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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54,101 | Motivations for experiment design in statistical learning? | This is an interesting question. The following stored google search gives many interesting hits, and both ways: Machine learning used in experimental design and experimental design used in machine learning.
Basically experimental design is about planning the collection of data. That must be useful in statistical lear... | Motivations for experiment design in statistical learning? | This is an interesting question. The following stored google search gives many interesting hits, and both ways: Machine learning used in experimental design and experimental design used in machine lea | Motivations for experiment design in statistical learning?
This is an interesting question. The following stored google search gives many interesting hits, and both ways: Machine learning used in experimental design and experimental design used in machine learning.
Basically experimental design is about planning the c... | Motivations for experiment design in statistical learning?
This is an interesting question. The following stored google search gives many interesting hits, and both ways: Machine learning used in experimental design and experimental design used in machine lea |
54,102 | Study design question: What's the best design to assess harm of an exposure? | I start with my methodological thoughts and I offer some footnotes with thoughts that came to my mind on the ethics. Take both of these with a large grain of salt, because we know very little on your specific case. That makes both methodological advice, as well as comments on the ethics difficult and my remarks could c... | Study design question: What's the best design to assess harm of an exposure? | I start with my methodological thoughts and I offer some footnotes with thoughts that came to my mind on the ethics. Take both of these with a large grain of salt, because we know very little on your | Study design question: What's the best design to assess harm of an exposure?
I start with my methodological thoughts and I offer some footnotes with thoughts that came to my mind on the ethics. Take both of these with a large grain of salt, because we know very little on your specific case. That makes both methodologic... | Study design question: What's the best design to assess harm of an exposure?
I start with my methodological thoughts and I offer some footnotes with thoughts that came to my mind on the ethics. Take both of these with a large grain of salt, because we know very little on your |
54,103 | Study design question: What's the best design to assess harm of an exposure? | We have retrospective data suggesting worse survival for patients who received steroids, even when controlling for the indication for the steroids. Therefore it's not ethical to randomize patients to steroids,
This is exactly why you have to do randomized controlled trials. The result is not surprising: someone who n... | Study design question: What's the best design to assess harm of an exposure? | We have retrospective data suggesting worse survival for patients who received steroids, even when controlling for the indication for the steroids. Therefore it's not ethical to randomize patients to | Study design question: What's the best design to assess harm of an exposure?
We have retrospective data suggesting worse survival for patients who received steroids, even when controlling for the indication for the steroids. Therefore it's not ethical to randomize patients to steroids,
This is exactly why you have to... | Study design question: What's the best design to assess harm of an exposure?
We have retrospective data suggesting worse survival for patients who received steroids, even when controlling for the indication for the steroids. Therefore it's not ethical to randomize patients to |
54,104 | Study design question: What's the best design to assess harm of an exposure? | The scholarly literature guiding you into the best way to test a scientific hypothesis of comparative clinical effectiveness is quite large.
Have a look for instance at Rosenbaum's Design of Observational Studies: https://www.amazon.com/Design-Observational-Studies-Springer-Statistics-ebook/dp/B00DZ0PT76/.
Having said ... | Study design question: What's the best design to assess harm of an exposure? | The scholarly literature guiding you into the best way to test a scientific hypothesis of comparative clinical effectiveness is quite large.
Have a look for instance at Rosenbaum's Design of Observati | Study design question: What's the best design to assess harm of an exposure?
The scholarly literature guiding you into the best way to test a scientific hypothesis of comparative clinical effectiveness is quite large.
Have a look for instance at Rosenbaum's Design of Observational Studies: https://www.amazon.com/Design... | Study design question: What's the best design to assess harm of an exposure?
The scholarly literature guiding you into the best way to test a scientific hypothesis of comparative clinical effectiveness is quite large.
Have a look for instance at Rosenbaum's Design of Observati |
54,105 | Family-wise Type I error OLS regression | If your goal is confirmation through hypothesis tests, you should correct for the FWER (or FDR), regardless of the type of model used. If you have a source for the claim to the contrary, please include it in your question.
However, confirmation isn't the only reason someone would use linear regression. You may want to ... | Family-wise Type I error OLS regression | If your goal is confirmation through hypothesis tests, you should correct for the FWER (or FDR), regardless of the type of model used. If you have a source for the claim to the contrary, please includ | Family-wise Type I error OLS regression
If your goal is confirmation through hypothesis tests, you should correct for the FWER (or FDR), regardless of the type of model used. If you have a source for the claim to the contrary, please include it in your question.
However, confirmation isn't the only reason someone would... | Family-wise Type I error OLS regression
If your goal is confirmation through hypothesis tests, you should correct for the FWER (or FDR), regardless of the type of model used. If you have a source for the claim to the contrary, please includ |
54,106 | Why are polynomial activation functions not used | There has been some work which experiments with quadratic activations -- see "neural tensor networks" but in general a disadvantage of second order and higher polynomials is that they don't have a bounded derivative, which could lead to exploding gradients. | Why are polynomial activation functions not used | There has been some work which experiments with quadratic activations -- see "neural tensor networks" but in general a disadvantage of second order and higher polynomials is that they don't have a bou | Why are polynomial activation functions not used
There has been some work which experiments with quadratic activations -- see "neural tensor networks" but in general a disadvantage of second order and higher polynomials is that they don't have a bounded derivative, which could lead to exploding gradients. | Why are polynomial activation functions not used
There has been some work which experiments with quadratic activations -- see "neural tensor networks" but in general a disadvantage of second order and higher polynomials is that they don't have a bou |
54,107 | Why are polynomial activation functions not used | Nutshell
So Polynomial activation functions don't work, since they fail to have the main property which makes neural networks interesting.
Mathematical Reason
Actually, there is a more rigorous reason why they are not used. In
this paper, it is shown that the collection of all feed-forward neural networks can approx... | Why are polynomial activation functions not used | Nutshell
So Polynomial activation functions don't work, since they fail to have the main property which makes neural networks interesting.
Mathematical Reason
Actually, there is a more rigorous reas | Why are polynomial activation functions not used
Nutshell
So Polynomial activation functions don't work, since they fail to have the main property which makes neural networks interesting.
Mathematical Reason
Actually, there is a more rigorous reason why they are not used. In
this paper, it is shown that the collecti... | Why are polynomial activation functions not used
Nutshell
So Polynomial activation functions don't work, since they fail to have the main property which makes neural networks interesting.
Mathematical Reason
Actually, there is a more rigorous reas |
54,108 | How to make sense out of integration over discrete data points? | $X_i$ is continuous a random variable, with pdf $f_{X_i}(x_i;\theta)$, and the expectation requires an integral. The integral limits contain the domain of $X_i$. Not $i$ from $1$ to $n$. The $n$ samples you have are just realizations of $X_i$, i.e. $X_1,X_2,...,X_n$. You're not integrating/summing across these variable... | How to make sense out of integration over discrete data points? | $X_i$ is continuous a random variable, with pdf $f_{X_i}(x_i;\theta)$, and the expectation requires an integral. The integral limits contain the domain of $X_i$. Not $i$ from $1$ to $n$. The $n$ sampl | How to make sense out of integration over discrete data points?
$X_i$ is continuous a random variable, with pdf $f_{X_i}(x_i;\theta)$, and the expectation requires an integral. The integral limits contain the domain of $X_i$. Not $i$ from $1$ to $n$. The $n$ samples you have are just realizations of $X_i$, i.e. $X_1,X_... | How to make sense out of integration over discrete data points?
$X_i$ is continuous a random variable, with pdf $f_{X_i}(x_i;\theta)$, and the expectation requires an integral. The integral limits contain the domain of $X_i$. Not $i$ from $1$ to $n$. The $n$ sampl |
54,109 | How to make sense out of integration over discrete data points? | A full understanding of this issue requires a theory of integration over probability distributions, not just functions. However, even in such an abstract theory it's possible to visualize the integrals as areas under curves. The universal principle is that in any "reasonable" theory of integration, it should be possi... | How to make sense out of integration over discrete data points? | A full understanding of this issue requires a theory of integration over probability distributions, not just functions. However, even in such an abstract theory it's possible to visualize the integra | How to make sense out of integration over discrete data points?
A full understanding of this issue requires a theory of integration over probability distributions, not just functions. However, even in such an abstract theory it's possible to visualize the integrals as areas under curves. The universal principle is th... | How to make sense out of integration over discrete data points?
A full understanding of this issue requires a theory of integration over probability distributions, not just functions. However, even in such an abstract theory it's possible to visualize the integra |
54,110 | How to make sense out of integration over discrete data points? | This proof corresponds to the case of a single data point (so $n=1$ in this context), where the distribution of the random variable $X_i$ is continuous, so it has a probability density function $f$. The proof uses the integral form from the law of the unconscious statistician, which holds that the expected value of th... | How to make sense out of integration over discrete data points? | This proof corresponds to the case of a single data point (so $n=1$ in this context), where the distribution of the random variable $X_i$ is continuous, so it has a probability density function $f$. | How to make sense out of integration over discrete data points?
This proof corresponds to the case of a single data point (so $n=1$ in this context), where the distribution of the random variable $X_i$ is continuous, so it has a probability density function $f$. The proof uses the integral form from the law of the unc... | How to make sense out of integration over discrete data points?
This proof corresponds to the case of a single data point (so $n=1$ in this context), where the distribution of the random variable $X_i$ is continuous, so it has a probability density function $f$. |
54,111 | How to make sense out of integration over discrete data points? | The proof you are examining starts by assuming $f(x_i; θ)$ is "a regular pdf." A pdf, or probability density function, is, by definition a continuous (i.e. not discrete) function. Since $X_i$ is continuous (hence pdf), you would use an integral to obtain the expected value of a function of $X_i$ by the Law of the Unc... | How to make sense out of integration over discrete data points? | The proof you are examining starts by assuming $f(x_i; θ)$ is "a regular pdf." A pdf, or probability density function, is, by definition a continuous (i.e. not discrete) function. Since $X_i$ is con | How to make sense out of integration over discrete data points?
The proof you are examining starts by assuming $f(x_i; θ)$ is "a regular pdf." A pdf, or probability density function, is, by definition a continuous (i.e. not discrete) function. Since $X_i$ is continuous (hence pdf), you would use an integral to obtain... | How to make sense out of integration over discrete data points?
The proof you are examining starts by assuming $f(x_i; θ)$ is "a regular pdf." A pdf, or probability density function, is, by definition a continuous (i.e. not discrete) function. Since $X_i$ is con |
54,112 | Kalman filter parameter estimation | Everything you will ever need regarding estimation of parameters in a state space model is in this document:
https://cran.r-project.org/web/packages/MARSS/vignettes/EMDerivation.pdf
Kalman Filter/Smoother assumes that the parameters are known in advance so that the unobserved state can be estimated. The initial values ... | Kalman filter parameter estimation | Everything you will ever need regarding estimation of parameters in a state space model is in this document:
https://cran.r-project.org/web/packages/MARSS/vignettes/EMDerivation.pdf
Kalman Filter/Smoo | Kalman filter parameter estimation
Everything you will ever need regarding estimation of parameters in a state space model is in this document:
https://cran.r-project.org/web/packages/MARSS/vignettes/EMDerivation.pdf
Kalman Filter/Smoother assumes that the parameters are known in advance so that the unobserved state ca... | Kalman filter parameter estimation
Everything you will ever need regarding estimation of parameters in a state space model is in this document:
https://cran.r-project.org/web/packages/MARSS/vignettes/EMDerivation.pdf
Kalman Filter/Smoo |
54,113 | Kalman filter parameter estimation | As mentioned in other answers, you need values for the parameters in all system matrices ($F$, $H$, $Q$) in order to run the Kalman filter. However, you may have a state-space model with unknown parameters that you need to estimate.
In order to do that, you may use the Kalman filter: running the Kalman filter with arb... | Kalman filter parameter estimation | As mentioned in other answers, you need values for the parameters in all system matrices ($F$, $H$, $Q$) in order to run the Kalman filter. However, you may have a state-space model with unknown param | Kalman filter parameter estimation
As mentioned in other answers, you need values for the parameters in all system matrices ($F$, $H$, $Q$) in order to run the Kalman filter. However, you may have a state-space model with unknown parameters that you need to estimate.
In order to do that, you may use the Kalman filter:... | Kalman filter parameter estimation
As mentioned in other answers, you need values for the parameters in all system matrices ($F$, $H$, $Q$) in order to run the Kalman filter. However, you may have a state-space model with unknown param |
54,114 | Kalman filter parameter estimation | In the usual state space model, the only things that are estimated are the state and its variance-covariance matrix (at each time point) - whether filtering or smoothing only changes what information you're conditioning on, but either way you end up with estimates of those things.
The $H$'s (and $F$, $Q$ and $R$ in you... | Kalman filter parameter estimation | In the usual state space model, the only things that are estimated are the state and its variance-covariance matrix (at each time point) - whether filtering or smoothing only changes what information | Kalman filter parameter estimation
In the usual state space model, the only things that are estimated are the state and its variance-covariance matrix (at each time point) - whether filtering or smoothing only changes what information you're conditioning on, but either way you end up with estimates of those things.
The... | Kalman filter parameter estimation
In the usual state space model, the only things that are estimated are the state and its variance-covariance matrix (at each time point) - whether filtering or smoothing only changes what information |
54,115 | Kalman filter parameter estimation | To address the question of initial values, I would suggest you read Time Series Analysis by Durbin and Koopman (2012) who go into great detail on the exact diffuse initialisation procedure (this is implemented in the R package KFAS). Which is probably what you want to use in the case of a non-stationary model. For a st... | Kalman filter parameter estimation | To address the question of initial values, I would suggest you read Time Series Analysis by Durbin and Koopman (2012) who go into great detail on the exact diffuse initialisation procedure (this is im | Kalman filter parameter estimation
To address the question of initial values, I would suggest you read Time Series Analysis by Durbin and Koopman (2012) who go into great detail on the exact diffuse initialisation procedure (this is implemented in the R package KFAS). Which is probably what you want to use in the case ... | Kalman filter parameter estimation
To address the question of initial values, I would suggest you read Time Series Analysis by Durbin and Koopman (2012) who go into great detail on the exact diffuse initialisation procedure (this is im |
54,116 | Kalman filter parameter estimation | Other answerers mentioned EM, which is the most traditional approach. There are many others, however.
you can do direct likelihood optimization, as various others have also remarked: run filter/smoother, obtain likelihood, iterate/optimize. Gradient expressions are available, see, e.g., Bayesian filtering and smoothin... | Kalman filter parameter estimation | Other answerers mentioned EM, which is the most traditional approach. There are many others, however.
you can do direct likelihood optimization, as various others have also remarked: run filter/smoot | Kalman filter parameter estimation
Other answerers mentioned EM, which is the most traditional approach. There are many others, however.
you can do direct likelihood optimization, as various others have also remarked: run filter/smoother, obtain likelihood, iterate/optimize. Gradient expressions are available, see, e.... | Kalman filter parameter estimation
Other answerers mentioned EM, which is the most traditional approach. There are many others, however.
you can do direct likelihood optimization, as various others have also remarked: run filter/smoot |
54,117 | name for histogram of nominal p-values under the null | This idea of the uniform distribution for P-values is fairly new
in statistics education and practice. I don't know if anyone has yet made up a name
for the related histograms that has come into general use. Below I just call them "Null P-value" histograms.
It is important to note that this uniform distribution for P-v... | name for histogram of nominal p-values under the null | This idea of the uniform distribution for P-values is fairly new
in statistics education and practice. I don't know if anyone has yet made up a name
for the related histograms that has come into gener | name for histogram of nominal p-values under the null
This idea of the uniform distribution for P-values is fairly new
in statistics education and practice. I don't know if anyone has yet made up a name
for the related histograms that has come into general use. Below I just call them "Null P-value" histograms.
It is im... | name for histogram of nominal p-values under the null
This idea of the uniform distribution for P-values is fairly new
in statistics education and practice. I don't know if anyone has yet made up a name
for the related histograms that has come into gener |
54,118 | name for histogram of nominal p-values under the null | ...is there a name for this type of histogram/method for assessing nominal p-values?
The true distribution of a quantity under a (simple) null hypothesis is called the null distribution of that quantity. There is no specific name for the histogram of a Monte-Carlo simulation of the distribution of the p-value. It wo... | name for histogram of nominal p-values under the null | ...is there a name for this type of histogram/method for assessing nominal p-values?
The true distribution of a quantity under a (simple) null hypothesis is called the null distribution of that quant | name for histogram of nominal p-values under the null
...is there a name for this type of histogram/method for assessing nominal p-values?
The true distribution of a quantity under a (simple) null hypothesis is called the null distribution of that quantity. There is no specific name for the histogram of a Monte-Carlo... | name for histogram of nominal p-values under the null
...is there a name for this type of histogram/method for assessing nominal p-values?
The true distribution of a quantity under a (simple) null hypothesis is called the null distribution of that quant |
54,119 | How to get top features that contribute to anomalies in Isolation forest | 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.
SHAP values and the shap Python library can be used fo... | How to get top features that contribute to anomalies in Isolation forest | 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.
| How to get top features that contribute to anomalies in Isolation forest
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.
... | How to get top features that contribute to anomalies in Isolation forest
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.
|
54,120 | How to get top features that contribute to anomalies in Isolation forest | One possible describing feature importance in unsupervised outlier detecion is described in Contextual Outlier Interpretation. Similar as in the Lime approach, local linearity is assumed and by sampling a data points around the outlier of interest a classification problem is generated. The authors suggest to apply a SV... | How to get top features that contribute to anomalies in Isolation forest | One possible describing feature importance in unsupervised outlier detecion is described in Contextual Outlier Interpretation. Similar as in the Lime approach, local linearity is assumed and by sampli | How to get top features that contribute to anomalies in Isolation forest
One possible describing feature importance in unsupervised outlier detecion is described in Contextual Outlier Interpretation. Similar as in the Lime approach, local linearity is assumed and by sampling a data points around the outlier of interest... | How to get top features that contribute to anomalies in Isolation forest
One possible describing feature importance in unsupervised outlier detecion is described in Contextual Outlier Interpretation. Similar as in the Lime approach, local linearity is assumed and by sampli |
54,121 | What is the acceptable level of concurvity? | This is a late bump to a relatively old question, but may be of help to future visitors.
In Noam Ross' course on GAMs, GAMs in R, Chapter 2, section 10 "checking concurvity" says that observing a value over 0.8 for the worst case requires closer inspection of the model. So in the image you pasted there's only one varia... | What is the acceptable level of concurvity? | This is a late bump to a relatively old question, but may be of help to future visitors.
In Noam Ross' course on GAMs, GAMs in R, Chapter 2, section 10 "checking concurvity" says that observing a valu | What is the acceptable level of concurvity?
This is a late bump to a relatively old question, but may be of help to future visitors.
In Noam Ross' course on GAMs, GAMs in R, Chapter 2, section 10 "checking concurvity" says that observing a value over 0.8 for the worst case requires closer inspection of the model. So in... | What is the acceptable level of concurvity?
This is a late bump to a relatively old question, but may be of help to future visitors.
In Noam Ross' course on GAMs, GAMs in R, Chapter 2, section 10 "checking concurvity" says that observing a valu |
54,122 | What is the acceptable level of concurvity? | I would like to get more clarity on this as well, but I did find one paper (Tree traits influence response to fire severity in the western Oregon Cascades, USA; 2019) that used the mgcv package where the authors used a cutoff of 0.3. It sounded like they applied that cutoff to all three measures of concurvity. Of cours... | What is the acceptable level of concurvity? | I would like to get more clarity on this as well, but I did find one paper (Tree traits influence response to fire severity in the western Oregon Cascades, USA; 2019) that used the mgcv package where th | What is the acceptable level of concurvity?
I would like to get more clarity on this as well, but I did find one paper (Tree traits influence response to fire severity in the western Oregon Cascades, USA; 2019) that used the mgcv package where the authors used a cutoff of 0.3. It sounded like they applied that cutoff to... | What is the acceptable level of concurvity?
I would like to get more clarity on this as well, but I did find one paper (Tree traits influence response to fire severity in the western Oregon Cascades, USA; 2019) that used the mgcv package where th |
54,123 | What is the acceptable level of concurvity? | Another source, from a doctoral dissertation Multi-city time series analyses of air pollution and mortality data using generalized geoadditive mixed models
by Lung-Chang Chien. Free online access.
So far, there is no strict criterion to identify the level of concurvity which can
severely affect model fitting. Ramsay e... | What is the acceptable level of concurvity? | Another source, from a doctoral dissertation Multi-city time series analyses of air pollution and mortality data using generalized geoadditive mixed models
by Lung-Chang Chien. Free online access.
So | What is the acceptable level of concurvity?
Another source, from a doctoral dissertation Multi-city time series analyses of air pollution and mortality data using generalized geoadditive mixed models
by Lung-Chang Chien. Free online access.
So far, there is no strict criterion to identify the level of concurvity which... | What is the acceptable level of concurvity?
Another source, from a doctoral dissertation Multi-city time series analyses of air pollution and mortality data using generalized geoadditive mixed models
by Lung-Chang Chien. Free online access.
So |
54,124 | Need help understanding what a natural log transformation is actually doing and why specific transformations are required for linear regression [duplicate] | There's a lot here to break down. I hate to say it, but some of the advice in your course is quite misguided and wrong.
What is that transformation actually doing? I don't mean the nitty gritty math, but what is it doing conceptually?
The math here is pretty simple. You have a bunch of measurements of people's age ... | Need help understanding what a natural log transformation is actually doing and why specific transfo | There's a lot here to break down. I hate to say it, but some of the advice in your course is quite misguided and wrong.
What is that transformation actually doing? I don't mean the nitty gritty math | Need help understanding what a natural log transformation is actually doing and why specific transformations are required for linear regression [duplicate]
There's a lot here to break down. I hate to say it, but some of the advice in your course is quite misguided and wrong.
What is that transformation actually doing... | Need help understanding what a natural log transformation is actually doing and why specific transfo
There's a lot here to break down. I hate to say it, but some of the advice in your course is quite misguided and wrong.
What is that transformation actually doing? I don't mean the nitty gritty math |
54,125 | What's the point in using identity matrix as weighting matrix in GMM? | Yes, getting a first step estimator is the canonical use. Of course, the error terms in $$S = \frac{1}{n}\sum_i\epsilon_i^2x_ix_i'$$ are not observable, so that you need to replace them with something feasible. As the efficient GMM estimator depends on $\hat S$, you first need some feasible preliminary estimator such a... | What's the point in using identity matrix as weighting matrix in GMM? | Yes, getting a first step estimator is the canonical use. Of course, the error terms in $$S = \frac{1}{n}\sum_i\epsilon_i^2x_ix_i'$$ are not observable, so that you need to replace them with something | What's the point in using identity matrix as weighting matrix in GMM?
Yes, getting a first step estimator is the canonical use. Of course, the error terms in $$S = \frac{1}{n}\sum_i\epsilon_i^2x_ix_i'$$ are not observable, so that you need to replace them with something feasible. As the efficient GMM estimator depends ... | What's the point in using identity matrix as weighting matrix in GMM?
Yes, getting a first step estimator is the canonical use. Of course, the error terms in $$S = \frac{1}{n}\sum_i\epsilon_i^2x_ix_i'$$ are not observable, so that you need to replace them with something |
54,126 | What's the point in using identity matrix as weighting matrix in GMM? | This second answer addresses the question posed in the comment to the first answer as to why the specific choice of $W$ results in an efficient GMM estimator.
The efficient weighting matrix results from the general one by setting $W=S^{-1}$ to get an asymptotic variance
\begin{eqnarray}
\mathrm{Avar}(\widehat{\delta}(\... | What's the point in using identity matrix as weighting matrix in GMM? | This second answer addresses the question posed in the comment to the first answer as to why the specific choice of $W$ results in an efficient GMM estimator.
The efficient weighting matrix results fr | What's the point in using identity matrix as weighting matrix in GMM?
This second answer addresses the question posed in the comment to the first answer as to why the specific choice of $W$ results in an efficient GMM estimator.
The efficient weighting matrix results from the general one by setting $W=S^{-1}$ to get an... | What's the point in using identity matrix as weighting matrix in GMM?
This second answer addresses the question posed in the comment to the first answer as to why the specific choice of $W$ results in an efficient GMM estimator.
The efficient weighting matrix results fr |
54,127 | Definition of Statistic | A statistic is a function that maps from the set of outcomes of the observable values to a real number. Thus, with $n$ data points, a statistic will be a function $s: \mathbb{R}^n\rightarrow \mathbb{R}$ as in your second form. However, it is also possible to view the statistic in its random sense by taking the approp... | Definition of Statistic | A statistic is a function that maps from the set of outcomes of the observable values to a real number. Thus, with $n$ data points, a statistic will be a function $s: \mathbb{R}^n\rightarrow \mathbb{ | Definition of Statistic
A statistic is a function that maps from the set of outcomes of the observable values to a real number. Thus, with $n$ data points, a statistic will be a function $s: \mathbb{R}^n\rightarrow \mathbb{R}$ as in your second form. However, it is also possible to view the statistic in its random se... | Definition of Statistic
A statistic is a function that maps from the set of outcomes of the observable values to a real number. Thus, with $n$ data points, a statistic will be a function $s: \mathbb{R}^n\rightarrow \mathbb{ |
54,128 | What's a mean field variational family? | Loosely speaking, the mean field family defines a specific class of joint distributions. So $z$ here is actually a parameter vector of length m. That means that $q(z)$ describes a joint distribution over all of the individual z's, and can be written as
$$q(z) = q(z_1, z_2, \ldots, z_m)$$
We can use the chain rule to f... | What's a mean field variational family? | Loosely speaking, the mean field family defines a specific class of joint distributions. So $z$ here is actually a parameter vector of length m. That means that $q(z)$ describes a joint distribution | What's a mean field variational family?
Loosely speaking, the mean field family defines a specific class of joint distributions. So $z$ here is actually a parameter vector of length m. That means that $q(z)$ describes a joint distribution over all of the individual z's, and can be written as
$$q(z) = q(z_1, z_2, \ldot... | What's a mean field variational family?
Loosely speaking, the mean field family defines a specific class of joint distributions. So $z$ here is actually a parameter vector of length m. That means that $q(z)$ describes a joint distribution |
54,129 | Is the sum of trends of two time series the trend of the sum of the time series? | Is the sum of trends of two time series the trend of the sum of the time series?
- as a general question, it depends: if the estimator is linear in the data then yes, but in general, no.
On the specific question of using Theil-Sen slope (median pairwise slope) as a trend estimate:
When using a Theil-Sen slope estimat... | Is the sum of trends of two time series the trend of the sum of the time series? | Is the sum of trends of two time series the trend of the sum of the time series?
- as a general question, it depends: if the estimator is linear in the data then yes, but in general, no.
On the spec | Is the sum of trends of two time series the trend of the sum of the time series?
Is the sum of trends of two time series the trend of the sum of the time series?
- as a general question, it depends: if the estimator is linear in the data then yes, but in general, no.
On the specific question of using Theil-Sen slope ... | Is the sum of trends of two time series the trend of the sum of the time series?
Is the sum of trends of two time series the trend of the sum of the time series?
- as a general question, it depends: if the estimator is linear in the data then yes, but in general, no.
On the spec |
54,130 | Coefficient Significance in Regression with Arima Errors | The forecast package does forecasting. For that purpose, the significance of variables is irrelevant. What matters is whether a variable is useful for forecasting. The AIC is a good guide for selecting variables for forecasting, so the package minimizes the AIC. If you really want to do a significance test on a variabl... | Coefficient Significance in Regression with Arima Errors | The forecast package does forecasting. For that purpose, the significance of variables is irrelevant. What matters is whether a variable is useful for forecasting. The AIC is a good guide for selectin | Coefficient Significance in Regression with Arima Errors
The forecast package does forecasting. For that purpose, the significance of variables is irrelevant. What matters is whether a variable is useful for forecasting. The AIC is a good guide for selecting variables for forecasting, so the package minimizes the AIC. ... | Coefficient Significance in Regression with Arima Errors
The forecast package does forecasting. For that purpose, the significance of variables is irrelevant. What matters is whether a variable is useful for forecasting. The AIC is a good guide for selectin |
54,131 | Coefficient Significance in Regression with Arima Errors | If you aren't interested in realistic(ie wide) confidence limits then this is ok, but if you want good confidence limits then this has a negative impact. The AR/MA parameters are significant, but the ACF/PACF didn't warrant them and in essence mathematically they cancel each other out so no harm done....for this examp... | Coefficient Significance in Regression with Arima Errors | If you aren't interested in realistic(ie wide) confidence limits then this is ok, but if you want good confidence limits then this has a negative impact. The AR/MA parameters are significant, but the | Coefficient Significance in Regression with Arima Errors
If you aren't interested in realistic(ie wide) confidence limits then this is ok, but if you want good confidence limits then this has a negative impact. The AR/MA parameters are significant, but the ACF/PACF didn't warrant them and in essence mathematically the... | Coefficient Significance in Regression with Arima Errors
If you aren't interested in realistic(ie wide) confidence limits then this is ok, but if you want good confidence limits then this has a negative impact. The AR/MA parameters are significant, but the |
54,132 | How is the Akaike information criterion (AIC) affected by sample size? | There is no particular meaning to AIC for comparison between different data sets. Yes, the AIC value can change for increased $n$. However, AIC is self-referential, which means that one can only compare different models using the SAME data set, not different data sets. This is also tricky, for example, it applies to pr... | How is the Akaike information criterion (AIC) affected by sample size? | There is no particular meaning to AIC for comparison between different data sets. Yes, the AIC value can change for increased $n$. However, AIC is self-referential, which means that one can only compa | How is the Akaike information criterion (AIC) affected by sample size?
There is no particular meaning to AIC for comparison between different data sets. Yes, the AIC value can change for increased $n$. However, AIC is self-referential, which means that one can only compare different models using the SAME data set, not ... | How is the Akaike information criterion (AIC) affected by sample size?
There is no particular meaning to AIC for comparison between different data sets. Yes, the AIC value can change for increased $n$. However, AIC is self-referential, which means that one can only compa |
54,133 | GLMM for count data using square root link in lme4 | It looks very much like you have a case of complete separation:
there is only one landform (ridge) that has seedlings, while other had no seedlings at al
large estimates ($|\hat \beta|>10$), and ridiculously large standard error estimates.
Basically what's happening is that the baseline level ("abandoned") has an ... | GLMM for count data using square root link in lme4 | It looks very much like you have a case of complete separation:
there is only one landform (ridge) that has seedlings, while other had no seedlings at al
large estimates ($|\hat \beta|>10$), and r | GLMM for count data using square root link in lme4
It looks very much like you have a case of complete separation:
there is only one landform (ridge) that has seedlings, while other had no seedlings at al
large estimates ($|\hat \beta|>10$), and ridiculously large standard error estimates.
Basically what's happeni... | GLMM for count data using square root link in lme4
It looks very much like you have a case of complete separation:
there is only one landform (ridge) that has seedlings, while other had no seedlings at al
large estimates ($|\hat \beta|>10$), and r |
54,134 | GLMM for count data using square root link in lme4 | Indeed this seems to be a separation issue. To account for these cases, in my GLMMadaptive package you can include a penalty for the fixed-effects coefficients in the form of a Students-t density (i.e., for large enough df equivalent to ridge regression). For a worked example, have a look at the last section of this vi... | GLMM for count data using square root link in lme4 | Indeed this seems to be a separation issue. To account for these cases, in my GLMMadaptive package you can include a penalty for the fixed-effects coefficients in the form of a Students-t density (i.e | GLMM for count data using square root link in lme4
Indeed this seems to be a separation issue. To account for these cases, in my GLMMadaptive package you can include a penalty for the fixed-effects coefficients in the form of a Students-t density (i.e., for large enough df equivalent to ridge regression). For a worked ... | GLMM for count data using square root link in lme4
Indeed this seems to be a separation issue. To account for these cases, in my GLMMadaptive package you can include a penalty for the fixed-effects coefficients in the form of a Students-t density (i.e |
54,135 | Sufficient statistic when $X\sim U(\theta,2 \theta)$ | Regarding 1., note that interpretation of a sufficient statistic is:
"no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter".
So, we need both the statistics to provide the "most information" possible about the value of the parameter. Not nec... | Sufficient statistic when $X\sim U(\theta,2 \theta)$ | Regarding 1., note that interpretation of a sufficient statistic is:
"no other statistic that can be calculated from the same sample provides any additional information as to the value of the paramete | Sufficient statistic when $X\sim U(\theta,2 \theta)$
Regarding 1., note that interpretation of a sufficient statistic is:
"no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter".
So, we need both the statistics to provide the "most informatio... | Sufficient statistic when $X\sim U(\theta,2 \theta)$
Regarding 1., note that interpretation of a sufficient statistic is:
"no other statistic that can be calculated from the same sample provides any additional information as to the value of the paramete |
54,136 | Show that if $E\psi(x-\theta)= 0 $ then $P(X< \theta) \leq p \leq P(X \leq \theta)$ | Your method assumes that $X$ is a continuous random variable, which is not stated as a condition of the problem. It is possible to get the result in a more general case, so long as there is some non-zero probability that $X \neq \theta$. From your stated form for $\psi$ you have:
$$\psi(X-\theta) = \mathbb{I}(X < \th... | Show that if $E\psi(x-\theta)= 0 $ then $P(X< \theta) \leq p \leq P(X \leq \theta)$ | Your method assumes that $X$ is a continuous random variable, which is not stated as a condition of the problem. It is possible to get the result in a more general case, so long as there is some non- | Show that if $E\psi(x-\theta)= 0 $ then $P(X< \theta) \leq p \leq P(X \leq \theta)$
Your method assumes that $X$ is a continuous random variable, which is not stated as a condition of the problem. It is possible to get the result in a more general case, so long as there is some non-zero probability that $X \neq \theta... | Show that if $E\psi(x-\theta)= 0 $ then $P(X< \theta) \leq p \leq P(X \leq \theta)$
Your method assumes that $X$ is a continuous random variable, which is not stated as a condition of the problem. It is possible to get the result in a more general case, so long as there is some non- |
54,137 | Show that if $E\psi(x-\theta)= 0 $ then $P(X< \theta) \leq p \leq P(X \leq \theta)$ | There are many ways to approach this problem.
The point of the following is to take you through a process of analyzing the question, performing the requisite calculations as simply and easily as possible, developing a strategy to carry out the proof, and applying that strategy. A section of concluding remarks highligh... | Show that if $E\psi(x-\theta)= 0 $ then $P(X< \theta) \leq p \leq P(X \leq \theta)$ | There are many ways to approach this problem.
The point of the following is to take you through a process of analyzing the question, performing the requisite calculations as simply and easily as possi | Show that if $E\psi(x-\theta)= 0 $ then $P(X< \theta) \leq p \leq P(X \leq \theta)$
There are many ways to approach this problem.
The point of the following is to take you through a process of analyzing the question, performing the requisite calculations as simply and easily as possible, developing a strategy to carry ... | Show that if $E\psi(x-\theta)= 0 $ then $P(X< \theta) \leq p \leq P(X \leq \theta)$
There are many ways to approach this problem.
The point of the following is to take you through a process of analyzing the question, performing the requisite calculations as simply and easily as possi |
54,138 | Why Standard Deviation is more popular than Mean Absolute Deviation? [duplicate] | Historically, Laplace started with the expected absolute deviation from the expectation and got mired into computational issues, beyond the Laplace (or double exponential) distribution, while Legendre and Gauss advocated the expected square difference from the expectation, which is more naturally connected with the Nor... | Why Standard Deviation is more popular than Mean Absolute Deviation? [duplicate] | Historically, Laplace started with the expected absolute deviation from the expectation and got mired into computational issues, beyond the Laplace (or double exponential) distribution, while Legendre | Why Standard Deviation is more popular than Mean Absolute Deviation? [duplicate]
Historically, Laplace started with the expected absolute deviation from the expectation and got mired into computational issues, beyond the Laplace (or double exponential) distribution, while Legendre and Gauss advocated the expected squar... | Why Standard Deviation is more popular than Mean Absolute Deviation? [duplicate]
Historically, Laplace started with the expected absolute deviation from the expectation and got mired into computational issues, beyond the Laplace (or double exponential) distribution, while Legendre |
54,139 | How to represent the probability of a point belonging to a cluster? | In general, this is a challenging problem, especially given the constraint that the relative positions in 2D space should be retained.
In the absence of that constraint, I would recommend a stacked bar plot. With thin bars and a sorted dataset, colours can easily be used to indicate the probability of belonging to dif... | How to represent the probability of a point belonging to a cluster? | In general, this is a challenging problem, especially given the constraint that the relative positions in 2D space should be retained.
In the absence of that constraint, I would recommend a stacked b | How to represent the probability of a point belonging to a cluster?
In general, this is a challenging problem, especially given the constraint that the relative positions in 2D space should be retained.
In the absence of that constraint, I would recommend a stacked bar plot. With thin bars and a sorted dataset, colour... | How to represent the probability of a point belonging to a cluster?
In general, this is a challenging problem, especially given the constraint that the relative positions in 2D space should be retained.
In the absence of that constraint, I would recommend a stacked b |
54,140 | How to represent the probability of a point belonging to a cluster? | Maybe you don't need to exactly encode the distribution.
Define a color for "mixed", e.g., gray.
Then interpolate between your cluster palette and gray depending on the difference between $p_\max$ and the second largest probability. | How to represent the probability of a point belonging to a cluster? | Maybe you don't need to exactly encode the distribution.
Define a color for "mixed", e.g., gray.
Then interpolate between your cluster palette and gray depending on the difference between $p_\max$ and | How to represent the probability of a point belonging to a cluster?
Maybe you don't need to exactly encode the distribution.
Define a color for "mixed", e.g., gray.
Then interpolate between your cluster palette and gray depending on the difference between $p_\max$ and the second largest probability. | How to represent the probability of a point belonging to a cluster?
Maybe you don't need to exactly encode the distribution.
Define a color for "mixed", e.g., gray.
Then interpolate between your cluster palette and gray depending on the difference between $p_\max$ and |
54,141 | To choose between linear or generalised mixed effects model, what is the most important thing to consider? | Linear mixed effects models are for continuous variables. Generalised ones are for non continuous, e.g., binomial.
This is not true. See the wiki page for generalized linear models. E.g., the gamma and exponential distribution are generalized linaer models and both are continuous. The difference is that you allow for ... | To choose between linear or generalised mixed effects model, what is the most important thing to con | Linear mixed effects models are for continuous variables. Generalised ones are for non continuous, e.g., binomial.
This is not true. See the wiki page for generalized linear models. E.g., the gamma a | To choose between linear or generalised mixed effects model, what is the most important thing to consider?
Linear mixed effects models are for continuous variables. Generalised ones are for non continuous, e.g., binomial.
This is not true. See the wiki page for generalized linear models. E.g., the gamma and exponentia... | To choose between linear or generalised mixed effects model, what is the most important thing to con
Linear mixed effects models are for continuous variables. Generalised ones are for non continuous, e.g., binomial.
This is not true. See the wiki page for generalized linear models. E.g., the gamma a |
54,142 | To choose between linear or generalised mixed effects model, what is the most important thing to consider? | The number of successes out of N trials is a Binomial distribution. Hence, it seems that you should go for a mixed-effects logistic regression. | To choose between linear or generalised mixed effects model, what is the most important thing to con | The number of successes out of N trials is a Binomial distribution. Hence, it seems that you should go for a mixed-effects logistic regression. | To choose between linear or generalised mixed effects model, what is the most important thing to consider?
The number of successes out of N trials is a Binomial distribution. Hence, it seems that you should go for a mixed-effects logistic regression. | To choose between linear or generalised mixed effects model, what is the most important thing to con
The number of successes out of N trials is a Binomial distribution. Hence, it seems that you should go for a mixed-effects logistic regression. |
54,143 | Can PMF have value greater than 1? | Your question has 2 parts
Probability Mass Function: It have discrete values and we count only those values for probability. So F(x):Pr(R=x) is only the probabilty which is always less than 1
Probability Density Distribution: Here we don't have discrete values and if we consider a point Pr(of single point)=0.
Hence we... | Can PMF have value greater than 1? | Your question has 2 parts
Probability Mass Function: It have discrete values and we count only those values for probability. So F(x):Pr(R=x) is only the probabilty which is always less than 1
Probabi | Can PMF have value greater than 1?
Your question has 2 parts
Probability Mass Function: It have discrete values and we count only those values for probability. So F(x):Pr(R=x) is only the probabilty which is always less than 1
Probability Density Distribution: Here we don't have discrete values and if we consider a po... | Can PMF have value greater than 1?
Your question has 2 parts
Probability Mass Function: It have discrete values and we count only those values for probability. So F(x):Pr(R=x) is only the probabilty which is always less than 1
Probabi |
54,144 | Can PMF have value greater than 1? | No, a probability mass function cannot have a value above 1. Quite simply, all the values of the probability mass function must sum to 1. Also, they must be non-negative. From here it follows that, if one of the values exceeded 1, the whole sum would exceed 1. And that is not allowed. | Can PMF have value greater than 1? | No, a probability mass function cannot have a value above 1. Quite simply, all the values of the probability mass function must sum to 1. Also, they must be non-negative. From here it follows that, if | Can PMF have value greater than 1?
No, a probability mass function cannot have a value above 1. Quite simply, all the values of the probability mass function must sum to 1. Also, they must be non-negative. From here it follows that, if one of the values exceeded 1, the whole sum would exceed 1. And that is not allowed. | Can PMF have value greater than 1?
No, a probability mass function cannot have a value above 1. Quite simply, all the values of the probability mass function must sum to 1. Also, they must be non-negative. From here it follows that, if |
54,145 | Can PMF have value greater than 1? | By PMF, I assume you mean what is usually called the pdf. For a continuous distribution the answer is yes. What has to be true is that:
$$\int_{-\infty}^{\infty}p(x) dx = 1 $$
Imagine a normal distribution, centered at zero (so a mean of zero), and a timy standard deviation (say, .01). Almost all of the points on ... | Can PMF have value greater than 1? | By PMF, I assume you mean what is usually called the pdf. For a continuous distribution the answer is yes. What has to be true is that:
$$\int_{-\infty}^{\infty}p(x) dx = 1 $$
Imagine a normal dis | Can PMF have value greater than 1?
By PMF, I assume you mean what is usually called the pdf. For a continuous distribution the answer is yes. What has to be true is that:
$$\int_{-\infty}^{\infty}p(x) dx = 1 $$
Imagine a normal distribution, centered at zero (so a mean of zero), and a timy standard deviation (say, ... | Can PMF have value greater than 1?
By PMF, I assume you mean what is usually called the pdf. For a continuous distribution the answer is yes. What has to be true is that:
$$\int_{-\infty}^{\infty}p(x) dx = 1 $$
Imagine a normal dis |
54,146 | mlogit package fails to recover synthetic mixed logit model | You appear to have hit upon an unlucky combination of optimization parameters, specifically, with respect to the Halton pseudo-random sequence, which may possibly have a bug in it. BFGS appears to be stopping prematurely with R = 300, but not with other significantly smaller or larger values. Fortunately, you don't n... | mlogit package fails to recover synthetic mixed logit model | You appear to have hit upon an unlucky combination of optimization parameters, specifically, with respect to the Halton pseudo-random sequence, which may possibly have a bug in it. BFGS appears to be | mlogit package fails to recover synthetic mixed logit model
You appear to have hit upon an unlucky combination of optimization parameters, specifically, with respect to the Halton pseudo-random sequence, which may possibly have a bug in it. BFGS appears to be stopping prematurely with R = 300, but not with other signi... | mlogit package fails to recover synthetic mixed logit model
You appear to have hit upon an unlucky combination of optimization parameters, specifically, with respect to the Halton pseudo-random sequence, which may possibly have a bug in it. BFGS appears to be |
54,147 | mlogit package fails to recover synthetic mixed logit model | I believe that the BFGS implementation is the culprit here. My first two clues were:
Calling mlogit() with the argument method='bhhh' instead of the default bfgs resulted in much more accurate estimates.
When I obtained inaccurate estimates from bfgs, the stop condition for the optimizer was last step couldn't find h... | mlogit package fails to recover synthetic mixed logit model | I believe that the BFGS implementation is the culprit here. My first two clues were:
Calling mlogit() with the argument method='bhhh' instead of the default bfgs resulted in much more accurate estima | mlogit package fails to recover synthetic mixed logit model
I believe that the BFGS implementation is the culprit here. My first two clues were:
Calling mlogit() with the argument method='bhhh' instead of the default bfgs resulted in much more accurate estimates.
When I obtained inaccurate estimates from bfgs, the st... | mlogit package fails to recover synthetic mixed logit model
I believe that the BFGS implementation is the culprit here. My first two clues were:
Calling mlogit() with the argument method='bhhh' instead of the default bfgs resulted in much more accurate estima |
54,148 | Lavaan SEM Ordinal and Categorical variables | Yes, there are special ways to handle ordinal and binary variables in Lavaan, you can enter them as numeric variables then when you use the sem() function you specify which are ordinal using the ordered argument.
I wrote up a longer response but then came across this link...
That should give you everything you need to ... | Lavaan SEM Ordinal and Categorical variables | Yes, there are special ways to handle ordinal and binary variables in Lavaan, you can enter them as numeric variables then when you use the sem() function you specify which are ordinal using the order | Lavaan SEM Ordinal and Categorical variables
Yes, there are special ways to handle ordinal and binary variables in Lavaan, you can enter them as numeric variables then when you use the sem() function you specify which are ordinal using the ordered argument.
I wrote up a longer response but then came across this link...... | Lavaan SEM Ordinal and Categorical variables
Yes, there are special ways to handle ordinal and binary variables in Lavaan, you can enter them as numeric variables then when you use the sem() function you specify which are ordinal using the order |
54,149 | Lavaan SEM Ordinal and Categorical variables | As both @Dimitris Rizopoulos and @Jeremy Miles say, it is possible to fit an SEM using categorical data (i.e., which includes your dichotomous and ordinal variables). There are generally two methods used to go about doing this$^1$. The first is the direct method, which treats categorical data as continuous and, as a re... | Lavaan SEM Ordinal and Categorical variables | As both @Dimitris Rizopoulos and @Jeremy Miles say, it is possible to fit an SEM using categorical data (i.e., which includes your dichotomous and ordinal variables). There are generally two methods u | Lavaan SEM Ordinal and Categorical variables
As both @Dimitris Rizopoulos and @Jeremy Miles say, it is possible to fit an SEM using categorical data (i.e., which includes your dichotomous and ordinal variables). There are generally two methods used to go about doing this$^1$. The first is the direct method, which treat... | Lavaan SEM Ordinal and Categorical variables
As both @Dimitris Rizopoulos and @Jeremy Miles say, it is possible to fit an SEM using categorical data (i.e., which includes your dichotomous and ordinal variables). There are generally two methods u |
54,150 | Lavaan SEM Ordinal and Categorical variables | Ordinal and binary variables are fine in SEM.
The fact that the model does not converge is (mostly) unrelated. We need more information to diagnose that. | Lavaan SEM Ordinal and Categorical variables | Ordinal and binary variables are fine in SEM.
The fact that the model does not converge is (mostly) unrelated. We need more information to diagnose that. | Lavaan SEM Ordinal and Categorical variables
Ordinal and binary variables are fine in SEM.
The fact that the model does not converge is (mostly) unrelated. We need more information to diagnose that. | Lavaan SEM Ordinal and Categorical variables
Ordinal and binary variables are fine in SEM.
The fact that the model does not converge is (mostly) unrelated. We need more information to diagnose that. |
54,151 | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha? | I have found the answer on my question which can be explained geometrically very well.
We know that the complementary condition of the KKT-conditions says:
$$\alpha\geq0, \alpha(y_i(w^Tx_i + b) - 1) = 0$$
Therefore, in a KKT-Point at least one of the following cases happens:
Case 1: $\alpha_i=0$
Case 2: $y_i(w^Tx_i +b)... | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha? | I have found the answer on my question which can be explained geometrically very well.
We know that the complementary condition of the KKT-conditions says:
$$\alpha\geq0, \alpha(y_i(w^Tx_i + b) - 1) = | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha?
I have found the answer on my question which can be explained geometrically very well.
We know that the complementary condition of the KKT-conditions says:
$$\alpha\geq0, \alpha(y_i(w^Tx_i + b) - 1) = 0$$
Therefore, in a KKT-Point at le... | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha?
I have found the answer on my question which can be explained geometrically very well.
We know that the complementary condition of the KKT-conditions says:
$$\alpha\geq0, \alpha(y_i(w^Tx_i + b) - 1) = |
54,152 | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha? | A support is actually a vector whose $\alpha$ is non-zero. It is a definition, there is nothing to prove from the equation here. | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha? | A support is actually a vector whose $\alpha$ is non-zero. It is a definition, there is nothing to prove from the equation here. | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha?
A support is actually a vector whose $\alpha$ is non-zero. It is a definition, there is nothing to prove from the equation here. | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha?
A support is actually a vector whose $\alpha$ is non-zero. It is a definition, there is nothing to prove from the equation here. |
54,153 | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha? | Support vectors can be defined as those vectors that lie on the positive or negative hyperplane, i.e. those vectors for which $y_i (w^Tx_i + b) -1=0$. For non-support vectors, $y_i (w^Tx_i + b) -1$ is non zero.
The dual form of the Lagrange multiplier is given by:
$L_p = min_{w,b}max_{\alpha\geq 0} \left(\quad\dfrac{1}... | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha? | Support vectors can be defined as those vectors that lie on the positive or negative hyperplane, i.e. those vectors for which $y_i (w^Tx_i + b) -1=0$. For non-support vectors, $y_i (w^Tx_i + b) -1$ is | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha?
Support vectors can be defined as those vectors that lie on the positive or negative hyperplane, i.e. those vectors for which $y_i (w^Tx_i + b) -1=0$. For non-support vectors, $y_i (w^Tx_i + b) -1$ is non zero.
The dual form of the Lagr... | SVM: Why alpha for non support vector is zero and why most vectors have zero alpha?
Support vectors can be defined as those vectors that lie on the positive or negative hyperplane, i.e. those vectors for which $y_i (w^Tx_i + b) -1=0$. For non-support vectors, $y_i (w^Tx_i + b) -1$ is |
54,154 | Computing Highest Density Region given multivariate normal distribution with dimension $d$ > 3 | The highest density region of an $N(0,H)$ random variable is an ellipsoid centered at its mean, $0$, and oriented per the covariance matrix $H$. The cutoff value for the ellipsoid can be determined from the Chi-square with $d$ degrees of freedom.
Let $y =$ value such that Chi-square with $d$ degrees of freedom $\le 0.... | Computing Highest Density Region given multivariate normal distribution with dimension $d$ > 3 | The highest density region of an $N(0,H)$ random variable is an ellipsoid centered at its mean, $0$, and oriented per the covariance matrix $H$. The cutoff value for the ellipsoid can be determined f | Computing Highest Density Region given multivariate normal distribution with dimension $d$ > 3
The highest density region of an $N(0,H)$ random variable is an ellipsoid centered at its mean, $0$, and oriented per the covariance matrix $H$. The cutoff value for the ellipsoid can be determined from the Chi-square with $... | Computing Highest Density Region given multivariate normal distribution with dimension $d$ > 3
The highest density region of an $N(0,H)$ random variable is an ellipsoid centered at its mean, $0$, and oriented per the covariance matrix $H$. The cutoff value for the ellipsoid can be determined f |
54,155 | Does decision tree need to use the same feature to split in the same layer? | The second option.
There's no reason to constrain a tree to split on the same variable at all nodes at a given level. | Does decision tree need to use the same feature to split in the same layer? | The second option.
There's no reason to constrain a tree to split on the same variable at all nodes at a given level. | Does decision tree need to use the same feature to split in the same layer?
The second option.
There's no reason to constrain a tree to split on the same variable at all nodes at a given level. | Does decision tree need to use the same feature to split in the same layer?
The second option.
There's no reason to constrain a tree to split on the same variable at all nodes at a given level. |
54,156 | Does decision tree need to use the same feature to split in the same layer? | Actually, there is a reason to do such a thing. Moreover, sometimes both a feature and a threshold are the same for the whole level.
Read about oblivious decision trees used in CatBoost algorithm - https://towardsdatascience.com/introduction-to-gradient-boosting-on-decision-trees-with-catboost-d511a9ccbd14
Such trees p... | Does decision tree need to use the same feature to split in the same layer? | Actually, there is a reason to do such a thing. Moreover, sometimes both a feature and a threshold are the same for the whole level.
Read about oblivious decision trees used in CatBoost algorithm - ht | Does decision tree need to use the same feature to split in the same layer?
Actually, there is a reason to do such a thing. Moreover, sometimes both a feature and a threshold are the same for the whole level.
Read about oblivious decision trees used in CatBoost algorithm - https://towardsdatascience.com/introduction-to... | Does decision tree need to use the same feature to split in the same layer?
Actually, there is a reason to do such a thing. Moreover, sometimes both a feature and a threshold are the same for the whole level.
Read about oblivious decision trees used in CatBoost algorithm - ht |
54,157 | Constant of Laplace approximation | This example is indeed rather poorly conducted and full of typos, apologies from one author!!!
First, there is no genuine $n$ (or related sample size) in the picture so the Laplace approximation cannot be universally adequate. The only thing that can replace $n$ in the integral
$$
\int_a^b \dfrac{x^{\alpha-1}}{\Gamma... | Constant of Laplace approximation | This example is indeed rather poorly conducted and full of typos, apologies from one author!!!
First, there is no genuine $n$ (or related sample size) in the picture so the Laplace approximation cann | Constant of Laplace approximation
This example is indeed rather poorly conducted and full of typos, apologies from one author!!!
First, there is no genuine $n$ (or related sample size) in the picture so the Laplace approximation cannot be universally adequate. The only thing that can replace $n$ in the integral
$$
\i... | Constant of Laplace approximation
This example is indeed rather poorly conducted and full of typos, apologies from one author!!!
First, there is no genuine $n$ (or related sample size) in the picture so the Laplace approximation cann |
54,158 | Survival Analysis or Not? | I agree that if there is no censoring, it is probably not really necessary to use the survival analysis. However, I would point out that the goal of your work is very important. If you just want to make a predictive model, then it actually does not matter which method you use as long as it gives you good (it is up to y... | Survival Analysis or Not? | I agree that if there is no censoring, it is probably not really necessary to use the survival analysis. However, I would point out that the goal of your work is very important. If you just want to ma | Survival Analysis or Not?
I agree that if there is no censoring, it is probably not really necessary to use the survival analysis. However, I would point out that the goal of your work is very important. If you just want to make a predictive model, then it actually does not matter which method you use as long as it giv... | Survival Analysis or Not?
I agree that if there is no censoring, it is probably not really necessary to use the survival analysis. However, I would point out that the goal of your work is very important. If you just want to ma |
54,159 | Survival Analysis or Not? | Survival Analysis does not require that your data be censored. Though not having censored data certainty does give you substantially more options regarding your choice of models.
The main factors that you should use to determine whether survival analysis is appropriate are:
Does the "time" component fit the distributi... | Survival Analysis or Not? | Survival Analysis does not require that your data be censored. Though not having censored data certainty does give you substantially more options regarding your choice of models.
The main factors that | Survival Analysis or Not?
Survival Analysis does not require that your data be censored. Though not having censored data certainty does give you substantially more options regarding your choice of models.
The main factors that you should use to determine whether survival analysis is appropriate are:
Does the "time" co... | Survival Analysis or Not?
Survival Analysis does not require that your data be censored. Though not having censored data certainty does give you substantially more options regarding your choice of models.
The main factors that |
54,160 | Survival Analysis or Not? | Stripped down to its mathematical technicalities, survival analysis is essentially just the analysis of continuous non-negative random variables, and certain common compositions of these random variables (e.g., looking at minimums or maximums of these random variables). While survival analysis can accommodate censored... | Survival Analysis or Not? | Stripped down to its mathematical technicalities, survival analysis is essentially just the analysis of continuous non-negative random variables, and certain common compositions of these random variab | Survival Analysis or Not?
Stripped down to its mathematical technicalities, survival analysis is essentially just the analysis of continuous non-negative random variables, and certain common compositions of these random variables (e.g., looking at minimums or maximums of these random variables). While survival analysi... | Survival Analysis or Not?
Stripped down to its mathematical technicalities, survival analysis is essentially just the analysis of continuous non-negative random variables, and certain common compositions of these random variab |
54,161 | How to find the expectation $\mathbb{E} \left[ \frac{|h|^4}{|h+w|^2} \right]$? | The expectation is infinite.
One way to see this is to condition on $H$. Preliminary changes of variable (merely involving rescaling $H$ and $W$ and then shifting to a new origin) reduce the conditional expectation to a positive constant times a two-dimensional integral of the form
$$\mathcal{I}(\lambda)=\iint_{\mathb... | How to find the expectation $\mathbb{E} \left[ \frac{|h|^4}{|h+w|^2} \right]$? | The expectation is infinite.
One way to see this is to condition on $H$. Preliminary changes of variable (merely involving rescaling $H$ and $W$ and then shifting to a new origin) reduce the conditio | How to find the expectation $\mathbb{E} \left[ \frac{|h|^4}{|h+w|^2} \right]$?
The expectation is infinite.
One way to see this is to condition on $H$. Preliminary changes of variable (merely involving rescaling $H$ and $W$ and then shifting to a new origin) reduce the conditional expectation to a positive constant ti... | How to find the expectation $\mathbb{E} \left[ \frac{|h|^4}{|h+w|^2} \right]$?
The expectation is infinite.
One way to see this is to condition on $H$. Preliminary changes of variable (merely involving rescaling $H$ and $W$ and then shifting to a new origin) reduce the conditio |
54,162 | In R package mgcv, is it valid to have a random effect smooth on two continuous variables? | Huh... I made my post as a guest on SO because I am still on a suspension, but then the question got migrated here!
So, if I understand you correctly, there's not really any similarity between the smooth s(x1, x2) and the random effect s(x1, x2, fac, bs = "re"), correct?
Correct. The function name "s" does not mean "... | In R package mgcv, is it valid to have a random effect smooth on two continuous variables? | Huh... I made my post as a guest on SO because I am still on a suspension, but then the question got migrated here!
So, if I understand you correctly, there's not really any similarity between the sm | In R package mgcv, is it valid to have a random effect smooth on two continuous variables?
Huh... I made my post as a guest on SO because I am still on a suspension, but then the question got migrated here!
So, if I understand you correctly, there's not really any similarity between the smooth s(x1, x2) and the random... | In R package mgcv, is it valid to have a random effect smooth on two continuous variables?
Huh... I made my post as a guest on SO because I am still on a suspension, but then the question got migrated here!
So, if I understand you correctly, there's not really any similarity between the sm |
54,163 | In R package mgcv, is it valid to have a random effect smooth on two continuous variables? | Consider the random effect part of your example
toy <- gam(y ~ s(x0, fac, bs = "re") + s(x1, x2, fac, bs="re"),
data = dat, method = "REML")
This is just the penalized version of the following linear regression model:
toy.lm <- lm(y ~ x0:fac + x1:x2:fac, data = dat)
where a ridge penalty is applied to x0:f... | In R package mgcv, is it valid to have a random effect smooth on two continuous variables? | Consider the random effect part of your example
toy <- gam(y ~ s(x0, fac, bs = "re") + s(x1, x2, fac, bs="re"),
data = dat, method = "REML")
This is just the penalized version of the follo | In R package mgcv, is it valid to have a random effect smooth on two continuous variables?
Consider the random effect part of your example
toy <- gam(y ~ s(x0, fac, bs = "re") + s(x1, x2, fac, bs="re"),
data = dat, method = "REML")
This is just the penalized version of the following linear regression model:... | In R package mgcv, is it valid to have a random effect smooth on two continuous variables?
Consider the random effect part of your example
toy <- gam(y ~ s(x0, fac, bs = "re") + s(x1, x2, fac, bs="re"),
data = dat, method = "REML")
This is just the penalized version of the follo |
54,164 | Why not set a static first layer in CNN? | My question is why don't we just set the first layer with static filters that find various angles of lines, and only train the rest?
Based on your description, what you are suggesting is called Extreme Learning Machine (ELM).
These are specific types of feed-forward neural networks that basically are different from th... | Why not set a static first layer in CNN? | My question is why don't we just set the first layer with static filters that find various angles of lines, and only train the rest?
Based on your description, what you are suggesting is called Extre | Why not set a static first layer in CNN?
My question is why don't we just set the first layer with static filters that find various angles of lines, and only train the rest?
Based on your description, what you are suggesting is called Extreme Learning Machine (ELM).
These are specific types of feed-forward neural netw... | Why not set a static first layer in CNN?
My question is why don't we just set the first layer with static filters that find various angles of lines, and only train the rest?
Based on your description, what you are suggesting is called Extre |
54,165 | Why not set a static first layer in CNN? | It seems like a lot of work to me for minimal benefit. Having one more layer to backprop through when there may already be many tens of layers means that it doesn't help to hard-code the filters performance wise.
In addition, you only artificially limit yourself -- we know CNNs tend to learn gabor filters in the first ... | Why not set a static first layer in CNN? | It seems like a lot of work to me for minimal benefit. Having one more layer to backprop through when there may already be many tens of layers means that it doesn't help to hard-code the filters perfo | Why not set a static first layer in CNN?
It seems like a lot of work to me for minimal benefit. Having one more layer to backprop through when there may already be many tens of layers means that it doesn't help to hard-code the filters performance wise.
In addition, you only artificially limit yourself -- we know CNNs ... | Why not set a static first layer in CNN?
It seems like a lot of work to me for minimal benefit. Having one more layer to backprop through when there may already be many tens of layers means that it doesn't help to hard-code the filters perfo |
54,166 | Why not set a static first layer in CNN? | The following quote from the 2002 review paper explains the role of preset initial layers in neural networks for image processing.
"According to Perlovsky, the key to restraining the highly Flexible learning algorithms for ANNs,
lies in the very combination with prior (geometric) knowledge. However, most pattern recog... | Why not set a static first layer in CNN? | The following quote from the 2002 review paper explains the role of preset initial layers in neural networks for image processing.
"According to Perlovsky, the key to restraining the highly Flexible l | Why not set a static first layer in CNN?
The following quote from the 2002 review paper explains the role of preset initial layers in neural networks for image processing.
"According to Perlovsky, the key to restraining the highly Flexible learning algorithms for ANNs,
lies in the very combination with prior (geometri... | Why not set a static first layer in CNN?
The following quote from the 2002 review paper explains the role of preset initial layers in neural networks for image processing.
"According to Perlovsky, the key to restraining the highly Flexible l |
54,167 | KL divergence invariant to affine transformation? | There are a few mistakes in your math. For example, when you expand the expectation, it seems you dropped the integral and also the $P_1(x)$ term.
Write $y(x) = mx + c$. Recall that $P(x) dx = P(y) dy$. This is easy to see since $dy/dx = m$ and it makes sense that $P(x) = mP(y)$.
Then we can go through with this proof... | KL divergence invariant to affine transformation? | There are a few mistakes in your math. For example, when you expand the expectation, it seems you dropped the integral and also the $P_1(x)$ term.
Write $y(x) = mx + c$. Recall that $P(x) dx = P(y) dy | KL divergence invariant to affine transformation?
There are a few mistakes in your math. For example, when you expand the expectation, it seems you dropped the integral and also the $P_1(x)$ term.
Write $y(x) = mx + c$. Recall that $P(x) dx = P(y) dy$. This is easy to see since $dy/dx = m$ and it makes sense that $P(x)... | KL divergence invariant to affine transformation?
There are a few mistakes in your math. For example, when you expand the expectation, it seems you dropped the integral and also the $P_1(x)$ term.
Write $y(x) = mx + c$. Recall that $P(x) dx = P(y) dy |
54,168 | KL divergence invariant to affine transformation? | I made a serious mistake while calculating the $KL$ divergence between the two 1D normal distributions. It is this mistake that causes me to doubt whether $KL$ divergence is invariant to affine transformation.
Where did I make the mistake:
When evaluating the expected value of $$(x' - \mu_1)^2$$ over the distribution $... | KL divergence invariant to affine transformation? | I made a serious mistake while calculating the $KL$ divergence between the two 1D normal distributions. It is this mistake that causes me to doubt whether $KL$ divergence is invariant to affine transf | KL divergence invariant to affine transformation?
I made a serious mistake while calculating the $KL$ divergence between the two 1D normal distributions. It is this mistake that causes me to doubt whether $KL$ divergence is invariant to affine transformation.
Where did I make the mistake:
When evaluating the expected v... | KL divergence invariant to affine transformation?
I made a serious mistake while calculating the $KL$ divergence between the two 1D normal distributions. It is this mistake that causes me to doubt whether $KL$ divergence is invariant to affine transf |
54,169 | Mixed-effect model single term deletion -- should I change my random effects? | As a rule for lme4 and other packages with a similar parameterization (at least at the level of the user interface), it does not make sense to have random slopes for terms not present in the fixed effects.
The reason for this is straightforward: the random effects (or more precisely, the BLUPs / conditional modes) are... | Mixed-effect model single term deletion -- should I change my random effects? | As a rule for lme4 and other packages with a similar parameterization (at least at the level of the user interface), it does not make sense to have random slopes for terms not present in the fixed eff | Mixed-effect model single term deletion -- should I change my random effects?
As a rule for lme4 and other packages with a similar parameterization (at least at the level of the user interface), it does not make sense to have random slopes for terms not present in the fixed effects.
The reason for this is straightforw... | Mixed-effect model single term deletion -- should I change my random effects?
As a rule for lme4 and other packages with a similar parameterization (at least at the level of the user interface), it does not make sense to have random slopes for terms not present in the fixed eff |
54,170 | Identify the original variable used to calculate the dummies | This answer suggests there is value in a graphical exploration of relationships among the variables and illustrates one useful way. It then provides a simple solution that rapidly and automatically identifies all possible variables that might be represented by a given categorical variable.
You can explore graphically... | Identify the original variable used to calculate the dummies | This answer suggests there is value in a graphical exploration of relationships among the variables and illustrates one useful way. It then provides a simple solution that rapidly and automatically i | Identify the original variable used to calculate the dummies
This answer suggests there is value in a graphical exploration of relationships among the variables and illustrates one useful way. It then provides a simple solution that rapidly and automatically identifies all possible variables that might be represented ... | Identify the original variable used to calculate the dummies
This answer suggests there is value in a graphical exploration of relationships among the variables and illustrates one useful way. It then provides a simple solution that rapidly and automatically i |
54,171 | Identify the original variable used to calculate the dummies | If you can perfectly reconstruct the dummies from a candidate predictor, then the dummies and the predictor carry the same information. If the dummies encode intervals of the predictor (the most common way of discretizing continuous predictors, which is a bad idea, as discussed often here on CV, but that's not the focu... | Identify the original variable used to calculate the dummies | If you can perfectly reconstruct the dummies from a candidate predictor, then the dummies and the predictor carry the same information. If the dummies encode intervals of the predictor (the most commo | Identify the original variable used to calculate the dummies
If you can perfectly reconstruct the dummies from a candidate predictor, then the dummies and the predictor carry the same information. If the dummies encode intervals of the predictor (the most common way of discretizing continuous predictors, which is a bad... | Identify the original variable used to calculate the dummies
If you can perfectly reconstruct the dummies from a candidate predictor, then the dummies and the predictor carry the same information. If the dummies encode intervals of the predictor (the most commo |
54,172 | Identify the original variable used to calculate the dummies | To detect that age2...5 are constructed from the same variable, you can check if the sum of those dummy variables equals 1 :
all(age2+age3+age4+age5==1)
But I don't know if there is a way to check if they come specifically from the variable age, it could be any other variable in the dataframe. | Identify the original variable used to calculate the dummies | To detect that age2...5 are constructed from the same variable, you can check if the sum of those dummy variables equals 1 :
all(age2+age3+age4+age5==1)
But I don't know if there is a way to check if | Identify the original variable used to calculate the dummies
To detect that age2...5 are constructed from the same variable, you can check if the sum of those dummy variables equals 1 :
all(age2+age3+age4+age5==1)
But I don't know if there is a way to check if they come specifically from the variable age, it could be ... | Identify the original variable used to calculate the dummies
To detect that age2...5 are constructed from the same variable, you can check if the sum of those dummy variables equals 1 :
all(age2+age3+age4+age5==1)
But I don't know if there is a way to check if |
54,173 | Continuous Version of Coupon-Collector Problem | This question reminds me of Wilfrid Kendall's dead leaves
simulation, which he uses to explain the difference between
forward and backward sampling.
Given that the problem can be formalised through uniform spacings, this highly detailed answer on CV is connected with this question.
Indeed, if $U_1,\ldots,U_T$ deno... | Continuous Version of Coupon-Collector Problem | This question reminds me of Wilfrid Kendall's dead leaves
simulation, which he uses to explain the difference between
forward and backward sampling.
Given that the problem can be formalised throu | Continuous Version of Coupon-Collector Problem
This question reminds me of Wilfrid Kendall's dead leaves
simulation, which he uses to explain the difference between
forward and backward sampling.
Given that the problem can be formalised through uniform spacings, this highly detailed answer on CV is connected with ... | Continuous Version of Coupon-Collector Problem
This question reminds me of Wilfrid Kendall's dead leaves
simulation, which he uses to explain the difference between
forward and backward sampling.
Given that the problem can be formalised throu |
54,174 | How to calculate the standard deviation for a Gaussian Process? | The closed form equation for the predicted covariance inverts $K(x_d, x_d)$. However, using the Cholesky decomposition is faster and more numerically stable than directly taking the inverse. You can see the procedure laid out in Algorithm 2.1 of Gaussian Processes for Machine Learning. However, they don't show why they... | How to calculate the standard deviation for a Gaussian Process? | The closed form equation for the predicted covariance inverts $K(x_d, x_d)$. However, using the Cholesky decomposition is faster and more numerically stable than directly taking the inverse. You can s | How to calculate the standard deviation for a Gaussian Process?
The closed form equation for the predicted covariance inverts $K(x_d, x_d)$. However, using the Cholesky decomposition is faster and more numerically stable than directly taking the inverse. You can see the procedure laid out in Algorithm 2.1 of Gaussian P... | How to calculate the standard deviation for a Gaussian Process?
The closed form equation for the predicted covariance inverts $K(x_d, x_d)$. However, using the Cholesky decomposition is faster and more numerically stable than directly taking the inverse. You can s |
54,175 | E[X| X>Y] for independent X, Y ~ N(0,1) | Rewriting and using linearity of expectation,
$$
E[X | X > Y] = E[X | X - Y > 0] = E[X - Y | X - Y > 0] + E[Y | X - Y > 0].
$$
Define now $X' = -X, Y' = -Y$. Then
$$
E[Y | X - Y > 0] = E[-Y' | Y' - X' > 0] = -E[Y' | Y' - X' > 0].
$$
However, note that $Y', X' \sim X, Y$, so we have $E[Y' | Y' - X' > 0] = E[X | X - Y > ... | E[X| X>Y] for independent X, Y ~ N(0,1) | Rewriting and using linearity of expectation,
$$
E[X | X > Y] = E[X | X - Y > 0] = E[X - Y | X - Y > 0] + E[Y | X - Y > 0].
$$
Define now $X' = -X, Y' = -Y$. Then
$$
E[Y | X - Y > 0] = E[-Y' | Y' - X' | E[X| X>Y] for independent X, Y ~ N(0,1)
Rewriting and using linearity of expectation,
$$
E[X | X > Y] = E[X | X - Y > 0] = E[X - Y | X - Y > 0] + E[Y | X - Y > 0].
$$
Define now $X' = -X, Y' = -Y$. Then
$$
E[Y | X - Y > 0] = E[-Y' | Y' - X' > 0] = -E[Y' | Y' - X' > 0].
$$
However, note that $Y', X' \sim X, Y$, so we ha... | E[X| X>Y] for independent X, Y ~ N(0,1)
Rewriting and using linearity of expectation,
$$
E[X | X > Y] = E[X | X - Y > 0] = E[X - Y | X - Y > 0] + E[Y | X - Y > 0].
$$
Define now $X' = -X, Y' = -Y$. Then
$$
E[Y | X - Y > 0] = E[-Y' | Y' - X' |
54,176 | The purpose of threshold in naive bayes algorithm | In short: The threshold is not a part of the Naive Bayes algorithm
A Naive Bayes algorithm will be able to say for a certain sample, that the probability of it being of C1 is 60% and of C2 is 40%. Then it's up to you to interpret this as a classification in class C1, which would be the case for a 50% threshold. When us... | The purpose of threshold in naive bayes algorithm | In short: The threshold is not a part of the Naive Bayes algorithm
A Naive Bayes algorithm will be able to say for a certain sample, that the probability of it being of C1 is 60% and of C2 is 40%. The | The purpose of threshold in naive bayes algorithm
In short: The threshold is not a part of the Naive Bayes algorithm
A Naive Bayes algorithm will be able to say for a certain sample, that the probability of it being of C1 is 60% and of C2 is 40%. Then it's up to you to interpret this as a classification in class C1, wh... | The purpose of threshold in naive bayes algorithm
In short: The threshold is not a part of the Naive Bayes algorithm
A Naive Bayes algorithm will be able to say for a certain sample, that the probability of it being of C1 is 60% and of C2 is 40%. The |
54,177 | What does word embedding weighted by tf-idf mean? | This quote is clearly talking about sentence embeddings, obtained from word embeddings.
If the sentence $s$ consists of words $(w_1, ..., w_n)$, we'd like to define an embedding vector $Emb_s(s) \in \mathbb{R}^d$ for some $d > 0$.
The authors of this paper propose to compute it from the embeddings of words $w_i$, let'... | What does word embedding weighted by tf-idf mean? | This quote is clearly talking about sentence embeddings, obtained from word embeddings.
If the sentence $s$ consists of words $(w_1, ..., w_n)$, we'd like to define an embedding vector $Emb_s(s) \in \ | What does word embedding weighted by tf-idf mean?
This quote is clearly talking about sentence embeddings, obtained from word embeddings.
If the sentence $s$ consists of words $(w_1, ..., w_n)$, we'd like to define an embedding vector $Emb_s(s) \in \mathbb{R}^d$ for some $d > 0$.
The authors of this paper propose to c... | What does word embedding weighted by tf-idf mean?
This quote is clearly talking about sentence embeddings, obtained from word embeddings.
If the sentence $s$ consists of words $(w_1, ..., w_n)$, we'd like to define an embedding vector $Emb_s(s) \in \ |
54,178 | Why is two-sided gradient checking more accurate? [closed] | One way to look at this is by Taylor approximation. Remember
$$f(x+\Delta x)\approx f(x)+\Delta x f'(x)+\frac 1 2 \Delta x^2 f''(x)+\frac 1 6 \Delta x^3f'''(x)+\dots$$
One sided looks like this
$$\frac{f(x+\Delta x)-f(x)}{\Delta x}\approx f'(x)+\frac 1 2 \Delta x f''(x)$$
Two sided looks like this
$$\frac{f(x+\Delta... | Why is two-sided gradient checking more accurate? [closed] | One way to look at this is by Taylor approximation. Remember
$$f(x+\Delta x)\approx f(x)+\Delta x f'(x)+\frac 1 2 \Delta x^2 f''(x)+\frac 1 6 \Delta x^3f'''(x)+\dots$$
One sided looks like this
$$\f | Why is two-sided gradient checking more accurate? [closed]
One way to look at this is by Taylor approximation. Remember
$$f(x+\Delta x)\approx f(x)+\Delta x f'(x)+\frac 1 2 \Delta x^2 f''(x)+\frac 1 6 \Delta x^3f'''(x)+\dots$$
One sided looks like this
$$\frac{f(x+\Delta x)-f(x)}{\Delta x}\approx f'(x)+\frac 1 2 \Del... | Why is two-sided gradient checking more accurate? [closed]
One way to look at this is by Taylor approximation. Remember
$$f(x+\Delta x)\approx f(x)+\Delta x f'(x)+\frac 1 2 \Delta x^2 f''(x)+\frac 1 6 \Delta x^3f'''(x)+\dots$$
One sided looks like this
$$\f |
54,179 | Why is two-sided gradient checking more accurate? [closed] | For a theoretical analysis you need to read a book on numerical analysis. But intuitively it seems reasonable to appriximate the tangent line with a secant between two point symmetric about the point of tangency. Lets look at a simple numerical example, let $f(x)=x^2$ and we are interested in the derivative at $x_0=0$,... | Why is two-sided gradient checking more accurate? [closed] | For a theoretical analysis you need to read a book on numerical analysis. But intuitively it seems reasonable to appriximate the tangent line with a secant between two point symmetric about the point | Why is two-sided gradient checking more accurate? [closed]
For a theoretical analysis you need to read a book on numerical analysis. But intuitively it seems reasonable to appriximate the tangent line with a secant between two point symmetric about the point of tangency. Lets look at a simple numerical example, let $f(... | Why is two-sided gradient checking more accurate? [closed]
For a theoretical analysis you need to read a book on numerical analysis. But intuitively it seems reasonable to appriximate the tangent line with a secant between two point symmetric about the point |
54,180 | Can random forest based feature selection method be used for multiple regression in machine learning | Firstly, a method that first looks at univariate correlations for pre-identifying things that should go into a final model, will tend to do badly for a number of reasons: ignoring model uncertainy (single selected model), using statistical significance/strength of correlation as a criterion to select (if it is about pr... | Can random forest based feature selection method be used for multiple regression in machine learning | Firstly, a method that first looks at univariate correlations for pre-identifying things that should go into a final model, will tend to do badly for a number of reasons: ignoring model uncertainy (si | Can random forest based feature selection method be used for multiple regression in machine learning
Firstly, a method that first looks at univariate correlations for pre-identifying things that should go into a final model, will tend to do badly for a number of reasons: ignoring model uncertainy (single selected model... | Can random forest based feature selection method be used for multiple regression in machine learning
Firstly, a method that first looks at univariate correlations for pre-identifying things that should go into a final model, will tend to do badly for a number of reasons: ignoring model uncertainy (si |
54,181 | Can random forest based feature selection method be used for multiple regression in machine learning | There are also variable selection methods (e.g. forward or backward) with the AIC or BIC. Be aware, that interpretation of p-values after variable selection is not any more completely correct. Search "post-selection inference" for more informations about this. | Can random forest based feature selection method be used for multiple regression in machine learning | There are also variable selection methods (e.g. forward or backward) with the AIC or BIC. Be aware, that interpretation of p-values after variable selection is not any more completely correct. Search | Can random forest based feature selection method be used for multiple regression in machine learning
There are also variable selection methods (e.g. forward or backward) with the AIC or BIC. Be aware, that interpretation of p-values after variable selection is not any more completely correct. Search "post-selection inf... | Can random forest based feature selection method be used for multiple regression in machine learning
There are also variable selection methods (e.g. forward or backward) with the AIC or BIC. Be aware, that interpretation of p-values after variable selection is not any more completely correct. Search |
54,182 | Can k-NN be ensembled? | Sure, k-NN can be ensembled. You could, for example, use resampling to generate different models (like with a Random Forest), or you could vary N, or you could use different functions for computing the distance. But, my experience is that k-NN rarely does well in high dimensional problems, so it would just be an ensemb... | Can k-NN be ensembled? | Sure, k-NN can be ensembled. You could, for example, use resampling to generate different models (like with a Random Forest), or you could vary N, or you could use different functions for computing th | Can k-NN be ensembled?
Sure, k-NN can be ensembled. You could, for example, use resampling to generate different models (like with a Random Forest), or you could vary N, or you could use different functions for computing the distance. But, my experience is that k-NN rarely does well in high dimensional problems, so it ... | Can k-NN be ensembled?
Sure, k-NN can be ensembled. You could, for example, use resampling to generate different models (like with a Random Forest), or you could vary N, or you could use different functions for computing th |
54,183 | Can k-NN be ensembled? | I see four abstract ways to do so from simplest to more complex.
By applying $k$-NN in different Random Projections latent space or other (eg Neural network autoencoder latent space) and combine them.
that is: $Ensemble(kNN_{raw},kNN_{projected}) $
apply different colaborative filtering scores eg. average distance, m... | Can k-NN be ensembled? | I see four abstract ways to do so from simplest to more complex.
By applying $k$-NN in different Random Projections latent space or other (eg Neural network autoencoder latent space) and combine them | Can k-NN be ensembled?
I see four abstract ways to do so from simplest to more complex.
By applying $k$-NN in different Random Projections latent space or other (eg Neural network autoencoder latent space) and combine them.
that is: $Ensemble(kNN_{raw},kNN_{projected}) $
apply different colaborative filtering scores ... | Can k-NN be ensembled?
I see four abstract ways to do so from simplest to more complex.
By applying $k$-NN in different Random Projections latent space or other (eg Neural network autoencoder latent space) and combine them |
54,184 | No change in accuracy using Adam Optimizer when SGD works fine | The benefits of Adam can be marginal, at best. The initial results were strong, but there is evidence that Adam converges to dramatically different minima compared to SGD (or SGD + momentum).
"The Marginal Value of Adaptive Gradient Methods in Machine Learning"
Ashia C. Wilson, Rebecca Roelofs, Mitchell Stern, Nathan S... | No change in accuracy using Adam Optimizer when SGD works fine | The benefits of Adam can be marginal, at best. The initial results were strong, but there is evidence that Adam converges to dramatically different minima compared to SGD (or SGD + momentum).
"The Mar | No change in accuracy using Adam Optimizer when SGD works fine
The benefits of Adam can be marginal, at best. The initial results were strong, but there is evidence that Adam converges to dramatically different minima compared to SGD (or SGD + momentum).
"The Marginal Value of Adaptive Gradient Methods in Machine Learn... | No change in accuracy using Adam Optimizer when SGD works fine
The benefits of Adam can be marginal, at best. The initial results were strong, but there is evidence that Adam converges to dramatically different minima compared to SGD (or SGD + momentum).
"The Mar |
54,185 | ARIMA, what is the interpretation for the sum of AR coefficients? | Just rearrange your $\text{AR}(p)$ polynomial $\phi(z) = 1 - \phi_1 z - \cdots - \phi_p z^p$. If $z'$ is a root, then $1 - \phi_1 z' - \cdots - \phi_p (z')^p = 0$. If $z'$ is a unit root, then you can rearrange that to get
$$
\sum_i \phi_i = 1.
$$
This suggests you can write your $\text{AR}(p)$ polynomial as $\phi(z) =... | ARIMA, what is the interpretation for the sum of AR coefficients? | Just rearrange your $\text{AR}(p)$ polynomial $\phi(z) = 1 - \phi_1 z - \cdots - \phi_p z^p$. If $z'$ is a root, then $1 - \phi_1 z' - \cdots - \phi_p (z')^p = 0$. If $z'$ is a unit root, then you can | ARIMA, what is the interpretation for the sum of AR coefficients?
Just rearrange your $\text{AR}(p)$ polynomial $\phi(z) = 1 - \phi_1 z - \cdots - \phi_p z^p$. If $z'$ is a root, then $1 - \phi_1 z' - \cdots - \phi_p (z')^p = 0$. If $z'$ is a unit root, then you can rearrange that to get
$$
\sum_i \phi_i = 1.
$$
This s... | ARIMA, what is the interpretation for the sum of AR coefficients?
Just rearrange your $\text{AR}(p)$ polynomial $\phi(z) = 1 - \phi_1 z - \cdots - \phi_p z^p$. If $z'$ is a root, then $1 - \phi_1 z' - \cdots - \phi_p (z')^p = 0$. If $z'$ is a unit root, then you can |
54,186 | ARIMA, what is the interpretation for the sum of AR coefficients? | Differencing like any other transformations like power transformations should only be done when deemed necessary. Assuming ( which I would never do ! ) that the exogenous predictors only have a contemporaneous effect , compute a regression , study the error processs's acf/pacf and cautiously/iteratively construct/iden... | ARIMA, what is the interpretation for the sum of AR coefficients? | Differencing like any other transformations like power transformations should only be done when deemed necessary. Assuming ( which I would never do ! ) that the exogenous predictors only have a conte | ARIMA, what is the interpretation for the sum of AR coefficients?
Differencing like any other transformations like power transformations should only be done when deemed necessary. Assuming ( which I would never do ! ) that the exogenous predictors only have a contemporaneous effect , compute a regression , study the e... | ARIMA, what is the interpretation for the sum of AR coefficients?
Differencing like any other transformations like power transformations should only be done when deemed necessary. Assuming ( which I would never do ! ) that the exogenous predictors only have a conte |
54,187 | Intuition for why sum of gaussian RVs is different from gaussian mixture | Forget the Gaussian part for a moment. Compare these two simple situations:
A) take a coin whose two sides are marked with 0 and 1 and a die with 20 sides numbered 1 to 20. Toss the coin and roll the die --- and add the results to get a total.
Consider these questions (and hints):
What's the chance you get a total of 0... | Intuition for why sum of gaussian RVs is different from gaussian mixture | Forget the Gaussian part for a moment. Compare these two simple situations:
A) take a coin whose two sides are marked with 0 and 1 and a die with 20 sides numbered 1 to 20. Toss the coin and roll the | Intuition for why sum of gaussian RVs is different from gaussian mixture
Forget the Gaussian part for a moment. Compare these two simple situations:
A) take a coin whose two sides are marked with 0 and 1 and a die with 20 sides numbered 1 to 20. Toss the coin and roll the die --- and add the results to get a total.
Con... | Intuition for why sum of gaussian RVs is different from gaussian mixture
Forget the Gaussian part for a moment. Compare these two simple situations:
A) take a coin whose two sides are marked with 0 and 1 and a die with 20 sides numbered 1 to 20. Toss the coin and roll the |
54,188 | When is $\mathbb{E}\left[\frac{1}{\sum X_{i}}\right] = \frac{1}{\mathbb{E}\left[\sum X_{i}\right]}$? [duplicate] | First note that the random variable $X_i$ is not defined on 0. So assume, for now that $X_i$s are defined on the positive reals. On the positive reals, the function $f(x) = 1/x$ is a convex function. Thus, using Jensen's inequality,
$$E \left[\dfrac{1}{\sum X_i} \right] \geq \dfrac{1}{E\left[ \sum X_i \right]} = \dfrac... | When is $\mathbb{E}\left[\frac{1}{\sum X_{i}}\right] = \frac{1}{\mathbb{E}\left[\sum X_{i}\right]}$? | First note that the random variable $X_i$ is not defined on 0. So assume, for now that $X_i$s are defined on the positive reals. On the positive reals, the function $f(x) = 1/x$ is a convex function. | When is $\mathbb{E}\left[\frac{1}{\sum X_{i}}\right] = \frac{1}{\mathbb{E}\left[\sum X_{i}\right]}$? [duplicate]
First note that the random variable $X_i$ is not defined on 0. So assume, for now that $X_i$s are defined on the positive reals. On the positive reals, the function $f(x) = 1/x$ is a convex function. Thus, u... | When is $\mathbb{E}\left[\frac{1}{\sum X_{i}}\right] = \frac{1}{\mathbb{E}\left[\sum X_{i}\right]}$?
First note that the random variable $X_i$ is not defined on 0. So assume, for now that $X_i$s are defined on the positive reals. On the positive reals, the function $f(x) = 1/x$ is a convex function. |
54,189 | When is $\mathbb{E}\left[\frac{1}{\sum X_{i}}\right] = \frac{1}{\mathbb{E}\left[\sum X_{i}\right]}$? [duplicate] | I worked through some equations, with the original intention of showing that it is in fact true, but finally convincing myself that it might not be. In case it's useful, here is the working that convinced me that it might not be generally true:
Initially, I thought that expectation being a linear operator was going to ... | When is $\mathbb{E}\left[\frac{1}{\sum X_{i}}\right] = \frac{1}{\mathbb{E}\left[\sum X_{i}\right]}$? | I worked through some equations, with the original intention of showing that it is in fact true, but finally convincing myself that it might not be. In case it's useful, here is the working that convi | When is $\mathbb{E}\left[\frac{1}{\sum X_{i}}\right] = \frac{1}{\mathbb{E}\left[\sum X_{i}\right]}$? [duplicate]
I worked through some equations, with the original intention of showing that it is in fact true, but finally convincing myself that it might not be. In case it's useful, here is the working that convinced me... | When is $\mathbb{E}\left[\frac{1}{\sum X_{i}}\right] = \frac{1}{\mathbb{E}\left[\sum X_{i}\right]}$?
I worked through some equations, with the original intention of showing that it is in fact true, but finally convincing myself that it might not be. In case it's useful, here is the working that convi |
54,190 | Taylor approximation of expected value of multivariate function | Taylor series approximation of multivariate function $f$ around $x_0$ is
$$
f(x) \approx f(x_0) + \nabla f(x_0)'(x-x_0) + \frac{1}{2} (x-x_0)' H_f(x_0) (x-x_0).
$$
If you substitute $x=X$ and $x_0 = \mathbb{E}X$ you get
$$
f(X) \approx f(\mathbb{E}X) + \nabla f(\mathbb{E}X)'(X-\mathbb{E}X) + \frac{1}{2} (X-\mathbb{... | Taylor approximation of expected value of multivariate function | Taylor series approximation of multivariate function $f$ around $x_0$ is
$$
f(x) \approx f(x_0) + \nabla f(x_0)'(x-x_0) + \frac{1}{2} (x-x_0)' H_f(x_0) (x-x_0).
$$
If you substitute $x=X$ and $x_0 = | Taylor approximation of expected value of multivariate function
Taylor series approximation of multivariate function $f$ around $x_0$ is
$$
f(x) \approx f(x_0) + \nabla f(x_0)'(x-x_0) + \frac{1}{2} (x-x_0)' H_f(x_0) (x-x_0).
$$
If you substitute $x=X$ and $x_0 = \mathbb{E}X$ you get
$$
f(X) \approx f(\mathbb{E}X) + ... | Taylor approximation of expected value of multivariate function
Taylor series approximation of multivariate function $f$ around $x_0$ is
$$
f(x) \approx f(x_0) + \nabla f(x_0)'(x-x_0) + \frac{1}{2} (x-x_0)' H_f(x_0) (x-x_0).
$$
If you substitute $x=X$ and $x_0 = |
54,191 | Survival Analysis - Delayed Entry? | Your scenario raises the issue of selection bias.
In order for an individual to be selected for measurement into your study, they must survive until their first period of measurement, and as you point out each individual has a different time of entry. This effectively means that individuals who start later have periods... | Survival Analysis - Delayed Entry? | Your scenario raises the issue of selection bias.
In order for an individual to be selected for measurement into your study, they must survive until their first period of measurement, and as you point | Survival Analysis - Delayed Entry?
Your scenario raises the issue of selection bias.
In order for an individual to be selected for measurement into your study, they must survive until their first period of measurement, and as you point out each individual has a different time of entry. This effectively means that indiv... | Survival Analysis - Delayed Entry?
Your scenario raises the issue of selection bias.
In order for an individual to be selected for measurement into your study, they must survive until their first period of measurement, and as you point |
54,192 | Probability of a sample being drawn from a continuous distribution is zero; so how to choose a more likely distribution? | Your approach is not correct. For a moment let's forget about the distributions and simplify to asking about simpler question: given $X$, what is the probability that it comes from the class $C_i$?, i.e. $p(C_i | X)$, while what you propose is looking at the probability that $X=x$ given that it comes from $C_i$. Those ... | Probability of a sample being drawn from a continuous distribution is zero; so how to choose a more | Your approach is not correct. For a moment let's forget about the distributions and simplify to asking about simpler question: given $X$, what is the probability that it comes from the class $C_i$?, i | Probability of a sample being drawn from a continuous distribution is zero; so how to choose a more likely distribution?
Your approach is not correct. For a moment let's forget about the distributions and simplify to asking about simpler question: given $X$, what is the probability that it comes from the class $C_i$?, ... | Probability of a sample being drawn from a continuous distribution is zero; so how to choose a more
Your approach is not correct. For a moment let's forget about the distributions and simplify to asking about simpler question: given $X$, what is the probability that it comes from the class $C_i$?, i |
54,193 | Probability of a sample being drawn from a continuous distribution is zero; so how to choose a more likely distribution? | The purpose of this answer is simply to expand on the answer by @Tim.
Suppose the likelihood of the parameters given the sample can be expressed as
\begin{equation}
p(X|\theta) = \prod_{i=1}^n \textsf{N}(x_i|\mu,\sigma^2) ,
\end{equation}
where $X = (x_1, \ldots, x_n)$ is the sample and $\theta = (\mu,\sigma^2)$ are t... | Probability of a sample being drawn from a continuous distribution is zero; so how to choose a more | The purpose of this answer is simply to expand on the answer by @Tim.
Suppose the likelihood of the parameters given the sample can be expressed as
\begin{equation}
p(X|\theta) = \prod_{i=1}^n \texts | Probability of a sample being drawn from a continuous distribution is zero; so how to choose a more likely distribution?
The purpose of this answer is simply to expand on the answer by @Tim.
Suppose the likelihood of the parameters given the sample can be expressed as
\begin{equation}
p(X|\theta) = \prod_{i=1}^n \text... | Probability of a sample being drawn from a continuous distribution is zero; so how to choose a more
The purpose of this answer is simply to expand on the answer by @Tim.
Suppose the likelihood of the parameters given the sample can be expressed as
\begin{equation}
p(X|\theta) = \prod_{i=1}^n \texts |
54,194 | Are regression coefficients in a model with interactions ALL made conditional, or just those involved in the interaction? | The interpretation is motivated by considering how the model predictions change when controlled, simple changes are induced in the original variables.
Let's frame this a little abstractly because it doesn't make the situation any more complicated while revealing the essence of the matter. If we denote those variables... | Are regression coefficients in a model with interactions ALL made conditional, or just those involve | The interpretation is motivated by considering how the model predictions change when controlled, simple changes are induced in the original variables.
Let's frame this a little abstractly because it | Are regression coefficients in a model with interactions ALL made conditional, or just those involved in the interaction?
The interpretation is motivated by considering how the model predictions change when controlled, simple changes are induced in the original variables.
Let's frame this a little abstractly because i... | Are regression coefficients in a model with interactions ALL made conditional, or just those involve
The interpretation is motivated by considering how the model predictions change when controlled, simple changes are induced in the original variables.
Let's frame this a little abstractly because it |
54,195 | Are regression coefficients in a model with interactions ALL made conditional, or just those involved in the interaction? | Using your example - including an interaction term won't affect the interpretation of the other 8 coefficients, but it may change the coefficient itself. For instance, if you have a model y ~ a*age + b*gender + c*age:gender + d*sex + ... + j*race, the interpretation of sex would be: "holding age, gender, ... , race con... | Are regression coefficients in a model with interactions ALL made conditional, or just those involve | Using your example - including an interaction term won't affect the interpretation of the other 8 coefficients, but it may change the coefficient itself. For instance, if you have a model y ~ a*age + | Are regression coefficients in a model with interactions ALL made conditional, or just those involved in the interaction?
Using your example - including an interaction term won't affect the interpretation of the other 8 coefficients, but it may change the coefficient itself. For instance, if you have a model y ~ a*age ... | Are regression coefficients in a model with interactions ALL made conditional, or just those involve
Using your example - including an interaction term won't affect the interpretation of the other 8 coefficients, but it may change the coefficient itself. For instance, if you have a model y ~ a*age + |
54,196 | Standard error of the estimate in logistic regression | Let's just say we have one parameter $\theta$ and univariate data $x_1, \ldots, x_n$.
The likelihood estimates are obtained by solving the score equations:
$$
\sum_i l'(\hat\theta,x_i) = 0
$$
where $l(\theta,x_i)$ is the log-likelihood associated with $i$-th observation, evaluated at parameter value $\theta$.
Near the... | Standard error of the estimate in logistic regression | Let's just say we have one parameter $\theta$ and univariate data $x_1, \ldots, x_n$.
The likelihood estimates are obtained by solving the score equations:
$$
\sum_i l'(\hat\theta,x_i) = 0
$$
where $ | Standard error of the estimate in logistic regression
Let's just say we have one parameter $\theta$ and univariate data $x_1, \ldots, x_n$.
The likelihood estimates are obtained by solving the score equations:
$$
\sum_i l'(\hat\theta,x_i) = 0
$$
where $l(\theta,x_i)$ is the log-likelihood associated with $i$-th observ... | Standard error of the estimate in logistic regression
Let's just say we have one parameter $\theta$ and univariate data $x_1, \ldots, x_n$.
The likelihood estimates are obtained by solving the score equations:
$$
\sum_i l'(\hat\theta,x_i) = 0
$$
where $ |
54,197 | Predicting sequence of integers / binary values | One approach you could consider is trying to learn a Markov Chain (MC) to represent each sequence and then predict future values based on this MC.
MCs are a way of representing types of learning automata (LA) and can be used when the subsequent state of a system depends solely on the current state. They can be intuitiv... | Predicting sequence of integers / binary values | One approach you could consider is trying to learn a Markov Chain (MC) to represent each sequence and then predict future values based on this MC.
MCs are a way of representing types of learning autom | Predicting sequence of integers / binary values
One approach you could consider is trying to learn a Markov Chain (MC) to represent each sequence and then predict future values based on this MC.
MCs are a way of representing types of learning automata (LA) and can be used when the subsequent state of a system depends s... | Predicting sequence of integers / binary values
One approach you could consider is trying to learn a Markov Chain (MC) to represent each sequence and then predict future values based on this MC.
MCs are a way of representing types of learning autom |
54,198 | Predicting sequence of integers / binary values | I may worth to try a neural network for classification, specifically an LSTM is doing quite what you would like to achieve.
It could be used as follows:
LSTM need input sequences to be the same length. This could be solved by padding the data by adding leading characters. The padding character should be not 0 or 1. An... | Predicting sequence of integers / binary values | I may worth to try a neural network for classification, specifically an LSTM is doing quite what you would like to achieve.
It could be used as follows:
LSTM need input sequences to be the same lengt | Predicting sequence of integers / binary values
I may worth to try a neural network for classification, specifically an LSTM is doing quite what you would like to achieve.
It could be used as follows:
LSTM need input sequences to be the same length. This could be solved by padding the data by adding leading characters... | Predicting sequence of integers / binary values
I may worth to try a neural network for classification, specifically an LSTM is doing quite what you would like to achieve.
It could be used as follows:
LSTM need input sequences to be the same lengt |
54,199 | Predicting sequence of integers / binary values | One way to do it is through classification. You need a binary output, which is exactly what classification algorithms can provide.
You can construct a data-set out of this time series. Assume you have $n$ values right now. Further assume that you think the value in $n+1$ can be determined based on the $t$ last values b... | Predicting sequence of integers / binary values | One way to do it is through classification. You need a binary output, which is exactly what classification algorithms can provide.
You can construct a data-set out of this time series. Assume you have | Predicting sequence of integers / binary values
One way to do it is through classification. You need a binary output, which is exactly what classification algorithms can provide.
You can construct a data-set out of this time series. Assume you have $n$ values right now. Further assume that you think the value in $n+1$ ... | Predicting sequence of integers / binary values
One way to do it is through classification. You need a binary output, which is exactly what classification algorithms can provide.
You can construct a data-set out of this time series. Assume you have |
54,200 | Predicting sequence of integers / binary values | Using a Neural Network (NN) would be a solution. NN learn/train on dataset to target dataset, and then make a forecast on that particular database set. NN are very good at processing binary data (some of them generalize input data for better processing).
There is no need to know what binary data represent or how they a... | Predicting sequence of integers / binary values | Using a Neural Network (NN) would be a solution. NN learn/train on dataset to target dataset, and then make a forecast on that particular database set. NN are very good at processing binary data (some | Predicting sequence of integers / binary values
Using a Neural Network (NN) would be a solution. NN learn/train on dataset to target dataset, and then make a forecast on that particular database set. NN are very good at processing binary data (some of them generalize input data for better processing).
There is no need ... | Predicting sequence of integers / binary values
Using a Neural Network (NN) would be a solution. NN learn/train on dataset to target dataset, and then make a forecast on that particular database set. NN are very good at processing binary data (some |
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