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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4,101 | How does saddlepoint approximation work? | The saddlepoint approximation to a probability density function (it works likewise for mass functions, but I will only talk here in terms of densities)
is a surprisingly well working approximation, that can be seen as a refinement on the central limit theorem. So, it will only work in settings where there is a central ... | How does saddlepoint approximation work? | The saddlepoint approximation to a probability density function (it works likewise for mass functions, but I will only talk here in terms of densities)
is a surprisingly well working approximation, th | How does saddlepoint approximation work?
The saddlepoint approximation to a probability density function (it works likewise for mass functions, but I will only talk here in terms of densities)
is a surprisingly well working approximation, that can be seen as a refinement on the central limit theorem. So, it will only w... | How does saddlepoint approximation work?
The saddlepoint approximation to a probability density function (it works likewise for mass functions, but I will only talk here in terms of densities)
is a surprisingly well working approximation, th |
4,102 | How does saddlepoint approximation work? | Here I expand upon kjetil's answer, and I focus on those situations where the Cumulant Generating Function (CGF) is unknown, but it can be estimated from the data $x_1,\dots,x_n$, where $x\in R^d$. The simplest CGF estimator is probably that of Davison and Hinkley (1988)
$$
\hat{K}(\lambda) = \frac{1}{n}\sum_{i=1}^{n}e... | How does saddlepoint approximation work? | Here I expand upon kjetil's answer, and I focus on those situations where the Cumulant Generating Function (CGF) is unknown, but it can be estimated from the data $x_1,\dots,x_n$, where $x\in R^d$. Th | How does saddlepoint approximation work?
Here I expand upon kjetil's answer, and I focus on those situations where the Cumulant Generating Function (CGF) is unknown, but it can be estimated from the data $x_1,\dots,x_n$, where $x\in R^d$. The simplest CGF estimator is probably that of Davison and Hinkley (1988)
$$
\hat... | How does saddlepoint approximation work?
Here I expand upon kjetil's answer, and I focus on those situations where the Cumulant Generating Function (CGF) is unknown, but it can be estimated from the data $x_1,\dots,x_n$, where $x\in R^d$. Th |
4,103 | How does saddlepoint approximation work? | Thanks to Kjetil's great answer I am trying to come up with a little example myself, which I would like to discuss because it seems to raise a relevant point:
Consider the $\chi^2(m)$ distribution. $K(t)$ and its derivatives may be found here and are reproduced in the functions in the code below.
x <- seq(0.01,20,by=... | How does saddlepoint approximation work? | Thanks to Kjetil's great answer I am trying to come up with a little example myself, which I would like to discuss because it seems to raise a relevant point:
Consider the $\chi^2(m)$ distribution. $K | How does saddlepoint approximation work?
Thanks to Kjetil's great answer I am trying to come up with a little example myself, which I would like to discuss because it seems to raise a relevant point:
Consider the $\chi^2(m)$ distribution. $K(t)$ and its derivatives may be found here and are reproduced in the functions ... | How does saddlepoint approximation work?
Thanks to Kjetil's great answer I am trying to come up with a little example myself, which I would like to discuss because it seems to raise a relevant point:
Consider the $\chi^2(m)$ distribution. $K |
4,104 | Box-Cox like transformation for independent variables? | John Tukey advocated his "three point method" for finding re-expressions of variables to linearize relationships.
I will illustrate with an exercise from his book, Exploratory Data Analysis. These are mercury vapor pressure data from an experiment in which temperature was varied and vapor pressure was measured.
pressu... | Box-Cox like transformation for independent variables? | John Tukey advocated his "three point method" for finding re-expressions of variables to linearize relationships.
I will illustrate with an exercise from his book, Exploratory Data Analysis. These ar | Box-Cox like transformation for independent variables?
John Tukey advocated his "three point method" for finding re-expressions of variables to linearize relationships.
I will illustrate with an exercise from his book, Exploratory Data Analysis. These are mercury vapor pressure data from an experiment in which tempera... | Box-Cox like transformation for independent variables?
John Tukey advocated his "three point method" for finding re-expressions of variables to linearize relationships.
I will illustrate with an exercise from his book, Exploratory Data Analysis. These ar |
4,105 | Box-Cox like transformation for independent variables? | Take a look at these slides on "Regression diagnostics" by John Fox (available from here, complete with references), which briefly discuss the issue of transforming nonlinearity. It covers Tukey's "bulging rule" for selecting power transformations (addressed by the accepted answer), but also mentions the Box-Cox and Ye... | Box-Cox like transformation for independent variables? | Take a look at these slides on "Regression diagnostics" by John Fox (available from here, complete with references), which briefly discuss the issue of transforming nonlinearity. It covers Tukey's "bu | Box-Cox like transformation for independent variables?
Take a look at these slides on "Regression diagnostics" by John Fox (available from here, complete with references), which briefly discuss the issue of transforming nonlinearity. It covers Tukey's "bulging rule" for selecting power transformations (addressed by the... | Box-Cox like transformation for independent variables?
Take a look at these slides on "Regression diagnostics" by John Fox (available from here, complete with references), which briefly discuss the issue of transforming nonlinearity. It covers Tukey's "bu |
4,106 | Box-Cox like transformation for independent variables? | There are many advantages to making estimation of covariate transformations a formal part of the estimation process. This will recognize the number of parameters involved and produced good confidence interval coverage and type I error preservation. Regression splines are some of the best approaches. And splines will... | Box-Cox like transformation for independent variables? | There are many advantages to making estimation of covariate transformations a formal part of the estimation process. This will recognize the number of parameters involved and produced good confidence | Box-Cox like transformation for independent variables?
There are many advantages to making estimation of covariate transformations a formal part of the estimation process. This will recognize the number of parameters involved and produced good confidence interval coverage and type I error preservation. Regression spl... | Box-Cox like transformation for independent variables?
There are many advantages to making estimation of covariate transformations a formal part of the estimation process. This will recognize the number of parameters involved and produced good confidence |
4,107 | Box-Cox like transformation for independent variables? | The method of fractional polynomials due to Royston and Altman (1994) https://doi.org/10.2307/2986270 (paywalled) may be just such a method you might use to handle the case of an optimal power law relating the X to the Y. In this case, you believe that the $Y$ (or an appropriate transformation) is truly normally distri... | Box-Cox like transformation for independent variables? | The method of fractional polynomials due to Royston and Altman (1994) https://doi.org/10.2307/2986270 (paywalled) may be just such a method you might use to handle the case of an optimal power law rel | Box-Cox like transformation for independent variables?
The method of fractional polynomials due to Royston and Altman (1994) https://doi.org/10.2307/2986270 (paywalled) may be just such a method you might use to handle the case of an optimal power law relating the X to the Y. In this case, you believe that the $Y$ (or ... | Box-Cox like transformation for independent variables?
The method of fractional polynomials due to Royston and Altman (1994) https://doi.org/10.2307/2986270 (paywalled) may be just such a method you might use to handle the case of an optimal power law rel |
4,108 | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis? | Traditionally, the null hypothesis is a point value. (It is typically $0$, but can in fact be any point value.) The alternative hypothesis is that the true value is any value other than the null value. Because a continuous variable (such as a mean difference) can take on a value which is indefinitely close to the nu... | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to ac | Traditionally, the null hypothesis is a point value. (It is typically $0$, but can in fact be any point value.) The alternative hypothesis is that the true value is any value other than the null val | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis?
Traditionally, the null hypothesis is a point value. (It is typically $0$, but can in fact be any point value.) The alternative hypothesis is that the true value is any value other than the... | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to ac
Traditionally, the null hypothesis is a point value. (It is typically $0$, but can in fact be any point value.) The alternative hypothesis is that the true value is any value other than the null val |
4,109 | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis? | Consider the case where the null hypothesis is that a coin is 2 headed, i.e. the probability of heads is 1. Now the data is the result of flipping a coin a single time and seeing heads. This results in a p-value of 1.0 which is greater than every reasonable alpha. Does this mean that the coin is 2 headed? it could ... | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to ac | Consider the case where the null hypothesis is that a coin is 2 headed, i.e. the probability of heads is 1. Now the data is the result of flipping a coin a single time and seeing heads. This results | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis?
Consider the case where the null hypothesis is that a coin is 2 headed, i.e. the probability of heads is 1. Now the data is the result of flipping a coin a single time and seeing heads. Thi... | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to ac
Consider the case where the null hypothesis is that a coin is 2 headed, i.e. the probability of heads is 1. Now the data is the result of flipping a coin a single time and seeing heads. This results |
4,110 | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis? | Absence of evidence is not evidence of an absence (the title of an Altman, Bland paper on BMJ). P-values only give us evidence of an absence when we consider them significant. Otherwise, they tell us nothing. Hence, absence of evidence. In other words: we don't know and more data may help. | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to ac | Absence of evidence is not evidence of an absence (the title of an Altman, Bland paper on BMJ). P-values only give us evidence of an absence when we consider them significant. Otherwise, they tell u | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis?
Absence of evidence is not evidence of an absence (the title of an Altman, Bland paper on BMJ). P-values only give us evidence of an absence when we consider them significant. Otherwise, th... | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to ac
Absence of evidence is not evidence of an absence (the title of an Altman, Bland paper on BMJ). P-values only give us evidence of an absence when we consider them significant. Otherwise, they tell u |
4,111 | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis? | The null hypothesis, $H_0$, is usually taken to be the thing you have reason to assume. Often times it is the "current state of knowledge" that you wish to show is statistically unlikely.
The usual set-up for hypothesis testing is minimize type I error, that is, minimize the chance that we reject the null hypothesis i... | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to ac | The null hypothesis, $H_0$, is usually taken to be the thing you have reason to assume. Often times it is the "current state of knowledge" that you wish to show is statistically unlikely.
The usual s | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis?
The null hypothesis, $H_0$, is usually taken to be the thing you have reason to assume. Often times it is the "current state of knowledge" that you wish to show is statistically unlikely.
Th... | Why do statisticians say a non-significant result means "you can't reject the null" as opposed to ac
The null hypothesis, $H_0$, is usually taken to be the thing you have reason to assume. Often times it is the "current state of knowledge" that you wish to show is statistically unlikely.
The usual s |
4,112 | Practical hyperparameter optimization: Random vs. grid search | Random search has a probability of 95% of finding a combination of parameters within the 5% optima with only 60 iterations. Also compared to other methods it doesn't bog down in local optima.
Check this great blog post at Dato by Alice Zheng, specifically the section Hyperparameter tuning algorithms.
I love movies whe... | Practical hyperparameter optimization: Random vs. grid search | Random search has a probability of 95% of finding a combination of parameters within the 5% optima with only 60 iterations. Also compared to other methods it doesn't bog down in local optima.
Check th | Practical hyperparameter optimization: Random vs. grid search
Random search has a probability of 95% of finding a combination of parameters within the 5% optima with only 60 iterations. Also compared to other methods it doesn't bog down in local optima.
Check this great blog post at Dato by Alice Zheng, specifically th... | Practical hyperparameter optimization: Random vs. grid search
Random search has a probability of 95% of finding a combination of parameters within the 5% optima with only 60 iterations. Also compared to other methods it doesn't bog down in local optima.
Check th |
4,113 | Practical hyperparameter optimization: Random vs. grid search | Look again at the graphic from the paper (Figure 1). Say that you have two parameters, with 3x3 grid search you check only three different parameter values from each of the parameters (three rows and three columns on the plot on the left), while with random search you check nine (!) different parameter values of each o... | Practical hyperparameter optimization: Random vs. grid search | Look again at the graphic from the paper (Figure 1). Say that you have two parameters, with 3x3 grid search you check only three different parameter values from each of the parameters (three rows and | Practical hyperparameter optimization: Random vs. grid search
Look again at the graphic from the paper (Figure 1). Say that you have two parameters, with 3x3 grid search you check only three different parameter values from each of the parameters (three rows and three columns on the plot on the left), while with random ... | Practical hyperparameter optimization: Random vs. grid search
Look again at the graphic from the paper (Figure 1). Say that you have two parameters, with 3x3 grid search you check only three different parameter values from each of the parameters (three rows and |
4,114 | Practical hyperparameter optimization: Random vs. grid search | If you can write a function to to grid search, it's probably even easier to write a function to do random search because you don't have to pre-specify and store the grid up front.
Setting that aside, methods like LIPO, particle swarm optimization and Bayesian optimization make intelligent choices about which hyperparam... | Practical hyperparameter optimization: Random vs. grid search | If you can write a function to to grid search, it's probably even easier to write a function to do random search because you don't have to pre-specify and store the grid up front.
Setting that aside, | Practical hyperparameter optimization: Random vs. grid search
If you can write a function to to grid search, it's probably even easier to write a function to do random search because you don't have to pre-specify and store the grid up front.
Setting that aside, methods like LIPO, particle swarm optimization and Bayesia... | Practical hyperparameter optimization: Random vs. grid search
If you can write a function to to grid search, it's probably even easier to write a function to do random search because you don't have to pre-specify and store the grid up front.
Setting that aside, |
4,115 | Practical hyperparameter optimization: Random vs. grid search | By default, random search and grid search are terrible algorithms unless one of the following holds.
Your problem does not have a global structure, e.g., if the problem is multimodal and the number of local optima is huge
Your problem is noisy, i.e., evaluating the same solution twice leads to different objective fun... | Practical hyperparameter optimization: Random vs. grid search | By default, random search and grid search are terrible algorithms unless one of the following holds.
Your problem does not have a global structure, e.g., if the problem is multimodal and the number | Practical hyperparameter optimization: Random vs. grid search
By default, random search and grid search are terrible algorithms unless one of the following holds.
Your problem does not have a global structure, e.g., if the problem is multimodal and the number of local optima is huge
Your problem is noisy, i.e., evalu... | Practical hyperparameter optimization: Random vs. grid search
By default, random search and grid search are terrible algorithms unless one of the following holds.
Your problem does not have a global structure, e.g., if the problem is multimodal and the number |
4,116 | Practical hyperparameter optimization: Random vs. grid search | Finding a spot within 95% of maxima in a 2D topography with only one maxima takes 100%/25 =25%, 6.25%, 1.5625%, or 16 observations. So long as the first four observations correctly determine which quadrant the maxima (extrema) is in. 1D topography takes 100/2= 50, 25, 12.5, 6.25, 3.125 or 5*2. I guess people searching ... | Practical hyperparameter optimization: Random vs. grid search | Finding a spot within 95% of maxima in a 2D topography with only one maxima takes 100%/25 =25%, 6.25%, 1.5625%, or 16 observations. So long as the first four observations correctly determine which qua | Practical hyperparameter optimization: Random vs. grid search
Finding a spot within 95% of maxima in a 2D topography with only one maxima takes 100%/25 =25%, 6.25%, 1.5625%, or 16 observations. So long as the first four observations correctly determine which quadrant the maxima (extrema) is in. 1D topography takes 100/... | Practical hyperparameter optimization: Random vs. grid search
Finding a spot within 95% of maxima in a 2D topography with only one maxima takes 100%/25 =25%, 6.25%, 1.5625%, or 16 observations. So long as the first four observations correctly determine which qua |
4,117 | Practical hyperparameter optimization: Random vs. grid search | As Tim showed you can test more parameter values with random search than with grid search. This is especially efficient if some of the parameters you test end up not being impactful for your problem, like the 'Unimportant parameter' on Fig 1 from the article.
I did a post about hyperparameters tuning where I explain ... | Practical hyperparameter optimization: Random vs. grid search | As Tim showed you can test more parameter values with random search than with grid search. This is especially efficient if some of the parameters you test end up not being impactful for your problem, | Practical hyperparameter optimization: Random vs. grid search
As Tim showed you can test more parameter values with random search than with grid search. This is especially efficient if some of the parameters you test end up not being impactful for your problem, like the 'Unimportant parameter' on Fig 1 from the article... | Practical hyperparameter optimization: Random vs. grid search
As Tim showed you can test more parameter values with random search than with grid search. This is especially efficient if some of the parameters you test end up not being impactful for your problem, |
4,118 | Confidence interval for Bernoulli sampling | If the average, $\hat{p}$, is not near $1$ or $0$, and sample size $n$ is sufficiently large (i.e. $n\hat{p}>5$ and $n(1-\hat{p})>5$, the confidence interval can be estimated by a normal distribution and the confidence interval constructed thus:
$$\hat{p}\pm z_{1-\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$
If $\hat... | Confidence interval for Bernoulli sampling | If the average, $\hat{p}$, is not near $1$ or $0$, and sample size $n$ is sufficiently large (i.e. $n\hat{p}>5$ and $n(1-\hat{p})>5$, the confidence interval can be estimated by a normal distribution | Confidence interval for Bernoulli sampling
If the average, $\hat{p}$, is not near $1$ or $0$, and sample size $n$ is sufficiently large (i.e. $n\hat{p}>5$ and $n(1-\hat{p})>5$, the confidence interval can be estimated by a normal distribution and the confidence interval constructed thus:
$$\hat{p}\pm z_{1-\alpha/2}\sqr... | Confidence interval for Bernoulli sampling
If the average, $\hat{p}$, is not near $1$ or $0$, and sample size $n$ is sufficiently large (i.e. $n\hat{p}>5$ and $n(1-\hat{p})>5$, the confidence interval can be estimated by a normal distribution |
4,119 | Confidence interval for Bernoulli sampling | Maximum likelihood confidence intervals
The normal approximation to the Bernoulli sample relies on having a relatively large sample size and sample proportions far from the tails. The maximum likelihood estimate focuses on the log-transformed odds and this provides non-symmetric, efficient intervals for $p$ that should... | Confidence interval for Bernoulli sampling | Maximum likelihood confidence intervals
The normal approximation to the Bernoulli sample relies on having a relatively large sample size and sample proportions far from the tails. The maximum likeliho | Confidence interval for Bernoulli sampling
Maximum likelihood confidence intervals
The normal approximation to the Bernoulli sample relies on having a relatively large sample size and sample proportions far from the tails. The maximum likelihood estimate focuses on the log-transformed odds and this provides non-symmetr... | Confidence interval for Bernoulli sampling
Maximum likelihood confidence intervals
The normal approximation to the Bernoulli sample relies on having a relatively large sample size and sample proportions far from the tails. The maximum likeliho |
4,120 | Confidence interval for Bernoulli sampling | The Wilson score interval performs well in general for inference for the binomial probability parameter. The performance of various confidence intervals is examined in Brown, Cai and DasGupta (2001) and the Wilson score interval performs well compared to other intervals; in particular, it performs better than the Wald... | Confidence interval for Bernoulli sampling | The Wilson score interval performs well in general for inference for the binomial probability parameter. The performance of various confidence intervals is examined in Brown, Cai and DasGupta (2001) | Confidence interval for Bernoulli sampling
The Wilson score interval performs well in general for inference for the binomial probability parameter. The performance of various confidence intervals is examined in Brown, Cai and DasGupta (2001) and the Wilson score interval performs well compared to other intervals; in p... | Confidence interval for Bernoulli sampling
The Wilson score interval performs well in general for inference for the binomial probability parameter. The performance of various confidence intervals is examined in Brown, Cai and DasGupta (2001) |
4,121 | Confidence interval for Bernoulli sampling | Suppose $X_1,...,X_n$ is a sample of successes and failures from a Bernoulli population with probability of success $p$, and we are asked to find a 75% confidence interval for $p$.
One solution is to invert the CDF of a binomial distribution. Since $Y=\sum X_i\sim \text{Binomial}(n,p)$ we can define a $100(1-\alpha)\%... | Confidence interval for Bernoulli sampling | Suppose $X_1,...,X_n$ is a sample of successes and failures from a Bernoulli population with probability of success $p$, and we are asked to find a 75% confidence interval for $p$.
One solution is to | Confidence interval for Bernoulli sampling
Suppose $X_1,...,X_n$ is a sample of successes and failures from a Bernoulli population with probability of success $p$, and we are asked to find a 75% confidence interval for $p$.
One solution is to invert the CDF of a binomial distribution. Since $Y=\sum X_i\sim \text{Binom... | Confidence interval for Bernoulli sampling
Suppose $X_1,...,X_n$ is a sample of successes and failures from a Bernoulli population with probability of success $p$, and we are asked to find a 75% confidence interval for $p$.
One solution is to |
4,122 | Introduction to statistics for mathematicians | As you said, it's not necessarily the case that a mathematician may want a rigorous book. Maybe the goal is to get some intuition of the concepts quickly, and then fill in the details. I recommend two books from CMU professors, both published by Springer: "All of Statistics" by Larry Wasserman is quick and informal. "T... | Introduction to statistics for mathematicians | As you said, it's not necessarily the case that a mathematician may want a rigorous book. Maybe the goal is to get some intuition of the concepts quickly, and then fill in the details. I recommend two | Introduction to statistics for mathematicians
As you said, it's not necessarily the case that a mathematician may want a rigorous book. Maybe the goal is to get some intuition of the concepts quickly, and then fill in the details. I recommend two books from CMU professors, both published by Springer: "All of Statistics... | Introduction to statistics for mathematicians
As you said, it's not necessarily the case that a mathematician may want a rigorous book. Maybe the goal is to get some intuition of the concepts quickly, and then fill in the details. I recommend two |
4,123 | Introduction to statistics for mathematicians | Mathematical Methods of Statistics, Harald Cramér is really great if you're coming to Statistics from the mathematical side. It's a bit dated, but still relevant for all the basic mathematical statistics.
Two other noteworthy books come to mind for inference and estimation theory:
Theory of Point Estimation, E. L. Le... | Introduction to statistics for mathematicians | Mathematical Methods of Statistics, Harald Cramér is really great if you're coming to Statistics from the mathematical side. It's a bit dated, but still relevant for all the basic mathematical statis | Introduction to statistics for mathematicians
Mathematical Methods of Statistics, Harald Cramér is really great if you're coming to Statistics from the mathematical side. It's a bit dated, but still relevant for all the basic mathematical statistics.
Two other noteworthy books come to mind for inference and estimation... | Introduction to statistics for mathematicians
Mathematical Methods of Statistics, Harald Cramér is really great if you're coming to Statistics from the mathematical side. It's a bit dated, but still relevant for all the basic mathematical statis |
4,124 | Introduction to statistics for mathematicians | I loved the Freedman, Pisani, Purves' Statistics text because it is extremely non-mathematical. As a mathematician, you will find it to be such a clear guide to the statistical concepts that you will be able to develop all the mathematical theory as an exercise: that's a rewarding thing to do. (The first edition of t... | Introduction to statistics for mathematicians | I loved the Freedman, Pisani, Purves' Statistics text because it is extremely non-mathematical. As a mathematician, you will find it to be such a clear guide to the statistical concepts that you will | Introduction to statistics for mathematicians
I loved the Freedman, Pisani, Purves' Statistics text because it is extremely non-mathematical. As a mathematician, you will find it to be such a clear guide to the statistical concepts that you will be able to develop all the mathematical theory as an exercise: that's a r... | Introduction to statistics for mathematicians
I loved the Freedman, Pisani, Purves' Statistics text because it is extremely non-mathematical. As a mathematician, you will find it to be such a clear guide to the statistical concepts that you will |
4,125 | Introduction to statistics for mathematicians | I think you should take a look to the similar post from mathoverflow.
My answer to this post was Asymptotic Statistics by Van der Vaart. | Introduction to statistics for mathematicians | I think you should take a look to the similar post from mathoverflow.
My answer to this post was Asymptotic Statistics by Van der Vaart. | Introduction to statistics for mathematicians
I think you should take a look to the similar post from mathoverflow.
My answer to this post was Asymptotic Statistics by Van der Vaart. | Introduction to statistics for mathematicians
I think you should take a look to the similar post from mathoverflow.
My answer to this post was Asymptotic Statistics by Van der Vaart. |
4,126 | Introduction to statistics for mathematicians | You will find many applications of Mathematical Statistics in 'Mathematical Statistics and Data Analysis' by John A. Rice. The 'Application Index' lists all applications discussed in the text. | Introduction to statistics for mathematicians | You will find many applications of Mathematical Statistics in 'Mathematical Statistics and Data Analysis' by John A. Rice. The 'Application Index' lists all applications discussed in the text. | Introduction to statistics for mathematicians
You will find many applications of Mathematical Statistics in 'Mathematical Statistics and Data Analysis' by John A. Rice. The 'Application Index' lists all applications discussed in the text. | Introduction to statistics for mathematicians
You will find many applications of Mathematical Statistics in 'Mathematical Statistics and Data Analysis' by John A. Rice. The 'Application Index' lists all applications discussed in the text. |
4,127 | Introduction to statistics for mathematicians | For you I would suggest:
Introduction to the Mathematical and Statistical Foundations of Econometrics by Herman J. Bierens, CUP. The word "Introduction" in the title is a sick joke for most PhD econometrics students.
Markov Chain Monte Carlo by Dani Gamerman, Chapman & Hall is also concise. | Introduction to statistics for mathematicians | For you I would suggest:
Introduction to the Mathematical and Statistical Foundations of Econometrics by Herman J. Bierens, CUP. The word "Introduction" in the title is a sick joke for most PhD econom | Introduction to statistics for mathematicians
For you I would suggest:
Introduction to the Mathematical and Statistical Foundations of Econometrics by Herman J. Bierens, CUP. The word "Introduction" in the title is a sick joke for most PhD econometrics students.
Markov Chain Monte Carlo by Dani Gamerman, Chapman & Hall... | Introduction to statistics for mathematicians
For you I would suggest:
Introduction to the Mathematical and Statistical Foundations of Econometrics by Herman J. Bierens, CUP. The word "Introduction" in the title is a sick joke for most PhD econom |
4,128 | Apply word embeddings to entire document, to get a feature vector | One simple technique that seems to work reasonably well for short texts (e.g., a sentence or a tweet) is to compute the vector for each word in the document, and then aggregate them using the coordinate-wise mean, min, or max.
Based on results in one recent paper, it seems that using the min and the max works reasonabl... | Apply word embeddings to entire document, to get a feature vector | One simple technique that seems to work reasonably well for short texts (e.g., a sentence or a tweet) is to compute the vector for each word in the document, and then aggregate them using the coordina | Apply word embeddings to entire document, to get a feature vector
One simple technique that seems to work reasonably well for short texts (e.g., a sentence or a tweet) is to compute the vector for each word in the document, and then aggregate them using the coordinate-wise mean, min, or max.
Based on results in one rec... | Apply word embeddings to entire document, to get a feature vector
One simple technique that seems to work reasonably well for short texts (e.g., a sentence or a tweet) is to compute the vector for each word in the document, and then aggregate them using the coordina |
4,129 | Apply word embeddings to entire document, to get a feature vector | You can use doc2vec similar to word2vec and use a pre-trained model from a large corpus. Then use something like .infer_vector() in gensim to construct a document vector. The doc2vec training doesn't necessary need to come from the training set.
Another method is to use an RNN, CNN or feed forward network to classify.... | Apply word embeddings to entire document, to get a feature vector | You can use doc2vec similar to word2vec and use a pre-trained model from a large corpus. Then use something like .infer_vector() in gensim to construct a document vector. The doc2vec training doesn't | Apply word embeddings to entire document, to get a feature vector
You can use doc2vec similar to word2vec and use a pre-trained model from a large corpus. Then use something like .infer_vector() in gensim to construct a document vector. The doc2vec training doesn't necessary need to come from the training set.
Another... | Apply word embeddings to entire document, to get a feature vector
You can use doc2vec similar to word2vec and use a pre-trained model from a large corpus. Then use something like .infer_vector() in gensim to construct a document vector. The doc2vec training doesn't |
4,130 | Apply word embeddings to entire document, to get a feature vector | If you are working with English text and want pre-trained word embeddings to begin with, then please see this: https://code.google.com/archive/p/word2vec/
This is the original C version of word2vec. Along with this release, they also released a model trained on 100 billion words taken from Google News articles (see sub... | Apply word embeddings to entire document, to get a feature vector | If you are working with English text and want pre-trained word embeddings to begin with, then please see this: https://code.google.com/archive/p/word2vec/
This is the original C version of word2vec. A | Apply word embeddings to entire document, to get a feature vector
If you are working with English text and want pre-trained word embeddings to begin with, then please see this: https://code.google.com/archive/p/word2vec/
This is the original C version of word2vec. Along with this release, they also released a model tra... | Apply word embeddings to entire document, to get a feature vector
If you are working with English text and want pre-trained word embeddings to begin with, then please see this: https://code.google.com/archive/p/word2vec/
This is the original C version of word2vec. A |
4,131 | Apply word embeddings to entire document, to get a feature vector | I'm impressed no one mentioned it, but other best practices are to pad the sentences into a fixed size, initialize an embedding layer with the weights of Word2Vec and feed it into an LSTM. So it is basically what OP mentioned here, but including padding for handling the different lengths:
Concatenating the vectors for... | Apply word embeddings to entire document, to get a feature vector | I'm impressed no one mentioned it, but other best practices are to pad the sentences into a fixed size, initialize an embedding layer with the weights of Word2Vec and feed it into an LSTM. So it is ba | Apply word embeddings to entire document, to get a feature vector
I'm impressed no one mentioned it, but other best practices are to pad the sentences into a fixed size, initialize an embedding layer with the weights of Word2Vec and feed it into an LSTM. So it is basically what OP mentioned here, but including padding ... | Apply word embeddings to entire document, to get a feature vector
I'm impressed no one mentioned it, but other best practices are to pad the sentences into a fixed size, initialize an embedding layer with the weights of Word2Vec and feed it into an LSTM. So it is ba |
4,132 | Apply word embeddings to entire document, to get a feature vector | I would suggest to use window-size approach. Given window-size=1024 (token) and you pre-define says 10 windows, then concatenating all vectors of the windows. This is similar to your solution 2, but rather than using word vectors, using window vectors. With this approach, you can try with other embedding such as BERT o... | Apply word embeddings to entire document, to get a feature vector | I would suggest to use window-size approach. Given window-size=1024 (token) and you pre-define says 10 windows, then concatenating all vectors of the windows. This is similar to your solution 2, but r | Apply word embeddings to entire document, to get a feature vector
I would suggest to use window-size approach. Given window-size=1024 (token) and you pre-define says 10 windows, then concatenating all vectors of the windows. This is similar to your solution 2, but rather than using word vectors, using window vectors. W... | Apply word embeddings to entire document, to get a feature vector
I would suggest to use window-size approach. Given window-size=1024 (token) and you pre-define says 10 windows, then concatenating all vectors of the windows. This is similar to your solution 2, but r |
4,133 | What is the difference between a Normal and a Gaussian Distribution | Wikipedia is right. The Gaussian is the same as the normal. Wikipedia can usually be trusted on this sort of question. | What is the difference between a Normal and a Gaussian Distribution | Wikipedia is right. The Gaussian is the same as the normal. Wikipedia can usually be trusted on this sort of question. | What is the difference between a Normal and a Gaussian Distribution
Wikipedia is right. The Gaussian is the same as the normal. Wikipedia can usually be trusted on this sort of question. | What is the difference between a Normal and a Gaussian Distribution
Wikipedia is right. The Gaussian is the same as the normal. Wikipedia can usually be trusted on this sort of question. |
4,134 | What is the difference between a Normal and a Gaussian Distribution | In http://mathworld.wolfram.com/NormalDistribution.html, there is a mention of a standard Normal distribution which looks like the one you were mentioning as mean = 0 and std = 1. But the Normal distribution is the same as Gaussian which can be converted to a standard normal distribution by representing using the varia... | What is the difference between a Normal and a Gaussian Distribution | In http://mathworld.wolfram.com/NormalDistribution.html, there is a mention of a standard Normal distribution which looks like the one you were mentioning as mean = 0 and std = 1. But the Normal distr | What is the difference between a Normal and a Gaussian Distribution
In http://mathworld.wolfram.com/NormalDistribution.html, there is a mention of a standard Normal distribution which looks like the one you were mentioning as mean = 0 and std = 1. But the Normal distribution is the same as Gaussian which can be convert... | What is the difference between a Normal and a Gaussian Distribution
In http://mathworld.wolfram.com/NormalDistribution.html, there is a mention of a standard Normal distribution which looks like the one you were mentioning as mean = 0 and std = 1. But the Normal distr |
4,135 | How does LSTM prevent the vanishing gradient problem? | The vanishing gradient is best explained in the one-dimensional case. The multi-dimensional is more complicated but essentially analogous. You can review it in this excellent paper [1].
Assume we have a hidden state $h_t$ at time step $t$. If we make things simple and remove biases and inputs, we have
$$h_t = \sigma(w ... | How does LSTM prevent the vanishing gradient problem? | The vanishing gradient is best explained in the one-dimensional case. The multi-dimensional is more complicated but essentially analogous. You can review it in this excellent paper [1].
Assume we have | How does LSTM prevent the vanishing gradient problem?
The vanishing gradient is best explained in the one-dimensional case. The multi-dimensional is more complicated but essentially analogous. You can review it in this excellent paper [1].
Assume we have a hidden state $h_t$ at time step $t$. If we make things simple a... | How does LSTM prevent the vanishing gradient problem?
The vanishing gradient is best explained in the one-dimensional case. The multi-dimensional is more complicated but essentially analogous. You can review it in this excellent paper [1].
Assume we have |
4,136 | How does LSTM prevent the vanishing gradient problem? | I'd like to add some detail to the accepted answer, because I think it's a bit more nuanced and the nuance may not be obvious to someone first learning about RNNs.
For the vanilla RNN, $$\frac{\partial h_{t'}}{\partial h_{t}} = \prod _{k=1} ^{t'-t} w
\sigma'(w h_{t'-k})$$.
For the LSTM, $$\frac{\partial s_{t'}}{\part... | How does LSTM prevent the vanishing gradient problem? | I'd like to add some detail to the accepted answer, because I think it's a bit more nuanced and the nuance may not be obvious to someone first learning about RNNs.
For the vanilla RNN, $$\frac{\partia | How does LSTM prevent the vanishing gradient problem?
I'd like to add some detail to the accepted answer, because I think it's a bit more nuanced and the nuance may not be obvious to someone first learning about RNNs.
For the vanilla RNN, $$\frac{\partial h_{t'}}{\partial h_{t}} = \prod _{k=1} ^{t'-t} w
\sigma'(w h_{... | How does LSTM prevent the vanishing gradient problem?
I'd like to add some detail to the accepted answer, because I think it's a bit more nuanced and the nuance may not be obvious to someone first learning about RNNs.
For the vanilla RNN, $$\frac{\partia |
4,137 | How does LSTM prevent the vanishing gradient problem? | http://www.felixgers.de/papers/phd.pdf Please refer to section 2.2 and 3.2.2 where the truncated error part is explained. They don't propagate the error if it leaks out of the cell memory (i.e. if there is a closed/activated input gate), but they update the weights of the gate based on the error only for that time i... | How does LSTM prevent the vanishing gradient problem? | http://www.felixgers.de/papers/phd.pdf Please refer to section 2.2 and 3.2.2 where the truncated error part is explained. They don't propagate the error if it leaks out of the cell memory (i.e. if | How does LSTM prevent the vanishing gradient problem?
http://www.felixgers.de/papers/phd.pdf Please refer to section 2.2 and 3.2.2 where the truncated error part is explained. They don't propagate the error if it leaks out of the cell memory (i.e. if there is a closed/activated input gate), but they update the weigh... | How does LSTM prevent the vanishing gradient problem?
http://www.felixgers.de/papers/phd.pdf Please refer to section 2.2 and 3.2.2 where the truncated error part is explained. They don't propagate the error if it leaks out of the cell memory (i.e. if |
4,138 | How does LSTM prevent the vanishing gradient problem? | The picture of LSTM block from Greff et al. (2015) describes a variant that the authors call vanilla LSTM. It's a bit different from the original definition from Hochreiter & Schmidhuber (1997). The original definition did not include the forget gate and the peephole connections.
The term Constant Error Carousel was us... | How does LSTM prevent the vanishing gradient problem? | The picture of LSTM block from Greff et al. (2015) describes a variant that the authors call vanilla LSTM. It's a bit different from the original definition from Hochreiter & Schmidhuber (1997). The o | How does LSTM prevent the vanishing gradient problem?
The picture of LSTM block from Greff et al. (2015) describes a variant that the authors call vanilla LSTM. It's a bit different from the original definition from Hochreiter & Schmidhuber (1997). The original definition did not include the forget gate and the peephol... | How does LSTM prevent the vanishing gradient problem?
The picture of LSTM block from Greff et al. (2015) describes a variant that the authors call vanilla LSTM. It's a bit different from the original definition from Hochreiter & Schmidhuber (1997). The o |
4,139 | Neural networks vs support vector machines: are the second definitely superior? | It is a matter of trade-offs. SVMs are in right now, NNs used to be in. You'll find a rising number of papers that claim Random Forests, Probabilistic Graphic Models or Nonparametric Bayesian methods are in. Someone should publish a forecasting model in the Annals of Improbable Research on what models will be considere... | Neural networks vs support vector machines: are the second definitely superior? | It is a matter of trade-offs. SVMs are in right now, NNs used to be in. You'll find a rising number of papers that claim Random Forests, Probabilistic Graphic Models or Nonparametric Bayesian methods | Neural networks vs support vector machines: are the second definitely superior?
It is a matter of trade-offs. SVMs are in right now, NNs used to be in. You'll find a rising number of papers that claim Random Forests, Probabilistic Graphic Models or Nonparametric Bayesian methods are in. Someone should publish a forecas... | Neural networks vs support vector machines: are the second definitely superior?
It is a matter of trade-offs. SVMs are in right now, NNs used to be in. You'll find a rising number of papers that claim Random Forests, Probabilistic Graphic Models or Nonparametric Bayesian methods |
4,140 | Neural networks vs support vector machines: are the second definitely superior? | The answer to your question is in my experience "no", SVMs are not definitely superior, and which works best depends on the nature of the dataset at hand and on the relative skill of the operator with each set of tools. In general SVMs are good because the training algorithm is efficient, and it has a regularisation p... | Neural networks vs support vector machines: are the second definitely superior? | The answer to your question is in my experience "no", SVMs are not definitely superior, and which works best depends on the nature of the dataset at hand and on the relative skill of the operator with | Neural networks vs support vector machines: are the second definitely superior?
The answer to your question is in my experience "no", SVMs are not definitely superior, and which works best depends on the nature of the dataset at hand and on the relative skill of the operator with each set of tools. In general SVMs are... | Neural networks vs support vector machines: are the second definitely superior?
The answer to your question is in my experience "no", SVMs are not definitely superior, and which works best depends on the nature of the dataset at hand and on the relative skill of the operator with |
4,141 | Neural networks vs support vector machines: are the second definitely superior? | I will just try to explain my opinion that appeared to be shared by most of my friends. I have the following concerns about NN that are not about SVM at all:
In a classic NN, the amount of parameters is enormously high. Let's say you have the vectors of the length 100 you want to classify into two classes. One hidden ... | Neural networks vs support vector machines: are the second definitely superior? | I will just try to explain my opinion that appeared to be shared by most of my friends. I have the following concerns about NN that are not about SVM at all:
In a classic NN, the amount of parameters | Neural networks vs support vector machines: are the second definitely superior?
I will just try to explain my opinion that appeared to be shared by most of my friends. I have the following concerns about NN that are not about SVM at all:
In a classic NN, the amount of parameters is enormously high. Let's say you have ... | Neural networks vs support vector machines: are the second definitely superior?
I will just try to explain my opinion that appeared to be shared by most of my friends. I have the following concerns about NN that are not about SVM at all:
In a classic NN, the amount of parameters |
4,142 | Neural networks vs support vector machines: are the second definitely superior? | I am using neural networks for most problem. The point is that it's in most cases more about the experience of the user than about the model. Here are some reasons why I like NNs.
They are flexible. I can throw whatever loss I want at them: hinge loss, squared, cross entropy, you name it. As long as it is differentiab... | Neural networks vs support vector machines: are the second definitely superior? | I am using neural networks for most problem. The point is that it's in most cases more about the experience of the user than about the model. Here are some reasons why I like NNs.
They are flexible. | Neural networks vs support vector machines: are the second definitely superior?
I am using neural networks for most problem. The point is that it's in most cases more about the experience of the user than about the model. Here are some reasons why I like NNs.
They are flexible. I can throw whatever loss I want at them... | Neural networks vs support vector machines: are the second definitely superior?
I am using neural networks for most problem. The point is that it's in most cases more about the experience of the user than about the model. Here are some reasons why I like NNs.
They are flexible. |
4,143 | Neural networks vs support vector machines: are the second definitely superior? | In some ways these two broad categories of machine learning techniques are related. Though not perfect, two papers I have found helpful in showing the similarities in these techniques are below
Ronan Collobert and Samy Bengio. 2004. Links between perceptrons, MLPs
and SVMs. In Proceedings of the twenty-first intern... | Neural networks vs support vector machines: are the second definitely superior? | In some ways these two broad categories of machine learning techniques are related. Though not perfect, two papers I have found helpful in showing the similarities in these techniques are below
Rona | Neural networks vs support vector machines: are the second definitely superior?
In some ways these two broad categories of machine learning techniques are related. Though not perfect, two papers I have found helpful in showing the similarities in these techniques are below
Ronan Collobert and Samy Bengio. 2004. Links... | Neural networks vs support vector machines: are the second definitely superior?
In some ways these two broad categories of machine learning techniques are related. Though not perfect, two papers I have found helpful in showing the similarities in these techniques are below
Rona |
4,144 | Examples where method of moments can beat maximum likelihood in small samples? | This may be considered... cheating, but the OLS estimator is a MoM estimator. Consider a standard linear regression specification (with $K$ stochastic regressors, so magnitudes are conditional on the regressor matrix), and a sample of size $n$. Denote $s^2$ the OLS estimator of the variance $\sigma^2$ of the error term... | Examples where method of moments can beat maximum likelihood in small samples? | This may be considered... cheating, but the OLS estimator is a MoM estimator. Consider a standard linear regression specification (with $K$ stochastic regressors, so magnitudes are conditional on the | Examples where method of moments can beat maximum likelihood in small samples?
This may be considered... cheating, but the OLS estimator is a MoM estimator. Consider a standard linear regression specification (with $K$ stochastic regressors, so magnitudes are conditional on the regressor matrix), and a sample of size $... | Examples where method of moments can beat maximum likelihood in small samples?
This may be considered... cheating, but the OLS estimator is a MoM estimator. Consider a standard linear regression specification (with $K$ stochastic regressors, so magnitudes are conditional on the |
4,145 | Examples where method of moments can beat maximum likelihood in small samples? | "In this article, we consider a new parametrization of the two-parameter Inverse
Gaussian distribution. We find the estimators for parameters of the Inverse Gaussian
distribution by the method of moments and the method of maximum likelihood. Then, we
compare the efficiency of the estimators for the two meth... | Examples where method of moments can beat maximum likelihood in small samples? | "In this article, we consider a new parametrization of the two-parameter Inverse
Gaussian distribution. We find the estimators for parameters of the Inverse Gaussian
distribution by the method | Examples where method of moments can beat maximum likelihood in small samples?
"In this article, we consider a new parametrization of the two-parameter Inverse
Gaussian distribution. We find the estimators for parameters of the Inverse Gaussian
distribution by the method of moments and the method of maximum lik... | Examples where method of moments can beat maximum likelihood in small samples?
"In this article, we consider a new parametrization of the two-parameter Inverse
Gaussian distribution. We find the estimators for parameters of the Inverse Gaussian
distribution by the method |
4,146 | Examples where method of moments can beat maximum likelihood in small samples? | I found one:
For the asymmetric exponential power distribution
$$f(x) = \frac{\alpha}{\sigma\Gamma(\frac{1}{\alpha})} \frac{\kappa}{1+\kappa^2}\exp\left(-\frac{\kappa^\alpha}{\sigma^\alpha}[(x-\theta)^+]^\alpha -\frac{1}{\kappa^\alpha \sigma^\alpha}[(x-\theta)^-]^\alpha\right)\,,\quad \alpha,\sigma,\kappa>0, \text{ and... | Examples where method of moments can beat maximum likelihood in small samples? | I found one:
For the asymmetric exponential power distribution
$$f(x) = \frac{\alpha}{\sigma\Gamma(\frac{1}{\alpha})} \frac{\kappa}{1+\kappa^2}\exp\left(-\frac{\kappa^\alpha}{\sigma^\alpha}[(x-\theta) | Examples where method of moments can beat maximum likelihood in small samples?
I found one:
For the asymmetric exponential power distribution
$$f(x) = \frac{\alpha}{\sigma\Gamma(\frac{1}{\alpha})} \frac{\kappa}{1+\kappa^2}\exp\left(-\frac{\kappa^\alpha}{\sigma^\alpha}[(x-\theta)^+]^\alpha -\frac{1}{\kappa^\alpha \sigma... | Examples where method of moments can beat maximum likelihood in small samples?
I found one:
For the asymmetric exponential power distribution
$$f(x) = \frac{\alpha}{\sigma\Gamma(\frac{1}{\alpha})} \frac{\kappa}{1+\kappa^2}\exp\left(-\frac{\kappa^\alpha}{\sigma^\alpha}[(x-\theta) |
4,147 | Examples where method of moments can beat maximum likelihood in small samples? | The method of moments (MM) can beat the maximum likelihood (ML) approach when it is possible to specify only some population moments. If the distribution is ill-defined, the ML estimators will not be consistent.
Assuming finite moments and i.i.d observations, the MM can provide good estimators with nice asymptotic pro... | Examples where method of moments can beat maximum likelihood in small samples? | The method of moments (MM) can beat the maximum likelihood (ML) approach when it is possible to specify only some population moments. If the distribution is ill-defined, the ML estimators will not be | Examples where method of moments can beat maximum likelihood in small samples?
The method of moments (MM) can beat the maximum likelihood (ML) approach when it is possible to specify only some population moments. If the distribution is ill-defined, the ML estimators will not be consistent.
Assuming finite moments and ... | Examples where method of moments can beat maximum likelihood in small samples?
The method of moments (MM) can beat the maximum likelihood (ML) approach when it is possible to specify only some population moments. If the distribution is ill-defined, the ML estimators will not be |
4,148 | Examples where method of moments can beat maximum likelihood in small samples? | According to simulations run by Hosking and Wallis (1987) in "Parameter and Quantile Estimation for the Generalized Pareto Distribution", the parameters of the two-parameter generalized Pareto distribution given by the cdf
$G(y)= \begin{cases} 1-\left(1+ \frac{\xi y}{\beta} \right)^{-\frac{1}{\xi}} & \xi \neq 0 \\
1-... | Examples where method of moments can beat maximum likelihood in small samples? | According to simulations run by Hosking and Wallis (1987) in "Parameter and Quantile Estimation for the Generalized Pareto Distribution", the parameters of the two-parameter generalized Pareto distrib | Examples where method of moments can beat maximum likelihood in small samples?
According to simulations run by Hosking and Wallis (1987) in "Parameter and Quantile Estimation for the Generalized Pareto Distribution", the parameters of the two-parameter generalized Pareto distribution given by the cdf
$G(y)= \begin{cas... | Examples where method of moments can beat maximum likelihood in small samples?
According to simulations run by Hosking and Wallis (1987) in "Parameter and Quantile Estimation for the Generalized Pareto Distribution", the parameters of the two-parameter generalized Pareto distrib |
4,149 | Examples where method of moments can beat maximum likelihood in small samples? | Additional sources in favor of MOM:
Hong, H. P., and W. Ye. 2014. Analysis of extreme ground snow loads for Canada using snow depth records. Natural Hazards 73 (2):355-371.
The use of
MML could give unrealistic predictions if the sample size is small (Hosking et al. 1985;
Martin and Stedinger 2000).
Martins, E. S., ... | Examples where method of moments can beat maximum likelihood in small samples? | Additional sources in favor of MOM:
Hong, H. P., and W. Ye. 2014. Analysis of extreme ground snow loads for Canada using snow depth records. Natural Hazards 73 (2):355-371.
The use of
MML could give | Examples where method of moments can beat maximum likelihood in small samples?
Additional sources in favor of MOM:
Hong, H. P., and W. Ye. 2014. Analysis of extreme ground snow loads for Canada using snow depth records. Natural Hazards 73 (2):355-371.
The use of
MML could give unrealistic predictions if the sample siz... | Examples where method of moments can beat maximum likelihood in small samples?
Additional sources in favor of MOM:
Hong, H. P., and W. Ye. 2014. Analysis of extreme ground snow loads for Canada using snow depth records. Natural Hazards 73 (2):355-371.
The use of
MML could give |
4,150 | Examples where method of moments can beat maximum likelihood in small samples? | In the process of answering this: Estimating parameters for a binomial
I stumbled over this paper:
Ingram Olkin, A John Petkau, James V Zidek: A comparison of N estimators for the Binomial Distribution. Jasa 1981.
which gives an example where method of moments, at least in some cases, beats maximum likelihood. The ... | Examples where method of moments can beat maximum likelihood in small samples? | In the process of answering this: Estimating parameters for a binomial
I stumbled over this paper:
Ingram Olkin, A John Petkau, James V Zidek: A comparison of N estimators for the Binomial Distribut | Examples where method of moments can beat maximum likelihood in small samples?
In the process of answering this: Estimating parameters for a binomial
I stumbled over this paper:
Ingram Olkin, A John Petkau, James V Zidek: A comparison of N estimators for the Binomial Distribution. Jasa 1981.
which gives an example w... | Examples where method of moments can beat maximum likelihood in small samples?
In the process of answering this: Estimating parameters for a binomial
I stumbled over this paper:
Ingram Olkin, A John Petkau, James V Zidek: A comparison of N estimators for the Binomial Distribut |
4,151 | Examples where method of moments can beat maximum likelihood in small samples? | An example that is admittedly connected with the James-Stein phenomenon, albeit in dimension one.
In the case of estimating the squared norm $\theta=||\mu||^2$ of a Gaussian mean vector, when observing $X\sim\mathcal N_p(\mu,\mathbf I_p)$, the MLE
$$\hat\theta^\text{MLE}=||x||^2$$
is doing quite poorly [in terms of squ... | Examples where method of moments can beat maximum likelihood in small samples? | An example that is admittedly connected with the James-Stein phenomenon, albeit in dimension one.
In the case of estimating the squared norm $\theta=||\mu||^2$ of a Gaussian mean vector, when observin | Examples where method of moments can beat maximum likelihood in small samples?
An example that is admittedly connected with the James-Stein phenomenon, albeit in dimension one.
In the case of estimating the squared norm $\theta=||\mu||^2$ of a Gaussian mean vector, when observing $X\sim\mathcal N_p(\mu,\mathbf I_p)$, t... | Examples where method of moments can beat maximum likelihood in small samples?
An example that is admittedly connected with the James-Stein phenomenon, albeit in dimension one.
In the case of estimating the squared norm $\theta=||\mu||^2$ of a Gaussian mean vector, when observin |
4,152 | How does centering the data get rid of the intercept in regression and PCA? | Can these pictures help?
The first 2 pictures are about regression. Centering the data does not alter the slope of regression line, but it makes intercept equal 0.
The pictures below are about PCA. PCA is a regressional model without intercept$^1$. Thus, principal components inevitably come through the origin. If you ... | How does centering the data get rid of the intercept in regression and PCA? | Can these pictures help?
The first 2 pictures are about regression. Centering the data does not alter the slope of regression line, but it makes intercept equal 0.
The pictures below are about PCA. P | How does centering the data get rid of the intercept in regression and PCA?
Can these pictures help?
The first 2 pictures are about regression. Centering the data does not alter the slope of regression line, but it makes intercept equal 0.
The pictures below are about PCA. PCA is a regressional model without intercept... | How does centering the data get rid of the intercept in regression and PCA?
Can these pictures help?
The first 2 pictures are about regression. Centering the data does not alter the slope of regression line, but it makes intercept equal 0.
The pictures below are about PCA. P |
4,153 | How does centering the data get rid of the intercept in regression and PCA? | At least two references that I can find, an earlier edition of which I have been familiar with for about thirty years, state that there are four basic variants of PCA, using:
Covariance about the origin
Covariance about the mean - this is the variant of PCA which is most commonly referred to as 'PCA' by e.g. sklearn
C... | How does centering the data get rid of the intercept in regression and PCA? | At least two references that I can find, an earlier edition of which I have been familiar with for about thirty years, state that there are four basic variants of PCA, using:
Covariance about the ori | How does centering the data get rid of the intercept in regression and PCA?
At least two references that I can find, an earlier edition of which I have been familiar with for about thirty years, state that there are four basic variants of PCA, using:
Covariance about the origin
Covariance about the mean - this is the ... | How does centering the data get rid of the intercept in regression and PCA?
At least two references that I can find, an earlier edition of which I have been familiar with for about thirty years, state that there are four basic variants of PCA, using:
Covariance about the ori |
4,154 | Alternatives to logistic regression in R | Popular right now are randomForest and gbm (called MART or Gradient Boosting in machine learning literature), rpart for simple trees. Also popular is bayesglm, which uses MAP with priors for regularization.
install.packages(c("randomForest", "gbm", "rpart", "arm"))
library(randomForest)
library(gbm)
library(rpart)
li... | Alternatives to logistic regression in R | Popular right now are randomForest and gbm (called MART or Gradient Boosting in machine learning literature), rpart for simple trees. Also popular is bayesglm, which uses MAP with priors for regulari | Alternatives to logistic regression in R
Popular right now are randomForest and gbm (called MART or Gradient Boosting in machine learning literature), rpart for simple trees. Also popular is bayesglm, which uses MAP with priors for regularization.
install.packages(c("randomForest", "gbm", "rpart", "arm"))
library(ran... | Alternatives to logistic regression in R
Popular right now are randomForest and gbm (called MART or Gradient Boosting in machine learning literature), rpart for simple trees. Also popular is bayesglm, which uses MAP with priors for regulari |
4,155 | Alternatives to logistic regression in R | Actually, that depends on what you want to obtain. If you perform logistic regression only for the predictions, you can use any supervised classification method suited for your data. Another possibility : discriminant analysis ( lda() and qda() from package MASS)
r <- lda(y~x) # use qda() for quadratic discriminant ana... | Alternatives to logistic regression in R | Actually, that depends on what you want to obtain. If you perform logistic regression only for the predictions, you can use any supervised classification method suited for your data. Another possibili | Alternatives to logistic regression in R
Actually, that depends on what you want to obtain. If you perform logistic regression only for the predictions, you can use any supervised classification method suited for your data. Another possibility : discriminant analysis ( lda() and qda() from package MASS)
r <- lda(y~x) #... | Alternatives to logistic regression in R
Actually, that depends on what you want to obtain. If you perform logistic regression only for the predictions, you can use any supervised classification method suited for your data. Another possibili |
4,156 | Alternatives to logistic regression in R | I agree with Joe, and would add:
Any classification method could in principle be used, although it will depend on the data/situation. For instance, you could also use a SVM, possibly with the popular C-SVM model. Here's an example from kernlab using a radial basis kernel function:
library(kernlab)
x <- rbind(matrix(r... | Alternatives to logistic regression in R | I agree with Joe, and would add:
Any classification method could in principle be used, although it will depend on the data/situation. For instance, you could also use a SVM, possibly with the popular | Alternatives to logistic regression in R
I agree with Joe, and would add:
Any classification method could in principle be used, although it will depend on the data/situation. For instance, you could also use a SVM, possibly with the popular C-SVM model. Here's an example from kernlab using a radial basis kernel funct... | Alternatives to logistic regression in R
I agree with Joe, and would add:
Any classification method could in principle be used, although it will depend on the data/situation. For instance, you could also use a SVM, possibly with the popular |
4,157 | Alternatives to logistic regression in R | There are around 100 classification and regression models which are trainable via the caret package. Any of the classification models will be an option for you (as opposed to regression models, which require a continuous response). For example to train a random forest:
library(caret)
train(response~., data, method="rf"... | Alternatives to logistic regression in R | There are around 100 classification and regression models which are trainable via the caret package. Any of the classification models will be an option for you (as opposed to regression models, which | Alternatives to logistic regression in R
There are around 100 classification and regression models which are trainable via the caret package. Any of the classification models will be an option for you (as opposed to regression models, which require a continuous response). For example to train a random forest:
library(c... | Alternatives to logistic regression in R
There are around 100 classification and regression models which are trainable via the caret package. Any of the classification models will be an option for you (as opposed to regression models, which |
4,158 | Alternatives to logistic regression in R | Naive Bayes is a good simple method of training data to find a binary response.
library(e1071)
fitNB <- naiveBayes(y~x)
predict(fitNB, x) | Alternatives to logistic regression in R | Naive Bayes is a good simple method of training data to find a binary response.
library(e1071)
fitNB <- naiveBayes(y~x)
predict(fitNB, x) | Alternatives to logistic regression in R
Naive Bayes is a good simple method of training data to find a binary response.
library(e1071)
fitNB <- naiveBayes(y~x)
predict(fitNB, x) | Alternatives to logistic regression in R
Naive Bayes is a good simple method of training data to find a binary response.
library(e1071)
fitNB <- naiveBayes(y~x)
predict(fitNB, x) |
4,159 | Alternatives to logistic regression in R | There are two variations of the logistic regression which are not yet outlined. Firstly the logistic regression estimates probabilities using a logistic function which is a cumulativ logistic distribution (also known as sigmoid). You can also estimate probabilities using functions derived from other distributions. The... | Alternatives to logistic regression in R | There are two variations of the logistic regression which are not yet outlined. Firstly the logistic regression estimates probabilities using a logistic function which is a cumulativ logistic distrib | Alternatives to logistic regression in R
There are two variations of the logistic regression which are not yet outlined. Firstly the logistic regression estimates probabilities using a logistic function which is a cumulativ logistic distribution (also known as sigmoid). You can also estimate probabilities using functi... | Alternatives to logistic regression in R
There are two variations of the logistic regression which are not yet outlined. Firstly the logistic regression estimates probabilities using a logistic function which is a cumulativ logistic distrib |
4,160 | Who are frequentists? | Some existing answers talk about statistical inference and some about interpretation of probability, and none clearly makes the distinction. The main purpose of this answer is to make this distinction.
The word "frequentism" (and "frequentist") can refer to TWO DIFFERENT THINGS:
One is the question about what is the ... | Who are frequentists? | Some existing answers talk about statistical inference and some about interpretation of probability, and none clearly makes the distinction. The main purpose of this answer is to make this distinction | Who are frequentists?
Some existing answers talk about statistical inference and some about interpretation of probability, and none clearly makes the distinction. The main purpose of this answer is to make this distinction.
The word "frequentism" (and "frequentist") can refer to TWO DIFFERENT THINGS:
One is the quest... | Who are frequentists?
Some existing answers talk about statistical inference and some about interpretation of probability, and none clearly makes the distinction. The main purpose of this answer is to make this distinction |
4,161 | Who are frequentists? | Kolmogorov's work on Foundations of Theory of Probability has the section called "Relation to Experimental Data" on p.3. This is what he wrote there:
He's showing how one could deduct his Axioms by observing experiments. This is quite a frequentist way of interpreting the probabilities.
He has another interesting quo... | Who are frequentists? | Kolmogorov's work on Foundations of Theory of Probability has the section called "Relation to Experimental Data" on p.3. This is what he wrote there:
He's showing how one could deduct his Axioms by | Who are frequentists?
Kolmogorov's work on Foundations of Theory of Probability has the section called "Relation to Experimental Data" on p.3. This is what he wrote there:
He's showing how one could deduct his Axioms by observing experiments. This is quite a frequentist way of interpreting the probabilities.
He has a... | Who are frequentists?
Kolmogorov's work on Foundations of Theory of Probability has the section called "Relation to Experimental Data" on p.3. This is what he wrote there:
He's showing how one could deduct his Axioms by |
4,162 | Who are frequentists? | I believe that it is relevant to mention Deborah Mayo, who writes the blog Error Statistics Philosophy.
I won't claim to have a deep understanding of her philosophical position, but the framework of error statistics, as described in a paper with Aris Spanos, does include what is regarded as classical frequentist stati... | Who are frequentists? | I believe that it is relevant to mention Deborah Mayo, who writes the blog Error Statistics Philosophy.
I won't claim to have a deep understanding of her philosophical position, but the framework of | Who are frequentists?
I believe that it is relevant to mention Deborah Mayo, who writes the blog Error Statistics Philosophy.
I won't claim to have a deep understanding of her philosophical position, but the framework of error statistics, as described in a paper with Aris Spanos, does include what is regarded as class... | Who are frequentists?
I believe that it is relevant to mention Deborah Mayo, who writes the blog Error Statistics Philosophy.
I won't claim to have a deep understanding of her philosophical position, but the framework of |
4,163 | Who are frequentists? | Referring to this thread and the comments on it I think that the frequentists are those that define ''probability'' of an event as the long run relative frequency of the occurence of that event. So if $n$ is the number of experiments and $n_A$ the number of occurences of event $A$ then the probability of the event $A$,... | Who are frequentists? | Referring to this thread and the comments on it I think that the frequentists are those that define ''probability'' of an event as the long run relative frequency of the occurence of that event. So if | Who are frequentists?
Referring to this thread and the comments on it I think that the frequentists are those that define ''probability'' of an event as the long run relative frequency of the occurence of that event. So if $n$ is the number of experiments and $n_A$ the number of occurences of event $A$ then the probabi... | Who are frequentists?
Referring to this thread and the comments on it I think that the frequentists are those that define ''probability'' of an event as the long run relative frequency of the occurence of that event. So if |
4,164 | Who are frequentists? | Let me offer an answer that connects this question with a matter of current and very practical importance -- Precision Medicine -- while at the same time answering it literally as it was asked: Who are frequentists?
Frequentists are people who say things such as [1] (emphasis mine):
What does a 10% risk of an event wi... | Who are frequentists? | Let me offer an answer that connects this question with a matter of current and very practical importance -- Precision Medicine -- while at the same time answering it literally as it was asked: Who ar | Who are frequentists?
Let me offer an answer that connects this question with a matter of current and very practical importance -- Precision Medicine -- while at the same time answering it literally as it was asked: Who are frequentists?
Frequentists are people who say things such as [1] (emphasis mine):
What does a 1... | Who are frequentists?
Let me offer an answer that connects this question with a matter of current and very practical importance -- Precision Medicine -- while at the same time answering it literally as it was asked: Who ar |
4,165 | Who are frequentists? | Really interesting question!
I'd put myself in the frequentist camp when it comes to understanding and interpreting probability statements, although I am not quite so hard-line about the need for an actual sequence of iid experiments to ground this probability. I suspect most people who don't buy the thesis that "prob... | Who are frequentists? | Really interesting question!
I'd put myself in the frequentist camp when it comes to understanding and interpreting probability statements, although I am not quite so hard-line about the need for an a | Who are frequentists?
Really interesting question!
I'd put myself in the frequentist camp when it comes to understanding and interpreting probability statements, although I am not quite so hard-line about the need for an actual sequence of iid experiments to ground this probability. I suspect most people who don't buy... | Who are frequentists?
Really interesting question!
I'd put myself in the frequentist camp when it comes to understanding and interpreting probability statements, although I am not quite so hard-line about the need for an a |
4,166 | Who are frequentists? | As @amoeba noticed, we have frequentist definition of probability and frequentist statistics. All the sources that I have seen until now say that frequentist inference is based on the frequentist definition of probability, i.e. understanding it as limit in proportion given infinite number random draws (as already notic... | Who are frequentists? | As @amoeba noticed, we have frequentist definition of probability and frequentist statistics. All the sources that I have seen until now say that frequentist inference is based on the frequentist defi | Who are frequentists?
As @amoeba noticed, we have frequentist definition of probability and frequentist statistics. All the sources that I have seen until now say that frequentist inference is based on the frequentist definition of probability, i.e. understanding it as limit in proportion given infinite number random d... | Who are frequentists?
As @amoeba noticed, we have frequentist definition of probability and frequentist statistics. All the sources that I have seen until now say that frequentist inference is based on the frequentist defi |
4,167 | Who are frequentists? | "Frequentists vs. Bayesians" from
XKCD (under CC-BY-NC 2.5), click to discuss:
The general point of the frequentist philosophy illustrated here is a belief in drawing conclusions about the relative likelihood of events based solely ("purely") on the observed data, without "polluting" that estimation process with pre-... | Who are frequentists? | "Frequentists vs. Bayesians" from
XKCD (under CC-BY-NC 2.5), click to discuss:
The general point of the frequentist philosophy illustrated here is a belief in drawing conclusions about the relative | Who are frequentists?
"Frequentists vs. Bayesians" from
XKCD (under CC-BY-NC 2.5), click to discuss:
The general point of the frequentist philosophy illustrated here is a belief in drawing conclusions about the relative likelihood of events based solely ("purely") on the observed data, without "polluting" that estima... | Who are frequentists?
"Frequentists vs. Bayesians" from
XKCD (under CC-BY-NC 2.5), click to discuss:
The general point of the frequentist philosophy illustrated here is a belief in drawing conclusions about the relative |
4,168 | Who are frequentists? | (A remark, only tangentially relevant for the question and the site.)
Probability is about objective status of individual things. Things cannot have intention and they receive their statuses from the universe. With a thing, an event (giving it its status) always shall have happened: the event is already there accomplis... | Who are frequentists? | (A remark, only tangentially relevant for the question and the site.)
Probability is about objective status of individual things. Things cannot have intention and they receive their statuses from the | Who are frequentists?
(A remark, only tangentially relevant for the question and the site.)
Probability is about objective status of individual things. Things cannot have intention and they receive their statuses from the universe. With a thing, an event (giving it its status) always shall have happened: the event is a... | Who are frequentists?
(A remark, only tangentially relevant for the question and the site.)
Probability is about objective status of individual things. Things cannot have intention and they receive their statuses from the |
4,169 | Who are frequentists? | Oh, I've been a frequentist for many's the year,
And I've spent all my time playing the data by ear,
But now I'm returning with Bayes in great store,
And I never will play the frequentist no more.
For it's no nay never, no nay never, no more,
Will I play the frequentist, no never, no more!
I went into a lab whe... | Who are frequentists? | Oh, I've been a frequentist for many's the year,
And I've spent all my time playing the data by ear,
But now I'm returning with Bayes in great store,
And I never will play the frequentist no mor | Who are frequentists?
Oh, I've been a frequentist for many's the year,
And I've spent all my time playing the data by ear,
But now I'm returning with Bayes in great store,
And I never will play the frequentist no more.
For it's no nay never, no nay never, no more,
Will I play the frequentist, no never, no more!... | Who are frequentists?
Oh, I've been a frequentist for many's the year,
And I've spent all my time playing the data by ear,
But now I'm returning with Bayes in great store,
And I never will play the frequentist no mor |
4,170 | When combining p-values, why not just averaging? | You can perfectly use the mean $p$-value.
Fisher’s method set sets a threshold $s_\alpha$ on $-2 \sum_{i=1}^n \log p_i$, such that if the null hypothesis $H_0$ : all $p$-values are $\sim U(0,1)$ holds, then $-2 \sum_i \log p_i$ exceeds $s_\alpha$ with probability $\alpha$. $H_0$ is rejected when this happens.
Usually o... | When combining p-values, why not just averaging? | You can perfectly use the mean $p$-value.
Fisher’s method set sets a threshold $s_\alpha$ on $-2 \sum_{i=1}^n \log p_i$, such that if the null hypothesis $H_0$ : all $p$-values are $\sim U(0,1)$ holds | When combining p-values, why not just averaging?
You can perfectly use the mean $p$-value.
Fisher’s method set sets a threshold $s_\alpha$ on $-2 \sum_{i=1}^n \log p_i$, such that if the null hypothesis $H_0$ : all $p$-values are $\sim U(0,1)$ holds, then $-2 \sum_i \log p_i$ exceeds $s_\alpha$ with probability $\alpha... | When combining p-values, why not just averaging?
You can perfectly use the mean $p$-value.
Fisher’s method set sets a threshold $s_\alpha$ on $-2 \sum_{i=1}^n \log p_i$, such that if the null hypothesis $H_0$ : all $p$-values are $\sim U(0,1)$ holds |
4,171 | When combining p-values, why not just averaging? | What is wrong with summing up all individual $p$-values?
As @whuber and @Glen_b argue in the comments, Fisher's method is essentially multiplying all individual $p$-values, and multiplying probabilities is a more natural thing to do than adding them.
Still one can add them up. In fact, precisely this was suggested by E... | When combining p-values, why not just averaging? | What is wrong with summing up all individual $p$-values?
As @whuber and @Glen_b argue in the comments, Fisher's method is essentially multiplying all individual $p$-values, and multiplying probabiliti | When combining p-values, why not just averaging?
What is wrong with summing up all individual $p$-values?
As @whuber and @Glen_b argue in the comments, Fisher's method is essentially multiplying all individual $p$-values, and multiplying probabilities is a more natural thing to do than adding them.
Still one can add th... | When combining p-values, why not just averaging?
What is wrong with summing up all individual $p$-values?
As @whuber and @Glen_b argue in the comments, Fisher's method is essentially multiplying all individual $p$-values, and multiplying probabiliti |
4,172 | When combining p-values, why not just averaging? | So if you did three studies of similar sizes and got a p-value of 0.05 on all three occasions, your intuition is that the "true value" should be 0.05? My intuition is different. Multiple similar results would seem to make the significance higher (and therefore the p-values which are probabilities should be lower). P-va... | When combining p-values, why not just averaging? | So if you did three studies of similar sizes and got a p-value of 0.05 on all three occasions, your intuition is that the "true value" should be 0.05? My intuition is different. Multiple similar resul | When combining p-values, why not just averaging?
So if you did three studies of similar sizes and got a p-value of 0.05 on all three occasions, your intuition is that the "true value" should be 0.05? My intuition is different. Multiple similar results would seem to make the significance higher (and therefore the p-valu... | When combining p-values, why not just averaging?
So if you did three studies of similar sizes and got a p-value of 0.05 on all three occasions, your intuition is that the "true value" should be 0.05? My intuition is different. Multiple similar resul |
4,173 | How to select a clustering method? How to validate a cluster solution (to warrant the method choice)? | Often they say that there is no other analytical technique as strongly of the "as you sow you shall mow" kind, as cluster analysis is.
I can imagine of a number dimensions or aspects of "rightness" of this or that clustering method:
Cluster metaphor. "I preferred this method because it constitutes clusters such (or su... | How to select a clustering method? How to validate a cluster solution (to warrant the method choice) | Often they say that there is no other analytical technique as strongly of the "as you sow you shall mow" kind, as cluster analysis is.
I can imagine of a number dimensions or aspects of "rightness" of | How to select a clustering method? How to validate a cluster solution (to warrant the method choice)?
Often they say that there is no other analytical technique as strongly of the "as you sow you shall mow" kind, as cluster analysis is.
I can imagine of a number dimensions or aspects of "rightness" of this or that clus... | How to select a clustering method? How to validate a cluster solution (to warrant the method choice)
Often they say that there is no other analytical technique as strongly of the "as you sow you shall mow" kind, as cluster analysis is.
I can imagine of a number dimensions or aspects of "rightness" of |
4,174 | How to select a clustering method? How to validate a cluster solution (to warrant the method choice)? | There are mostly red flag criteria. Properties of data that tell you that a certain approach will fail for sure.
if you have no idea what your data means stop analyzing it. you are just guessing animals in clouds.
if attributes vary in scale and are nonlinear or skewed. this can ruin your analysis unless you have a ... | How to select a clustering method? How to validate a cluster solution (to warrant the method choice) | There are mostly red flag criteria. Properties of data that tell you that a certain approach will fail for sure.
if you have no idea what your data means stop analyzing it. you are just guessing ani | How to select a clustering method? How to validate a cluster solution (to warrant the method choice)?
There are mostly red flag criteria. Properties of data that tell you that a certain approach will fail for sure.
if you have no idea what your data means stop analyzing it. you are just guessing animals in clouds.
i... | How to select a clustering method? How to validate a cluster solution (to warrant the method choice)
There are mostly red flag criteria. Properties of data that tell you that a certain approach will fail for sure.
if you have no idea what your data means stop analyzing it. you are just guessing ani |
4,175 | How to select a clustering method? How to validate a cluster solution (to warrant the method choice)? | I don't think there is a good formal way to do this; I think that the good solutions are the ones that make sense, substantively.
Of course, you can try splitting the data and clustering multiple times and so one, but then there is still the question of which one is useful. | How to select a clustering method? How to validate a cluster solution (to warrant the method choice) | I don't think there is a good formal way to do this; I think that the good solutions are the ones that make sense, substantively.
Of course, you can try splitting the data and clustering multiple tim | How to select a clustering method? How to validate a cluster solution (to warrant the method choice)?
I don't think there is a good formal way to do this; I think that the good solutions are the ones that make sense, substantively.
Of course, you can try splitting the data and clustering multiple times and so one, but... | How to select a clustering method? How to validate a cluster solution (to warrant the method choice)
I don't think there is a good formal way to do this; I think that the good solutions are the ones that make sense, substantively.
Of course, you can try splitting the data and clustering multiple tim |
4,176 | Why sigmoid function instead of anything else? | Quoting myself from this answer to a different question:
In section 4.2 of Pattern Recognition and Machine Learning (Springer 2006), Bishop shows that the logit arises naturally as the form of the posterior probability distribution in a Bayesian treatment of two-class classification. He then goes on to show that the s... | Why sigmoid function instead of anything else? | Quoting myself from this answer to a different question:
In section 4.2 of Pattern Recognition and Machine Learning (Springer 2006), Bishop shows that the logit arises naturally as the form of the po | Why sigmoid function instead of anything else?
Quoting myself from this answer to a different question:
In section 4.2 of Pattern Recognition and Machine Learning (Springer 2006), Bishop shows that the logit arises naturally as the form of the posterior probability distribution in a Bayesian treatment of two-class cla... | Why sigmoid function instead of anything else?
Quoting myself from this answer to a different question:
In section 4.2 of Pattern Recognition and Machine Learning (Springer 2006), Bishop shows that the logit arises naturally as the form of the po |
4,177 | Why sigmoid function instead of anything else? | I have asked myself this question for months. The answers on CrossValidated and Quora all list nice properties of the logistic sigmoid function, but it all seems like we cleverly guessed this function. What I missed was the justification for choosing it. I finally found one in section 6.2.2.2 of the "Deep Learning" boo... | Why sigmoid function instead of anything else? | I have asked myself this question for months. The answers on CrossValidated and Quora all list nice properties of the logistic sigmoid function, but it all seems like we cleverly guessed this function | Why sigmoid function instead of anything else?
I have asked myself this question for months. The answers on CrossValidated and Quora all list nice properties of the logistic sigmoid function, but it all seems like we cleverly guessed this function. What I missed was the justification for choosing it. I finally found on... | Why sigmoid function instead of anything else?
I have asked myself this question for months. The answers on CrossValidated and Quora all list nice properties of the logistic sigmoid function, but it all seems like we cleverly guessed this function |
4,178 | Why sigmoid function instead of anything else? | One reason this function might seem more "natural" than others is that it happens to be the inverse of the canonical parameter of the Bernoulli distribution:
\begin{align}
f(y) &= p^y (1 - p)^{1 - y} \\
&= (1 - p) \exp \left \{ y \log \left ( \frac{p}{1 - p} \right ) \right \} .
\end{align}
(The function of $p$ within ... | Why sigmoid function instead of anything else? | One reason this function might seem more "natural" than others is that it happens to be the inverse of the canonical parameter of the Bernoulli distribution:
\begin{align}
f(y) &= p^y (1 - p)^{1 - y} | Why sigmoid function instead of anything else?
One reason this function might seem more "natural" than others is that it happens to be the inverse of the canonical parameter of the Bernoulli distribution:
\begin{align}
f(y) &= p^y (1 - p)^{1 - y} \\
&= (1 - p) \exp \left \{ y \log \left ( \frac{p}{1 - p} \right ) \righ... | Why sigmoid function instead of anything else?
One reason this function might seem more "natural" than others is that it happens to be the inverse of the canonical parameter of the Bernoulli distribution:
\begin{align}
f(y) &= p^y (1 - p)^{1 - y} |
4,179 | Why sigmoid function instead of anything else? | Since the original question mentioned the decaying gradient problem, I'd just like to add that, for intermediate layers (where you don't need to interpret activations as class probabilities or regression outputs), other nonlinearities are often preferred over sigmoidal functions. The most prominent are rectifier functi... | Why sigmoid function instead of anything else? | Since the original question mentioned the decaying gradient problem, I'd just like to add that, for intermediate layers (where you don't need to interpret activations as class probabilities or regress | Why sigmoid function instead of anything else?
Since the original question mentioned the decaying gradient problem, I'd just like to add that, for intermediate layers (where you don't need to interpret activations as class probabilities or regression outputs), other nonlinearities are often preferred over sigmoidal fun... | Why sigmoid function instead of anything else?
Since the original question mentioned the decaying gradient problem, I'd just like to add that, for intermediate layers (where you don't need to interpret activations as class probabilities or regress |
4,180 | What is the difference between N and N-1 in calculating population variance? | Instead of going into maths I'll try to put it in plain words. If you have the whole population at your disposal then its variance (population variance) is computed with the denominator N. Likewise, if you have only sample and want to compute this sample's variance, you use denominator N (n of the sample, in this case)... | What is the difference between N and N-1 in calculating population variance? | Instead of going into maths I'll try to put it in plain words. If you have the whole population at your disposal then its variance (population variance) is computed with the denominator N. Likewise, i | What is the difference between N and N-1 in calculating population variance?
Instead of going into maths I'll try to put it in plain words. If you have the whole population at your disposal then its variance (population variance) is computed with the denominator N. Likewise, if you have only sample and want to compute ... | What is the difference between N and N-1 in calculating population variance?
Instead of going into maths I'll try to put it in plain words. If you have the whole population at your disposal then its variance (population variance) is computed with the denominator N. Likewise, i |
4,181 | What is the difference between N and N-1 in calculating population variance? | $N$ is the population size and $n$ is the sample size. The question asks why the population variance is the mean squared deviation from the mean rather than $(N-1)/N = 1-(1/N)$ times it. For that matter, why stop there? Why not multiply the mean squared deviation by $1-2/N$, or $1-17/N$, or $\exp(-1/N)$, for instanc... | What is the difference between N and N-1 in calculating population variance? | $N$ is the population size and $n$ is the sample size. The question asks why the population variance is the mean squared deviation from the mean rather than $(N-1)/N = 1-(1/N)$ times it. For that ma | What is the difference between N and N-1 in calculating population variance?
$N$ is the population size and $n$ is the sample size. The question asks why the population variance is the mean squared deviation from the mean rather than $(N-1)/N = 1-(1/N)$ times it. For that matter, why stop there? Why not multiply the... | What is the difference between N and N-1 in calculating population variance?
$N$ is the population size and $n$ is the sample size. The question asks why the population variance is the mean squared deviation from the mean rather than $(N-1)/N = 1-(1/N)$ times it. For that ma |
4,182 | What is the difference between N and N-1 in calculating population variance? | There has, in the past been an argument that you should use N for a non-inferential variance but I wouldn't recommended that anymore. You should always use N-1. As sample size decreases N-1 is a pretty good correction for the fact that the sample variance gets lower (you're just more likely to sample near the peak of... | What is the difference between N and N-1 in calculating population variance? | There has, in the past been an argument that you should use N for a non-inferential variance but I wouldn't recommended that anymore. You should always use N-1. As sample size decreases N-1 is a pre | What is the difference between N and N-1 in calculating population variance?
There has, in the past been an argument that you should use N for a non-inferential variance but I wouldn't recommended that anymore. You should always use N-1. As sample size decreases N-1 is a pretty good correction for the fact that the s... | What is the difference between N and N-1 in calculating population variance?
There has, in the past been an argument that you should use N for a non-inferential variance but I wouldn't recommended that anymore. You should always use N-1. As sample size decreases N-1 is a pre |
4,183 | What is the difference between N and N-1 in calculating population variance? | Generally, when one has only a fraction of the population, i.e. a sample, you should divide by n-1. There is a good reason to do so, we know that the sample variance, which multiplies the mean squared deviation from the sample mean by (n−1)/n, is an unbiased estimator of the population variance.
You can find a proof th... | What is the difference between N and N-1 in calculating population variance? | Generally, when one has only a fraction of the population, i.e. a sample, you should divide by n-1. There is a good reason to do so, we know that the sample variance, which multiplies the mean squared | What is the difference between N and N-1 in calculating population variance?
Generally, when one has only a fraction of the population, i.e. a sample, you should divide by n-1. There is a good reason to do so, we know that the sample variance, which multiplies the mean squared deviation from the sample mean by (n−1)/n,... | What is the difference between N and N-1 in calculating population variance?
Generally, when one has only a fraction of the population, i.e. a sample, you should divide by n-1. There is a good reason to do so, we know that the sample variance, which multiplies the mean squared |
4,184 | What is the difference between N and N-1 in calculating population variance? | The population variance is the sum of the squared deviations of all of the values in the population divided by the number of values in the population. When we are estimating the variance of a population from a sample, though, we encounter the problem that the deviations of the sample values from the mean of the sample ... | What is the difference between N and N-1 in calculating population variance? | The population variance is the sum of the squared deviations of all of the values in the population divided by the number of values in the population. When we are estimating the variance of a populati | What is the difference between N and N-1 in calculating population variance?
The population variance is the sum of the squared deviations of all of the values in the population divided by the number of values in the population. When we are estimating the variance of a population from a sample, though, we encounter the ... | What is the difference between N and N-1 in calculating population variance?
The population variance is the sum of the squared deviations of all of the values in the population divided by the number of values in the population. When we are estimating the variance of a populati |
4,185 | Where does the misconception that Y must be normally distributed come from? | 'Y must be normally distributed'
must?
In the cases that you mention it is sloppy language (abbreviating 'the error in Y must be normally distributed'), but they don't really (strongly) say that the response must be normally distributed, or at least it does not seem to me that their words were intended like that.
The ... | Where does the misconception that Y must be normally distributed come from? | 'Y must be normally distributed'
must?
In the cases that you mention it is sloppy language (abbreviating 'the error in Y must be normally distributed'), but they don't really (strongly) say that the | Where does the misconception that Y must be normally distributed come from?
'Y must be normally distributed'
must?
In the cases that you mention it is sloppy language (abbreviating 'the error in Y must be normally distributed'), but they don't really (strongly) say that the response must be normally distributed, or at... | Where does the misconception that Y must be normally distributed come from?
'Y must be normally distributed'
must?
In the cases that you mention it is sloppy language (abbreviating 'the error in Y must be normally distributed'), but they don't really (strongly) say that the |
4,186 | Where does the misconception that Y must be normally distributed come from? | Is there a good explanation for how/why this misconception has spread? Is its origin known?
We generally teach undergraduates a "simplified" version of statistics in many disciplines. I am in psychology, and when I try to tell undergraduates that p-values are "the probability of the data—or more extreme data—given tha... | Where does the misconception that Y must be normally distributed come from? | Is there a good explanation for how/why this misconception has spread? Is its origin known?
We generally teach undergraduates a "simplified" version of statistics in many disciplines. I am in psychol | Where does the misconception that Y must be normally distributed come from?
Is there a good explanation for how/why this misconception has spread? Is its origin known?
We generally teach undergraduates a "simplified" version of statistics in many disciplines. I am in psychology, and when I try to tell undergraduates t... | Where does the misconception that Y must be normally distributed come from?
Is there a good explanation for how/why this misconception has spread? Is its origin known?
We generally teach undergraduates a "simplified" version of statistics in many disciplines. I am in psychol |
4,187 | Where does the misconception that Y must be normally distributed come from? | Regression analysis is difficult for beginners because there are different results that are implied by different starting assumptions. Weaker starting assumptions can justify some of the results, but you can get stronger results when you add stronger assumptions. People who are unfamiliar with the full mathematical d... | Where does the misconception that Y must be normally distributed come from? | Regression analysis is difficult for beginners because there are different results that are implied by different starting assumptions. Weaker starting assumptions can justify some of the results, but | Where does the misconception that Y must be normally distributed come from?
Regression analysis is difficult for beginners because there are different results that are implied by different starting assumptions. Weaker starting assumptions can justify some of the results, but you can get stronger results when you add s... | Where does the misconception that Y must be normally distributed come from?
Regression analysis is difficult for beginners because there are different results that are implied by different starting assumptions. Weaker starting assumptions can justify some of the results, but |
4,188 | Relationship between $R^2$ and correlation coefficient | This is true that $SS_{tot}$ will change ... but you forgot the fact that the regression sum of of squares will change as well. So let's consider the simple regression model and denote the Correlation Coefficient as $r_{xy}^2=\dfrac{S_{xy}^2}{S_{xx}S_{yy}}$, where I used the sub-index $xy$ to emphasize the fact that $... | Relationship between $R^2$ and correlation coefficient | This is true that $SS_{tot}$ will change ... but you forgot the fact that the regression sum of of squares will change as well. So let's consider the simple regression model and denote the Correlatio | Relationship between $R^2$ and correlation coefficient
This is true that $SS_{tot}$ will change ... but you forgot the fact that the regression sum of of squares will change as well. So let's consider the simple regression model and denote the Correlation Coefficient as $r_{xy}^2=\dfrac{S_{xy}^2}{S_{xx}S_{yy}}$, where... | Relationship between $R^2$ and correlation coefficient
This is true that $SS_{tot}$ will change ... but you forgot the fact that the regression sum of of squares will change as well. So let's consider the simple regression model and denote the Correlatio |
4,189 | Relationship between $R^2$ and correlation coefficient | One way of interpreting the coefficient of determination $R^{2}$ is to look at it as the Squared Pearson Correlation Coefficient between the observed values $y_{i}$ and the fitted values $\hat{y}_{i}$.
The complete proof of how to derive the coefficient of determination R2 from the Squared Pearson Correlation Coeffici... | Relationship between $R^2$ and correlation coefficient | One way of interpreting the coefficient of determination $R^{2}$ is to look at it as the Squared Pearson Correlation Coefficient between the observed values $y_{i}$ and the fitted values $\hat{y}_{i}$ | Relationship between $R^2$ and correlation coefficient
One way of interpreting the coefficient of determination $R^{2}$ is to look at it as the Squared Pearson Correlation Coefficient between the observed values $y_{i}$ and the fitted values $\hat{y}_{i}$.
The complete proof of how to derive the coefficient of determi... | Relationship between $R^2$ and correlation coefficient
One way of interpreting the coefficient of determination $R^{2}$ is to look at it as the Squared Pearson Correlation Coefficient between the observed values $y_{i}$ and the fitted values $\hat{y}_{i}$ |
4,190 | Relationship between $R^2$ and correlation coefficient | In case of simple linear regression with only one predictor $R^2 = r^2 = Corr(x,y)^2$.
But in multiple linear regression with more than one predictors the concept of correlation
between the predictors and the response does not extend automatically. The formula gets:
$$R^2 = Corr(y_{estimated},y_{observed})^2$$
The... | Relationship between $R^2$ and correlation coefficient | In case of simple linear regression with only one predictor $R^2 = r^2 = Corr(x,y)^2$.
But in multiple linear regression with more than one predictors the concept of correlation
between the predictors | Relationship between $R^2$ and correlation coefficient
In case of simple linear regression with only one predictor $R^2 = r^2 = Corr(x,y)^2$.
But in multiple linear regression with more than one predictors the concept of correlation
between the predictors and the response does not extend automatically. The formula gets... | Relationship between $R^2$ and correlation coefficient
In case of simple linear regression with only one predictor $R^2 = r^2 = Corr(x,y)^2$.
But in multiple linear regression with more than one predictors the concept of correlation
between the predictors |
4,191 | Relationship between $R^2$ and correlation coefficient | @Stat has provided a detailed answer. In my short answer I'll show briefly in somewhat different way what is the similarity and difference between $r$ and $r^2$.
$r$ is the standardized regression coefficient beta of $Y$ by $X$ or of $X$ by $Y$ and as such, it is a measure of the (mutual) effect size. Which is most cle... | Relationship between $R^2$ and correlation coefficient | @Stat has provided a detailed answer. In my short answer I'll show briefly in somewhat different way what is the similarity and difference between $r$ and $r^2$.
$r$ is the standardized regression coe | Relationship between $R^2$ and correlation coefficient
@Stat has provided a detailed answer. In my short answer I'll show briefly in somewhat different way what is the similarity and difference between $r$ and $r^2$.
$r$ is the standardized regression coefficient beta of $Y$ by $X$ or of $X$ by $Y$ and as such, it is a... | Relationship between $R^2$ and correlation coefficient
@Stat has provided a detailed answer. In my short answer I'll show briefly in somewhat different way what is the similarity and difference between $r$ and $r^2$.
$r$ is the standardized regression coe |
4,192 | Relationship between $R^2$ and correlation coefficient | I think you might be mistaken. If $R^2=r^2$, I assume you have a bivariate model: one DV, one IV. I don't think $R^2$ will change if you swap these, nor if you replace the IV with the predictions of the DV that are based on the IV. Here's code for a demonstration in R:
x=rnorm(1000); y=rnorm(1000) # store ... | Relationship between $R^2$ and correlation coefficient | I think you might be mistaken. If $R^2=r^2$, I assume you have a bivariate model: one DV, one IV. I don't think $R^2$ will change if you swap these, nor if you replace the IV with the predictions of t | Relationship between $R^2$ and correlation coefficient
I think you might be mistaken. If $R^2=r^2$, I assume you have a bivariate model: one DV, one IV. I don't think $R^2$ will change if you swap these, nor if you replace the IV with the predictions of the DV that are based on the IV. Here's code for a demonstration i... | Relationship between $R^2$ and correlation coefficient
I think you might be mistaken. If $R^2=r^2$, I assume you have a bivariate model: one DV, one IV. I don't think $R^2$ will change if you swap these, nor if you replace the IV with the predictions of t |
4,193 | Relationship between $R^2$ and correlation coefficient | If the prediction is not a projection onto the space spanned by the independent variables, the first definition is wrong. It can even be negative. The second definition is the same as the first if the prediction is a linear regression. Otherwise they are not the same. That said the second (correlation squared) definiti... | Relationship between $R^2$ and correlation coefficient | If the prediction is not a projection onto the space spanned by the independent variables, the first definition is wrong. It can even be negative. The second definition is the same as the first if the | Relationship between $R^2$ and correlation coefficient
If the prediction is not a projection onto the space spanned by the independent variables, the first definition is wrong. It can even be negative. The second definition is the same as the first if the prediction is a linear regression. Otherwise they are not the sa... | Relationship between $R^2$ and correlation coefficient
If the prediction is not a projection onto the space spanned by the independent variables, the first definition is wrong. It can even be negative. The second definition is the same as the first if the |
4,194 | Is there any gold standard for modeling irregularly spaced time series? | If the observations of a stochastic process are irregularly spaced the most natural way to model the observations is as discrete time observations from a continuous time process.
What is generally needed of a model specification is the joint distribution of the observations $X_{1}, \ldots, X_n$ observed at times $t_1 ... | Is there any gold standard for modeling irregularly spaced time series? | If the observations of a stochastic process are irregularly spaced the most natural way to model the observations is as discrete time observations from a continuous time process.
What is generally ne | Is there any gold standard for modeling irregularly spaced time series?
If the observations of a stochastic process are irregularly spaced the most natural way to model the observations is as discrete time observations from a continuous time process.
What is generally needed of a model specification is the joint distr... | Is there any gold standard for modeling irregularly spaced time series?
If the observations of a stochastic process are irregularly spaced the most natural way to model the observations is as discrete time observations from a continuous time process.
What is generally ne |
4,195 | Is there any gold standard for modeling irregularly spaced time series? | For irregular spaced time series it's easy to construct a Kalman filter.
There is a paper how to transfer ARIMA into state space form here
And one paper that compares Kalman to GARCH here$^{(1)}$
$(1)$ Choudhry, Taufiq and Wu, Hao (2008)
Forecasting ability of GARCH vs Kalman filter method: evidence from daily UK time-... | Is there any gold standard for modeling irregularly spaced time series? | For irregular spaced time series it's easy to construct a Kalman filter.
There is a paper how to transfer ARIMA into state space form here
And one paper that compares Kalman to GARCH here$^{(1)}$
$(1) | Is there any gold standard for modeling irregularly spaced time series?
For irregular spaced time series it's easy to construct a Kalman filter.
There is a paper how to transfer ARIMA into state space form here
And one paper that compares Kalman to GARCH here$^{(1)}$
$(1)$ Choudhry, Taufiq and Wu, Hao (2008)
Forecastin... | Is there any gold standard for modeling irregularly spaced time series?
For irregular spaced time series it's easy to construct a Kalman filter.
There is a paper how to transfer ARIMA into state space form here
And one paper that compares Kalman to GARCH here$^{(1)}$
$(1) |
4,196 | Is there any gold standard for modeling irregularly spaced time series? | When I was looking for a way to measure the amount of fluctuation in irregularly sampled data I came across these two papers on exponential smoothing for irregular data by Cipra [1, 2 ].
These build further on the smoothing techniques of Brown, Winters and Holt (see the Wikipedia-entry for Exponential Smoothing), and ... | Is there any gold standard for modeling irregularly spaced time series? | When I was looking for a way to measure the amount of fluctuation in irregularly sampled data I came across these two papers on exponential smoothing for irregular data by Cipra [1, 2 ].
These build | Is there any gold standard for modeling irregularly spaced time series?
When I was looking for a way to measure the amount of fluctuation in irregularly sampled data I came across these two papers on exponential smoothing for irregular data by Cipra [1, 2 ].
These build further on the smoothing techniques of Brown, Wi... | Is there any gold standard for modeling irregularly spaced time series?
When I was looking for a way to measure the amount of fluctuation in irregularly sampled data I came across these two papers on exponential smoothing for irregular data by Cipra [1, 2 ].
These build |
4,197 | Is there any gold standard for modeling irregularly spaced time series? | The analysis of irregularly sampled time series can be tricky, as there aren't many tools available. Sometimes the practice is to apply regular algorithms and hope for the best. This isn't necessarily the best approach. Other times people try to interpolate the data in the gaps. I have even seen cases where gaps are fi... | Is there any gold standard for modeling irregularly spaced time series? | The analysis of irregularly sampled time series can be tricky, as there aren't many tools available. Sometimes the practice is to apply regular algorithms and hope for the best. This isn't necessarily | Is there any gold standard for modeling irregularly spaced time series?
The analysis of irregularly sampled time series can be tricky, as there aren't many tools available. Sometimes the practice is to apply regular algorithms and hope for the best. This isn't necessarily the best approach. Other times people try to in... | Is there any gold standard for modeling irregularly spaced time series?
The analysis of irregularly sampled time series can be tricky, as there aren't many tools available. Sometimes the practice is to apply regular algorithms and hope for the best. This isn't necessarily |
4,198 | Is there any gold standard for modeling irregularly spaced time series? | If you want a "local" time-domain model -- as opposed to estimating correlation functions or power spectra), say in order to detect and characterize transient pulses, jumps, and the like -- then the Bayesian Block algorithm may be useful. It provides an optimal piecewise constant representation of time series in any d... | Is there any gold standard for modeling irregularly spaced time series? | If you want a "local" time-domain model -- as opposed to estimating correlation functions or power spectra), say in order to detect and characterize transient pulses, jumps, and the like -- then the | Is there any gold standard for modeling irregularly spaced time series?
If you want a "local" time-domain model -- as opposed to estimating correlation functions or power spectra), say in order to detect and characterize transient pulses, jumps, and the like -- then the Bayesian Block algorithm may be useful. It provi... | Is there any gold standard for modeling irregularly spaced time series?
If you want a "local" time-domain model -- as opposed to estimating correlation functions or power spectra), say in order to detect and characterize transient pulses, jumps, and the like -- then the |
4,199 | Is there any gold standard for modeling irregularly spaced time series? | In spatial data analysis data is most of the time sampled irregularly in space. So one idea would be to see what is done there, and implement variogram estimation, kriging, and so on for one-dimensional "time" domain. Variograms could be interesting even for regularly spaced time series data, as it has diferent propert... | Is there any gold standard for modeling irregularly spaced time series? | In spatial data analysis data is most of the time sampled irregularly in space. So one idea would be to see what is done there, and implement variogram estimation, kriging, and so on for one-dimension | Is there any gold standard for modeling irregularly spaced time series?
In spatial data analysis data is most of the time sampled irregularly in space. So one idea would be to see what is done there, and implement variogram estimation, kriging, and so on for one-dimensional "time" domain. Variograms could be interestin... | Is there any gold standard for modeling irregularly spaced time series?
In spatial data analysis data is most of the time sampled irregularly in space. So one idea would be to see what is done there, and implement variogram estimation, kriging, and so on for one-dimension |
4,200 | Is there any gold standard for modeling irregularly spaced time series? | This is too long for a comment, but I believe it's an important comment here. What is discussed here is a mathematical approach under some specific assumptions on the process being measured, but we can have time series data that do not follow these assumptions!
The modelling approach must answer the question of «why is... | Is there any gold standard for modeling irregularly spaced time series? | This is too long for a comment, but I believe it's an important comment here. What is discussed here is a mathematical approach under some specific assumptions on the process being measured, but we ca | Is there any gold standard for modeling irregularly spaced time series?
This is too long for a comment, but I believe it's an important comment here. What is discussed here is a mathematical approach under some specific assumptions on the process being measured, but we can have time series data that do not follow these... | Is there any gold standard for modeling irregularly spaced time series?
This is too long for a comment, but I believe it's an important comment here. What is discussed here is a mathematical approach under some specific assumptions on the process being measured, but we ca |
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