efficient way to compute the solutio... | Least-angle regression vs. lasso | The computation of the lasso solutions is a quadratic programming problem, and can be tackled by standard numerical analysis algorithms. But the least angle regression procedure is a better approach. | Least-angle regression vs. lasso
The computation of the lasso solutions is a quadratic programming problem, and can be tackled by standard numerical analysis algorithms. But the least angle regression procedure is a better approach. This algorithm exploits the special structure of the lasso problem, and provides an eff... | Least-angle regression vs. lasso
The computation of the lasso solutions is a quadratic programming problem, and can be tackled by standard numerical analysis algorithms. But the least angle regression procedure is a better approach. |
6,392 | Least-angle regression vs. lasso | In some contexts a regularized version of the least squares solution may be preferable. The LASSO (least absolute shrinkage and selection operator) algorithm, for example, finds a least-squares solution with the constraint that | β | 1, the L1-norm of the parameter vector, is no greater than a given value. Equivalently... | Least-angle regression vs. lasso | In some contexts a regularized version of the least squares solution may be preferable. The LASSO (least absolute shrinkage and selection operator) algorithm, for example, finds a least-squares soluti | Least-angle regression vs. lasso
In some contexts a regularized version of the least squares solution may be preferable. The LASSO (least absolute shrinkage and selection operator) algorithm, for example, finds a least-squares solution with the constraint that | β | 1, the L1-norm of the parameter vector, is no greater... | Least-angle regression vs. lasso
In some contexts a regularized version of the least squares solution may be preferable. The LASSO (least absolute shrinkage and selection operator) algorithm, for example, finds a least-squares soluti |
6,393 | Are neural networks better than SVMs? | Short answer: On small data sets, SVM might be preferred.
Long answer:
Historically, neural networks are older than SVMs and SVMs were initially developed as a method of efficiently training the neural networks. So, when SVMs matured in 1990s, there was a reason why people switched from neural networks to SVMs. Later, ... | Are neural networks better than SVMs? | Short answer: On small data sets, SVM might be preferred.
Long answer:
Historically, neural networks are older than SVMs and SVMs were initially developed as a method of efficiently training the neura | Are neural networks better than SVMs?
Short answer: On small data sets, SVM might be preferred.
Long answer:
Historically, neural networks are older than SVMs and SVMs were initially developed as a method of efficiently training the neural networks. So, when SVMs matured in 1990s, there was a reason why people switched... | Are neural networks better than SVMs?
Short answer: On small data sets, SVM might be preferred.
Long answer:
Historically, neural networks are older than SVMs and SVMs were initially developed as a method of efficiently training the neura |
6,394 | Are neural networks better than SVMs? | You may have heard of the "no free lunch theorem" in machine learning. For each model, there are pros and cons for specific data and use case.
So. NN is not better than SVM and I can give couple examples easily. One important argument is SVM is convex but NN is generally not. Having a convex problem is desirable becaus... | Are neural networks better than SVMs? | You may have heard of the "no free lunch theorem" in machine learning. For each model, there are pros and cons for specific data and use case.
So. NN is not better than SVM and I can give couple examp | Are neural networks better than SVMs?
You may have heard of the "no free lunch theorem" in machine learning. For each model, there are pros and cons for specific data and use case.
So. NN is not better than SVM and I can give couple examples easily. One important argument is SVM is convex but NN is generally not. Havin... | Are neural networks better than SVMs?
You may have heard of the "no free lunch theorem" in machine learning. For each model, there are pros and cons for specific data and use case.
So. NN is not better than SVM and I can give couple examp |
6,395 | Are neural networks better than SVMs? | SVM is interesting if you have a kernel in mind that you know is appropriate, or a domain-specific kernel that would be difficult to express in a differentiable way (a common example might be a string-similarity space for DNA sequences). But what if you have no idea what kind of kernel you should use? What if your data... | Are neural networks better than SVMs? | SVM is interesting if you have a kernel in mind that you know is appropriate, or a domain-specific kernel that would be difficult to express in a differentiable way (a common example might be a string | Are neural networks better than SVMs?
SVM is interesting if you have a kernel in mind that you know is appropriate, or a domain-specific kernel that would be difficult to express in a differentiable way (a common example might be a string-similarity space for DNA sequences). But what if you have no idea what kind of ke... | Are neural networks better than SVMs?
SVM is interesting if you have a kernel in mind that you know is appropriate, or a domain-specific kernel that would be difficult to express in a differentiable way (a common example might be a string |
6,396 | Are neural networks better than SVMs? | The paper "Every Model Learned by Gradient Descent Is Approximately a Kernel Machine" by Pedro Domingos, shows that every NN learned by gradient descent (not stochastic) is in essence a kernel machine. The kernel has rather a complicated form:
$$
K(x, x^{'}) = \int_{c(t)} \nabla_w y(x) \nabla_w y(x^{'}) dt
$$
Where $c... | Are neural networks better than SVMs? | The paper "Every Model Learned by Gradient Descent Is Approximately a Kernel Machine" by Pedro Domingos, shows that every NN learned by gradient descent (not stochastic) is in essence a kernel machine | Are neural networks better than SVMs?
The paper "Every Model Learned by Gradient Descent Is Approximately a Kernel Machine" by Pedro Domingos, shows that every NN learned by gradient descent (not stochastic) is in essence a kernel machine. The kernel has rather a complicated form:
$$
K(x, x^{'}) = \int_{c(t)} \nabla_w ... | Are neural networks better than SVMs?
The paper "Every Model Learned by Gradient Descent Is Approximately a Kernel Machine" by Pedro Domingos, shows that every NN learned by gradient descent (not stochastic) is in essence a kernel machine |
6,397 | Are neural networks better than SVMs? | I am not an expert, so consider this as an opinion from someone who is still learning about these two fields.
Short Answer
Theoretically, No. DNNs can perform all the functions of SVMs and more.
Practically, mostly no. For most modern problems DNNs are a better choice. If your input data size is small and you are suc... | Are neural networks better than SVMs? | I am not an expert, so consider this as an opinion from someone who is still learning about these two fields.
Short Answer
Theoretically, No. DNNs can perform all the functions of SVMs and more.
Pract | Are neural networks better than SVMs?
I am not an expert, so consider this as an opinion from someone who is still learning about these two fields.
Short Answer
Theoretically, No. DNNs can perform all the functions of SVMs and more.
Practically, mostly no. For most modern problems DNNs are a better choice. If your in... | Are neural networks better than SVMs?
I am not an expert, so consider this as an opinion from someone who is still learning about these two fields.
Short Answer
Theoretically, No. DNNs can perform all the functions of SVMs and more.
Pract |
6,398 | Are neural networks better than SVMs? | 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.
One specific benefit that these models have over SVMs ... | Are neural networks better than SVMs? | 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.
| Are neural networks better than SVMs?
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.
One specific ben... | Are neural networks better than SVMs?
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.
|
6,399 | When to use fixed effects vs using cluster SEs? | Both approaches, using group fixed effects and/or cluster-adjusted standard error take into account different issues related to clustered (or panel) data and I would clearly view them as distinct approaches. Often you want to use both of them:
First of all, cluster-adjusted standard error account for within-cluster cor... | When to use fixed effects vs using cluster SEs? | Both approaches, using group fixed effects and/or cluster-adjusted standard error take into account different issues related to clustered (or panel) data and I would clearly view them as distinct appr | When to use fixed effects vs using cluster SEs?
Both approaches, using group fixed effects and/or cluster-adjusted standard error take into account different issues related to clustered (or panel) data and I would clearly view them as distinct approaches. Often you want to use both of them:
First of all, cluster-adjust... | When to use fixed effects vs using cluster SEs?
Both approaches, using group fixed effects and/or cluster-adjusted standard error take into account different issues related to clustered (or panel) data and I would clearly view them as distinct appr |
6,400 | When to use fixed effects vs using cluster SEs? | Fixed effects are for removing unobserved heterogeneity BETWEEN different groups in your data.
I disagree with the implication in the accepted response that the decision to use a FE model will depend on whether you want to use "less variation or not". If your dependent variable is affected by unobservable variables th... | When to use fixed effects vs using cluster SEs? | Fixed effects are for removing unobserved heterogeneity BETWEEN different groups in your data.
I disagree with the implication in the accepted response that the decision to use a FE model will depend | When to use fixed effects vs using cluster SEs?
Fixed effects are for removing unobserved heterogeneity BETWEEN different groups in your data.
I disagree with the implication in the accepted response that the decision to use a FE model will depend on whether you want to use "less variation or not". If your dependent v... | When to use fixed effects vs using cluster SEs?
Fixed effects are for removing unobserved heterogeneity BETWEEN different groups in your data.
I disagree with the implication in the accepted response that the decision to use a FE model will depend |
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