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14,601
Why is leave-one-out cross-validation (LOOCV) variance about the mean estimate for error high? [duplicate]
It's like taking a test with just one question - it's a lot more hit-and-miss. This is an intuitive explanation of the standard deviation of an instance versus that of a mean - the score on a batch of instances has less variance. Here are some more details.
Why is leave-one-out cross-validation (LOOCV) variance about the mean estimate for error high? [dupl
It's like taking a test with just one question - it's a lot more hit-and-miss. This is an intuitive explanation of the standard deviation of an instance versus that of a mean - the score on a batch of
Why is leave-one-out cross-validation (LOOCV) variance about the mean estimate for error high? [duplicate] It's like taking a test with just one question - it's a lot more hit-and-miss. This is an intuitive explanation of the standard deviation of an instance versus that of a mean - the score on a batch of instances ha...
Why is leave-one-out cross-validation (LOOCV) variance about the mean estimate for error high? [dupl It's like taking a test with just one question - it's a lot more hit-and-miss. This is an intuitive explanation of the standard deviation of an instance versus that of a mean - the score on a batch of
14,602
Weibull distribution parameters $k$ and $c$ for wind speed data
Because @zaynah posted in the comments that the data are thought to follow a Weibull distribution, I'm gonna provide a short tutorial on how to estimate the parameters of such a distribution using MLE (Maximum likelihood estimation). There is a similar post about wind speeds and Weibull distribution on the site. Downl...
Weibull distribution parameters $k$ and $c$ for wind speed data
Because @zaynah posted in the comments that the data are thought to follow a Weibull distribution, I'm gonna provide a short tutorial on how to estimate the parameters of such a distribution using MLE
Weibull distribution parameters $k$ and $c$ for wind speed data Because @zaynah posted in the comments that the data are thought to follow a Weibull distribution, I'm gonna provide a short tutorial on how to estimate the parameters of such a distribution using MLE (Maximum likelihood estimation). There is a similar pos...
Weibull distribution parameters $k$ and $c$ for wind speed data Because @zaynah posted in the comments that the data are thought to follow a Weibull distribution, I'm gonna provide a short tutorial on how to estimate the parameters of such a distribution using MLE
14,603
Using neural network for trading in stock exchange
There are severe flaws with this approach. First, there are many gambles which usually win, but which are bad gambles. Suppose you have the chance to win \$1 $90\%$ of the time and lose \$100 $10\%$ of the time. This has a negative expected value, but the way you are training the neural network would teach it to recomm...
Using neural network for trading in stock exchange
There are severe flaws with this approach. First, there are many gambles which usually win, but which are bad gambles. Suppose you have the chance to win \$1 $90\%$ of the time and lose \$100 $10\%$ o
Using neural network for trading in stock exchange There are severe flaws with this approach. First, there are many gambles which usually win, but which are bad gambles. Suppose you have the chance to win \$1 $90\%$ of the time and lose \$100 $10\%$ of the time. This has a negative expected value, but the way you are t...
Using neural network for trading in stock exchange There are severe flaws with this approach. First, there are many gambles which usually win, but which are bad gambles. Suppose you have the chance to win \$1 $90\%$ of the time and lose \$100 $10\%$ o
14,604
Using neural network for trading in stock exchange
A single human may never see this, but I'd still like to give my input as someone who has found themselves engrossed in both finance and computer science. I will never say a neural network won't be successful in equity trading, but you need to think at the differences between how a human trades stocks and how a neural ...
Using neural network for trading in stock exchange
A single human may never see this, but I'd still like to give my input as someone who has found themselves engrossed in both finance and computer science. I will never say a neural network won't be su
Using neural network for trading in stock exchange A single human may never see this, but I'd still like to give my input as someone who has found themselves engrossed in both finance and computer science. I will never say a neural network won't be successful in equity trading, but you need to think at the differences ...
Using neural network for trading in stock exchange A single human may never see this, but I'd still like to give my input as someone who has found themselves engrossed in both finance and computer science. I will never say a neural network won't be su
14,605
Using neural network for trading in stock exchange
i realise this is an old thread, but just in case anyone stumbles on it, what the OP needed to do was squish his desired field down into the 0 to 1 space. ie just remap -1 = 0.0, 0 = 0.5, and 1 = 1. Then you can just use the standard logistic sigmoid activation function.
Using neural network for trading in stock exchange
i realise this is an old thread, but just in case anyone stumbles on it, what the OP needed to do was squish his desired field down into the 0 to 1 space. ie just remap -1 = 0.0, 0 = 0.5, and 1 = 1. T
Using neural network for trading in stock exchange i realise this is an old thread, but just in case anyone stumbles on it, what the OP needed to do was squish his desired field down into the 0 to 1 space. ie just remap -1 = 0.0, 0 = 0.5, and 1 = 1. Then you can just use the standard logistic sigmoid activation functio...
Using neural network for trading in stock exchange i realise this is an old thread, but just in case anyone stumbles on it, what the OP needed to do was squish his desired field down into the 0 to 1 space. ie just remap -1 = 0.0, 0 = 0.5, and 1 = 1. T
14,606
How to tune smoothing in mgcv GAM model
The k argument effectively sets up the dimensionality of the smoothing matrix for each term. gam() is using a GCV or UBRE score to select an optimal amount of smoothness, but it can only work within the dimensionality of the smoothing matrix. By default, te() smooths have k = 5^2 for 2d surfaces. I forget what it is fo...
How to tune smoothing in mgcv GAM model
The k argument effectively sets up the dimensionality of the smoothing matrix for each term. gam() is using a GCV or UBRE score to select an optimal amount of smoothness, but it can only work within t
How to tune smoothing in mgcv GAM model The k argument effectively sets up the dimensionality of the smoothing matrix for each term. gam() is using a GCV or UBRE score to select an optimal amount of smoothness, but it can only work within the dimensionality of the smoothing matrix. By default, te() smooths have k = 5^2...
How to tune smoothing in mgcv GAM model The k argument effectively sets up the dimensionality of the smoothing matrix for each term. gam() is using a GCV or UBRE score to select an optimal amount of smoothness, but it can only work within t
14,607
How to tune smoothing in mgcv GAM model
There are a number of options to make a gam less wiggly: Set the default s(..., k = 10) to a smaller value. Set the default s(...,bs = 'tp') to ts. Set gam(..., select = TRUE). Set the default gam(..., gamma = 1) to a larger value. Try values between 1 and 2. Set the default s(..., m = 2) to m = 1. Set the default met...
How to tune smoothing in mgcv GAM model
There are a number of options to make a gam less wiggly: Set the default s(..., k = 10) to a smaller value. Set the default s(...,bs = 'tp') to ts. Set gam(..., select = TRUE). Set the default gam(..
How to tune smoothing in mgcv GAM model There are a number of options to make a gam less wiggly: Set the default s(..., k = 10) to a smaller value. Set the default s(...,bs = 'tp') to ts. Set gam(..., select = TRUE). Set the default gam(..., gamma = 1) to a larger value. Try values between 1 and 2. Set the default s(....
How to tune smoothing in mgcv GAM model There are a number of options to make a gam less wiggly: Set the default s(..., k = 10) to a smaller value. Set the default s(...,bs = 'tp') to ts. Set gam(..., select = TRUE). Set the default gam(..
14,608
Is it bad to have error bars constructed with standard deviation that spans to the negative scale while the variable itself shouldn't be negative?
No, in this case, it does not make sense to draw error bars using SDs. Take a step back. Why do we draw error bars with SDs? As you write, it's to show where "much" of the data lies. This makes sense if your data come from a normal distribution: 68% of your data will lie within $\pm 1$ SD from the mean, so showing the ...
Is it bad to have error bars constructed with standard deviation that spans to the negative scale wh
No, in this case, it does not make sense to draw error bars using SDs. Take a step back. Why do we draw error bars with SDs? As you write, it's to show where "much" of the data lies. This makes sense
Is it bad to have error bars constructed with standard deviation that spans to the negative scale while the variable itself shouldn't be negative? No, in this case, it does not make sense to draw error bars using SDs. Take a step back. Why do we draw error bars with SDs? As you write, it's to show where "much" of the d...
Is it bad to have error bars constructed with standard deviation that spans to the negative scale wh No, in this case, it does not make sense to draw error bars using SDs. Take a step back. Why do we draw error bars with SDs? As you write, it's to show where "much" of the data lies. This makes sense
14,609
What to do with random effects correlation that equals 1 or -1?
Singular random-effect covariance matrices Obtaining a random effect correlation estimate of +1 or -1 means that the optimization algorithm hit "a boundary": correlations cannot be higher than +1 or lower than -1. Even if there are no explicit convergence errors or warnings, this potentially indicates some problems wit...
What to do with random effects correlation that equals 1 or -1?
Singular random-effect covariance matrices Obtaining a random effect correlation estimate of +1 or -1 means that the optimization algorithm hit "a boundary": correlations cannot be higher than +1 or l
What to do with random effects correlation that equals 1 or -1? Singular random-effect covariance matrices Obtaining a random effect correlation estimate of +1 or -1 means that the optimization algorithm hit "a boundary": correlations cannot be higher than +1 or lower than -1. Even if there are no explicit convergence ...
What to do with random effects correlation that equals 1 or -1? Singular random-effect covariance matrices Obtaining a random effect correlation estimate of +1 or -1 means that the optimization algorithm hit "a boundary": correlations cannot be higher than +1 or l
14,610
What to do with random effects correlation that equals 1 or -1?
I agree with everything said in amoeba's answer which provides a great summary of the current discussion on this issue. I will try to add a few additional points and otherwise refer to the handout of my recent mixed model course which also summarizes these points. Suppressing the correlation parameters (options 2 and ...
What to do with random effects correlation that equals 1 or -1?
I agree with everything said in amoeba's answer which provides a great summary of the current discussion on this issue. I will try to add a few additional points and otherwise refer to the handout of
What to do with random effects correlation that equals 1 or -1? I agree with everything said in amoeba's answer which provides a great summary of the current discussion on this issue. I will try to add a few additional points and otherwise refer to the handout of my recent mixed model course which also summarizes these...
What to do with random effects correlation that equals 1 or -1? I agree with everything said in amoeba's answer which provides a great summary of the current discussion on this issue. I will try to add a few additional points and otherwise refer to the handout of
14,611
What to do with random effects correlation that equals 1 or -1?
I too have had this problem when using maximum likelihood estimation - only I use Goldstein IGLS algorithm as implemented through the MLwiN software and not LME4 in R. However in each and very case the problem has resolved when I have switched to MCMC estimation using the same software. I have even had a correlation in...
What to do with random effects correlation that equals 1 or -1?
I too have had this problem when using maximum likelihood estimation - only I use Goldstein IGLS algorithm as implemented through the MLwiN software and not LME4 in R. However in each and very case th
What to do with random effects correlation that equals 1 or -1? I too have had this problem when using maximum likelihood estimation - only I use Goldstein IGLS algorithm as implemented through the MLwiN software and not LME4 in R. However in each and very case the problem has resolved when I have switched to MCMC esti...
What to do with random effects correlation that equals 1 or -1? I too have had this problem when using maximum likelihood estimation - only I use Goldstein IGLS algorithm as implemented through the MLwiN software and not LME4 in R. However in each and very case th
14,612
The reason of superiority of Limited-memory BFGS over ADAM solver
There are a lot of reasons that this could be the case. Off the top of my head I can think of one plausible cause, but without knowing more about the problem it is difficult to suggest that it is the one. An L-BFGS solver is a true quasi-Newton method in that it estimates the curvature of the parameter space via an ap...
The reason of superiority of Limited-memory BFGS over ADAM solver
There are a lot of reasons that this could be the case. Off the top of my head I can think of one plausible cause, but without knowing more about the problem it is difficult to suggest that it is the
The reason of superiority of Limited-memory BFGS over ADAM solver There are a lot of reasons that this could be the case. Off the top of my head I can think of one plausible cause, but without knowing more about the problem it is difficult to suggest that it is the one. An L-BFGS solver is a true quasi-Newton method i...
The reason of superiority of Limited-memory BFGS over ADAM solver There are a lot of reasons that this could be the case. Off the top of my head I can think of one plausible cause, but without knowing more about the problem it is difficult to suggest that it is the
14,613
The reason of superiority of Limited-memory BFGS over ADAM solver
In my opinion, they are two different heuristics to scale the gradient, however, they are motivated differently. Nowadays people try to find a trade-off between Adam which converges fast with possibly bad generalization and SGD which converges poorly but results in better generalizations. Maybe you should also consider...
The reason of superiority of Limited-memory BFGS over ADAM solver
In my opinion, they are two different heuristics to scale the gradient, however, they are motivated differently. Nowadays people try to find a trade-off between Adam which converges fast with possibly
The reason of superiority of Limited-memory BFGS over ADAM solver In my opinion, they are two different heuristics to scale the gradient, however, they are motivated differently. Nowadays people try to find a trade-off between Adam which converges fast with possibly bad generalization and SGD which converges poorly but...
The reason of superiority of Limited-memory BFGS over ADAM solver In my opinion, they are two different heuristics to scale the gradient, however, they are motivated differently. Nowadays people try to find a trade-off between Adam which converges fast with possibly
14,614
Artificial neural networks EQUIVALENT to linear regression with polynomial features?
Here's the deal: Technically you did write true sentences(both models can approximate any 'not too crazy' function given enough parameters), but those sentences do not get you anywhere at all! Why is that? Well, take a closer look at the universal approximation theory, or any other formal proof that a neural network ca...
Artificial neural networks EQUIVALENT to linear regression with polynomial features?
Here's the deal: Technically you did write true sentences(both models can approximate any 'not too crazy' function given enough parameters), but those sentences do not get you anywhere at all! Why is
Artificial neural networks EQUIVALENT to linear regression with polynomial features? Here's the deal: Technically you did write true sentences(both models can approximate any 'not too crazy' function given enough parameters), but those sentences do not get you anywhere at all! Why is that? Well, take a closer look at t...
Artificial neural networks EQUIVALENT to linear regression with polynomial features? Here's the deal: Technically you did write true sentences(both models can approximate any 'not too crazy' function given enough parameters), but those sentences do not get you anywhere at all! Why is
14,615
Artificial neural networks EQUIVALENT to linear regression with polynomial features?
It is true that any function can be approximated arbitrarily close both by something that counts as a neural network and something that counts as a polynomial. First of all, keep in mind that this is true for a lot of constructs. You could approximate any function by combining sines and cosines (Fourier transforms), o...
Artificial neural networks EQUIVALENT to linear regression with polynomial features?
It is true that any function can be approximated arbitrarily close both by something that counts as a neural network and something that counts as a polynomial. First of all, keep in mind that this is
Artificial neural networks EQUIVALENT to linear regression with polynomial features? It is true that any function can be approximated arbitrarily close both by something that counts as a neural network and something that counts as a polynomial. First of all, keep in mind that this is true for a lot of constructs. You ...
Artificial neural networks EQUIVALENT to linear regression with polynomial features? It is true that any function can be approximated arbitrarily close both by something that counts as a neural network and something that counts as a polynomial. First of all, keep in mind that this is
14,616
Artificial neural networks EQUIVALENT to linear regression with polynomial features?
Maybe this paper can help you: Polynomial Regression As an Alternative to Neural Nets The abstract says: Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they work? Here we present a simple analytic argument that NNs are in fact essentially p...
Artificial neural networks EQUIVALENT to linear regression with polynomial features?
Maybe this paper can help you: Polynomial Regression As an Alternative to Neural Nets The abstract says: Despite the success of neural networks (NNs), there is still a concern among many over their
Artificial neural networks EQUIVALENT to linear regression with polynomial features? Maybe this paper can help you: Polynomial Regression As an Alternative to Neural Nets The abstract says: Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they wo...
Artificial neural networks EQUIVALENT to linear regression with polynomial features? Maybe this paper can help you: Polynomial Regression As an Alternative to Neural Nets The abstract says: Despite the success of neural networks (NNs), there is still a concern among many over their
14,617
Artificial neural networks EQUIVALENT to linear regression with polynomial features?
Since no answers have yet been provided (though I would accept the comment of user1952009 was it posted as an answer), let me share what I have learned in the meantime: (1) It seems to me that my understanding is generally right, but the devil is in the details. (2) One thing that missed in "my understanding": How goo...
Artificial neural networks EQUIVALENT to linear regression with polynomial features?
Since no answers have yet been provided (though I would accept the comment of user1952009 was it posted as an answer), let me share what I have learned in the meantime: (1) It seems to me that my und
Artificial neural networks EQUIVALENT to linear regression with polynomial features? Since no answers have yet been provided (though I would accept the comment of user1952009 was it posted as an answer), let me share what I have learned in the meantime: (1) It seems to me that my understanding is generally right, but ...
Artificial neural networks EQUIVALENT to linear regression with polynomial features? Since no answers have yet been provided (though I would accept the comment of user1952009 was it posted as an answer), let me share what I have learned in the meantime: (1) It seems to me that my und
14,618
What does pooled variance "actually" mean?
Put simply, the pooled variance is an (unbiased) estimate of the variance within each sample, under the assumption/constraint that those variances are equal. This is explained, motivated, and analyzed in some detail in the Wikipedia entry for pooled variance. It does not estimate the variance of a new "meta-sample" for...
What does pooled variance "actually" mean?
Put simply, the pooled variance is an (unbiased) estimate of the variance within each sample, under the assumption/constraint that those variances are equal. This is explained, motivated, and analyzed
What does pooled variance "actually" mean? Put simply, the pooled variance is an (unbiased) estimate of the variance within each sample, under the assumption/constraint that those variances are equal. This is explained, motivated, and analyzed in some detail in the Wikipedia entry for pooled variance. It does not estim...
What does pooled variance "actually" mean? Put simply, the pooled variance is an (unbiased) estimate of the variance within each sample, under the assumption/constraint that those variances are equal. This is explained, motivated, and analyzed
14,619
What does pooled variance "actually" mean?
Pooled variance is used to combine together variances from different samples by taking their weighted average, to get the "overall" variance. The problem with your example is that it is a pathological case, since each of the sub-samples has variance equal to zero. Such pathological case has very little in common with t...
What does pooled variance "actually" mean?
Pooled variance is used to combine together variances from different samples by taking their weighted average, to get the "overall" variance. The problem with your example is that it is a pathological
What does pooled variance "actually" mean? Pooled variance is used to combine together variances from different samples by taking their weighted average, to get the "overall" variance. The problem with your example is that it is a pathological case, since each of the sub-samples has variance equal to zero. Such patholo...
What does pooled variance "actually" mean? Pooled variance is used to combine together variances from different samples by taking their weighted average, to get the "overall" variance. The problem with your example is that it is a pathological
14,620
What does pooled variance "actually" mean?
Through pooled variance we are not trying to estimate the variance of a bigger sample, using smaller samples. Hence, the two examples you gave don't exactly refer to the question. Pooled variance is required to get a better estimate of population variance, from two samples that have been randomly taken from that popula...
What does pooled variance "actually" mean?
Through pooled variance we are not trying to estimate the variance of a bigger sample, using smaller samples. Hence, the two examples you gave don't exactly refer to the question. Pooled variance is r
What does pooled variance "actually" mean? Through pooled variance we are not trying to estimate the variance of a bigger sample, using smaller samples. Hence, the two examples you gave don't exactly refer to the question. Pooled variance is required to get a better estimate of population variance, from two samples tha...
What does pooled variance "actually" mean? Through pooled variance we are not trying to estimate the variance of a bigger sample, using smaller samples. Hence, the two examples you gave don't exactly refer to the question. Pooled variance is r
14,621
What does pooled variance "actually" mean?
The problem is if you just concatenate the samples and estimate its variance you're assuming they're from the same distribution therefore have the same mean. But we are in general interested in several samples with different mean. Does this make sense?
What does pooled variance "actually" mean?
The problem is if you just concatenate the samples and estimate its variance you're assuming they're from the same distribution therefore have the same mean. But we are in general interested in severa
What does pooled variance "actually" mean? The problem is if you just concatenate the samples and estimate its variance you're assuming they're from the same distribution therefore have the same mean. But we are in general interested in several samples with different mean. Does this make sense?
What does pooled variance "actually" mean? The problem is if you just concatenate the samples and estimate its variance you're assuming they're from the same distribution therefore have the same mean. But we are in general interested in severa
14,622
What does pooled variance "actually" mean?
The use-case of pooled variance is when you have two samples from distributions that: may have different means, but which you expect to have an equal true variance. An example of this is a situation where you measure the length of Alice's nose $n$ times for one sample, and measure the length of Bob's nose $m$ times f...
What does pooled variance "actually" mean?
The use-case of pooled variance is when you have two samples from distributions that: may have different means, but which you expect to have an equal true variance. An example of this is a situation
What does pooled variance "actually" mean? The use-case of pooled variance is when you have two samples from distributions that: may have different means, but which you expect to have an equal true variance. An example of this is a situation where you measure the length of Alice's nose $n$ times for one sample, and m...
What does pooled variance "actually" mean? The use-case of pooled variance is when you have two samples from distributions that: may have different means, but which you expect to have an equal true variance. An example of this is a situation
14,623
What does pooled variance "actually" mean?
Although I am very late to the conversation maybe I can add something helpful: It seems to me that the OP wants to know why (what for) we would need a pooled variability estimate $\hat\sigma_{pooled}$ as a weighted average of two samples (be it variance or standard deviation). As far as I am aware the main practical ne...
What does pooled variance "actually" mean?
Although I am very late to the conversation maybe I can add something helpful: It seems to me that the OP wants to know why (what for) we would need a pooled variability estimate $\hat\sigma_{pooled}$
What does pooled variance "actually" mean? Although I am very late to the conversation maybe I can add something helpful: It seems to me that the OP wants to know why (what for) we would need a pooled variability estimate $\hat\sigma_{pooled}$ as a weighted average of two samples (be it variance or standard deviation)....
What does pooled variance "actually" mean? Although I am very late to the conversation maybe I can add something helpful: It seems to me that the OP wants to know why (what for) we would need a pooled variability estimate $\hat\sigma_{pooled}$
14,624
What is maxnorm constraint? How is it useful in Convolutional Neural Networks?
From http://cs231n.github.io/neural-networks-2/#reg: Max norm constraints. Another form of regularization is to enforce an absolute upper bound on the magnitude of the weight vector for every neuron and use projected gradient descent to enforce the constraint. In practice, this corresponds to performing the parameter ...
What is maxnorm constraint? How is it useful in Convolutional Neural Networks?
From http://cs231n.github.io/neural-networks-2/#reg: Max norm constraints. Another form of regularization is to enforce an absolute upper bound on the magnitude of the weight vector for every neuron
What is maxnorm constraint? How is it useful in Convolutional Neural Networks? From http://cs231n.github.io/neural-networks-2/#reg: Max norm constraints. Another form of regularization is to enforce an absolute upper bound on the magnitude of the weight vector for every neuron and use projected gradient descent to enf...
What is maxnorm constraint? How is it useful in Convolutional Neural Networks? From http://cs231n.github.io/neural-networks-2/#reg: Max norm constraints. Another form of regularization is to enforce an absolute upper bound on the magnitude of the weight vector for every neuron
14,625
What is maxnorm constraint? How is it useful in Convolutional Neural Networks?
I found an answer by McLawrence in another question to be very helpful. Reproduced below: What does a weight constraint of max_normdo? maxnorm(m) will, if the L2-Norm of your weights exceeds m, scale your whole weight matrix by a factor that reduces the norm to m. As you can find in the keras code in class MaxNorm(...
What is maxnorm constraint? How is it useful in Convolutional Neural Networks?
I found an answer by McLawrence in another question to be very helpful. Reproduced below: What does a weight constraint of max_normdo? maxnorm(m) will, if the L2-Norm of your weights exceeds m, scale
What is maxnorm constraint? How is it useful in Convolutional Neural Networks? I found an answer by McLawrence in another question to be very helpful. Reproduced below: What does a weight constraint of max_normdo? maxnorm(m) will, if the L2-Norm of your weights exceeds m, scale your whole weight matrix by a factor tha...
What is maxnorm constraint? How is it useful in Convolutional Neural Networks? I found an answer by McLawrence in another question to be very helpful. Reproduced below: What does a weight constraint of max_normdo? maxnorm(m) will, if the L2-Norm of your weights exceeds m, scale
14,626
Why do we estimate mean using MLE when we already know that mean is average of the data?
Why do we need to estimate mean using MLE when we already know that mean is average of the data? The text book problem states that $x_1,x_2,\dots,x_N$ is from $$x\sim\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$ They tell you that $\sigma$ is known, but $\mu$ has to be estimated. Is it really that obvi...
Why do we estimate mean using MLE when we already know that mean is average of the data?
Why do we need to estimate mean using MLE when we already know that mean is average of the data? The text book problem states that $x_1,x_2,\dots,x_N$ is from $$x\sim\frac{1}{\sqrt{2\pi}\sigma}e^{-\f
Why do we estimate mean using MLE when we already know that mean is average of the data? Why do we need to estimate mean using MLE when we already know that mean is average of the data? The text book problem states that $x_1,x_2,\dots,x_N$ is from $$x\sim\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$ Th...
Why do we estimate mean using MLE when we already know that mean is average of the data? Why do we need to estimate mean using MLE when we already know that mean is average of the data? The text book problem states that $x_1,x_2,\dots,x_N$ is from $$x\sim\frac{1}{\sqrt{2\pi}\sigma}e^{-\f
14,627
Why do we estimate mean using MLE when we already know that mean is average of the data?
In this case, the average of your sample happens to also be the maximum likelihood estimator. So doing all the work derive the MLE feels like an unnecessary exercise, as you get back to your intuitive estimate of the mean you would have used in the first place. Well, this wasn't "just by chance"; this was specifically ...
Why do we estimate mean using MLE when we already know that mean is average of the data?
In this case, the average of your sample happens to also be the maximum likelihood estimator. So doing all the work derive the MLE feels like an unnecessary exercise, as you get back to your intuitive
Why do we estimate mean using MLE when we already know that mean is average of the data? In this case, the average of your sample happens to also be the maximum likelihood estimator. So doing all the work derive the MLE feels like an unnecessary exercise, as you get back to your intuitive estimate of the mean you would...
Why do we estimate mean using MLE when we already know that mean is average of the data? In this case, the average of your sample happens to also be the maximum likelihood estimator. So doing all the work derive the MLE feels like an unnecessary exercise, as you get back to your intuitive
14,628
Why do we estimate mean using MLE when we already know that mean is average of the data?
It is a matter of confusing vocabulary, as illustrated by those quotes, straight from google: average noun: average; plural noun: averages a number expressing the central or typical value in a set of data, in particular the mode, median, or (most commonly) the mean, which is calculated by dividing the sum of the ...
Why do we estimate mean using MLE when we already know that mean is average of the data?
It is a matter of confusing vocabulary, as illustrated by those quotes, straight from google: average noun: average; plural noun: averages a number expressing the central or typical value in a set
Why do we estimate mean using MLE when we already know that mean is average of the data? It is a matter of confusing vocabulary, as illustrated by those quotes, straight from google: average noun: average; plural noun: averages a number expressing the central or typical value in a set of data, in particular the mod...
Why do we estimate mean using MLE when we already know that mean is average of the data? It is a matter of confusing vocabulary, as illustrated by those quotes, straight from google: average noun: average; plural noun: averages a number expressing the central or typical value in a set
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What fast algorithms exist for computing truncated SVD?
Very broadly speaking, there are two approaches to compute eigenvalue or singular value decompositions. One approach is to diagonalize the matrix and this essentially yields the whole eigenvalue / singular value decomposition (the whole eigenvalue spectrum) at the same time, see some overview here: What are efficient a...
What fast algorithms exist for computing truncated SVD?
Very broadly speaking, there are two approaches to compute eigenvalue or singular value decompositions. One approach is to diagonalize the matrix and this essentially yields the whole eigenvalue / sin
What fast algorithms exist for computing truncated SVD? Very broadly speaking, there are two approaches to compute eigenvalue or singular value decompositions. One approach is to diagonalize the matrix and this essentially yields the whole eigenvalue / singular value decomposition (the whole eigenvalue spectrum) at the...
What fast algorithms exist for computing truncated SVD? Very broadly speaking, there are two approaches to compute eigenvalue or singular value decompositions. One approach is to diagonalize the matrix and this essentially yields the whole eigenvalue / sin
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What fast algorithms exist for computing truncated SVD?
I just stumbled on the thread via googling fast SVDs, so I'm trying to figure out things myself, but maybe you should look into adaptive cross approximation (ACA). I don't really know what problem is like or what you need, but if your matrix $M$ is calculated from smooth functions, and you just need an approximate sepa...
What fast algorithms exist for computing truncated SVD?
I just stumbled on the thread via googling fast SVDs, so I'm trying to figure out things myself, but maybe you should look into adaptive cross approximation (ACA). I don't really know what problem is
What fast algorithms exist for computing truncated SVD? I just stumbled on the thread via googling fast SVDs, so I'm trying to figure out things myself, but maybe you should look into adaptive cross approximation (ACA). I don't really know what problem is like or what you need, but if your matrix $M$ is calculated from...
What fast algorithms exist for computing truncated SVD? I just stumbled on the thread via googling fast SVDs, so I'm trying to figure out things myself, but maybe you should look into adaptive cross approximation (ACA). I don't really know what problem is
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What fast algorithms exist for computing truncated SVD?
Here's a technique I have used successfully in the past for computing a truncated SVD (on the Netflix dataset). It is taken from this paper. In a collaborative filtering setting, I should note that most of the values are missing and the point is to predict them, so to use truncated SVD to solve such a problem, you have...
What fast algorithms exist for computing truncated SVD?
Here's a technique I have used successfully in the past for computing a truncated SVD (on the Netflix dataset). It is taken from this paper. In a collaborative filtering setting, I should note that mo
What fast algorithms exist for computing truncated SVD? Here's a technique I have used successfully in the past for computing a truncated SVD (on the Netflix dataset). It is taken from this paper. In a collaborative filtering setting, I should note that most of the values are missing and the point is to predict them, s...
What fast algorithms exist for computing truncated SVD? Here's a technique I have used successfully in the past for computing a truncated SVD (on the Netflix dataset). It is taken from this paper. In a collaborative filtering setting, I should note that mo
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Which one is better maximum likelihood or marginal likelihood and why?
Each of these will give different results with a different interpretation. The first finds the pair $\beta$,$\theta$ which is most probable, while the second finds the $\beta$ which is (marginally) most probable. Imagine that your distribution looks like this: Β Β Β Β $\beta=1$$\beta=2$ $\theta=1$0.0Β 0.2Β  $\theta=2$0.1Β 0.2...
Which one is better maximum likelihood or marginal likelihood and why?
Each of these will give different results with a different interpretation. The first finds the pair $\beta$,$\theta$ which is most probable, while the second finds the $\beta$ which is (marginally) mo
Which one is better maximum likelihood or marginal likelihood and why? Each of these will give different results with a different interpretation. The first finds the pair $\beta$,$\theta$ which is most probable, while the second finds the $\beta$ which is (marginally) most probable. Imagine that your distribution looks...
Which one is better maximum likelihood or marginal likelihood and why? Each of these will give different results with a different interpretation. The first finds the pair $\beta$,$\theta$ which is most probable, while the second finds the $\beta$ which is (marginally) mo
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Which one is better maximum likelihood or marginal likelihood and why?
I'm grappling with this question myself right now. Here's a result that may be helpful. Consider the linear model $$y = X\beta + \epsilon, \quad \epsilon \sim N(0,\sigma^2)$$ where $y \in \mathbb{R}^n, \beta \in \mathbb{R}^p,$ and $\beta$ and $\sigma^2$ are the parameters of interest. The joint likelihood is $$L(\beta,...
Which one is better maximum likelihood or marginal likelihood and why?
I'm grappling with this question myself right now. Here's a result that may be helpful. Consider the linear model $$y = X\beta + \epsilon, \quad \epsilon \sim N(0,\sigma^2)$$ where $y \in \mathbb{R}^n
Which one is better maximum likelihood or marginal likelihood and why? I'm grappling with this question myself right now. Here's a result that may be helpful. Consider the linear model $$y = X\beta + \epsilon, \quad \epsilon \sim N(0,\sigma^2)$$ where $y \in \mathbb{R}^n, \beta \in \mathbb{R}^p,$ and $\beta$ and $\sigm...
Which one is better maximum likelihood or marginal likelihood and why? I'm grappling with this question myself right now. Here's a result that may be helpful. Consider the linear model $$y = X\beta + \epsilon, \quad \epsilon \sim N(0,\sigma^2)$$ where $y \in \mathbb{R}^n
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Which one is better maximum likelihood or marginal likelihood and why?
This is usually not a matter of choice. If we are interested in the estimation of $\beta$ (e.g. when $\beta$ is a model hyperparameter and $\theta$ is a latent variable) and there is not a single value for $\theta$ and instead the distribution of $\theta$ in known, we need to integrate out $\theta$. You can think of ...
Which one is better maximum likelihood or marginal likelihood and why?
This is usually not a matter of choice. If we are interested in the estimation of $\beta$ (e.g. when $\beta$ is a model hyperparameter and $\theta$ is a latent variable) and there is not a single val
Which one is better maximum likelihood or marginal likelihood and why? This is usually not a matter of choice. If we are interested in the estimation of $\beta$ (e.g. when $\beta$ is a model hyperparameter and $\theta$ is a latent variable) and there is not a single value for $\theta$ and instead the distribution of $...
Which one is better maximum likelihood or marginal likelihood and why? This is usually not a matter of choice. If we are interested in the estimation of $\beta$ (e.g. when $\beta$ is a model hyperparameter and $\theta$ is a latent variable) and there is not a single val
14,635
In R how to compute the p-value for area under ROC
In your situation it would be fine to plot a ROC curve, and to calculate the area under that curve, but this should be thought of as supplemental to your main analysis, rather than the primary analysis itself. Instead, you want to fit a logistic regression model. The logistic regression model will come standard with...
In R how to compute the p-value for area under ROC
In your situation it would be fine to plot a ROC curve, and to calculate the area under that curve, but this should be thought of as supplemental to your main analysis, rather than the primary analysi
In R how to compute the p-value for area under ROC In your situation it would be fine to plot a ROC curve, and to calculate the area under that curve, but this should be thought of as supplemental to your main analysis, rather than the primary analysis itself. Instead, you want to fit a logistic regression model. Th...
In R how to compute the p-value for area under ROC In your situation it would be fine to plot a ROC curve, and to calculate the area under that curve, but this should be thought of as supplemental to your main analysis, rather than the primary analysi
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In R how to compute the p-value for area under ROC
Basically you want to test H0 = "The AUC is equal to 0.5". This is in fact equivalent as saying H0 = "The distribution of the ranks in the two groups are equal". The latter is the null hypothesis of the Mann-Whitney (Wilcoxon) test (see for instance Gold, 1999). In other words, you can safely use a Mann-Whitney-Wilcoxo...
In R how to compute the p-value for area under ROC
Basically you want to test H0 = "The AUC is equal to 0.5". This is in fact equivalent as saying H0 = "The distribution of the ranks in the two groups are equal". The latter is the null hypothesis of t
In R how to compute the p-value for area under ROC Basically you want to test H0 = "The AUC is equal to 0.5". This is in fact equivalent as saying H0 = "The distribution of the ranks in the two groups are equal". The latter is the null hypothesis of the Mann-Whitney (Wilcoxon) test (see for instance Gold, 1999). In oth...
In R how to compute the p-value for area under ROC Basically you want to test H0 = "The AUC is equal to 0.5". This is in fact equivalent as saying H0 = "The distribution of the ranks in the two groups are equal". The latter is the null hypothesis of t
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In R how to compute the p-value for area under ROC
You can use roc.area() from the package verification: install.packages("verification") library("verification") # Data used from Mason and Graham (2002). a<- c(1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995) d<- c(.928,.576, .008, .944, .832, .816, .136, .584, .032, .016, .28,...
In R how to compute the p-value for area under ROC
You can use roc.area() from the package verification: install.packages("verification") library("verification") # Data used from Mason and Graham (2002). a<- c(1981, 1982, 1983, 1984, 1985, 1986, 1987
In R how to compute the p-value for area under ROC You can use roc.area() from the package verification: install.packages("verification") library("verification") # Data used from Mason and Graham (2002). a<- c(1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995) d<- c(.928,.576, ....
In R how to compute the p-value for area under ROC You can use roc.area() from the package verification: install.packages("verification") library("verification") # Data used from Mason and Graham (2002). a<- c(1981, 1982, 1983, 1984, 1985, 1986, 1987
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In R how to compute the p-value for area under ROC
Two ROC curves can be compared in pROC using roc.test(). This also produces a p-value. In addition, using roc(..., auc=TRUE, ci=TRUE) will give you the lower and higher confidence intervals along with the AUC in the output while creating the ROC object, which may be useful. The following is working example code that te...
In R how to compute the p-value for area under ROC
Two ROC curves can be compared in pROC using roc.test(). This also produces a p-value. In addition, using roc(..., auc=TRUE, ci=TRUE) will give you the lower and higher confidence intervals along with
In R how to compute the p-value for area under ROC Two ROC curves can be compared in pROC using roc.test(). This also produces a p-value. In addition, using roc(..., auc=TRUE, ci=TRUE) will give you the lower and higher confidence intervals along with the AUC in the output while creating the ROC object, which may be us...
In R how to compute the p-value for area under ROC Two ROC curves can be compared in pROC using roc.test(). This also produces a p-value. In addition, using roc(..., auc=TRUE, ci=TRUE) will give you the lower and higher confidence intervals along with
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Machine learning curse of dimensionality explained?
Translating that paragraph: Let there be a set of features that describe a data point. Maybe you're looking at the weather. That set of features might include things like temperature, humidity, time of day, etc. So each data point might have one feature (if you're only looking at temperature) or it might have 2 feature...
Machine learning curse of dimensionality explained?
Translating that paragraph: Let there be a set of features that describe a data point. Maybe you're looking at the weather. That set of features might include things like temperature, humidity, time o
Machine learning curse of dimensionality explained? Translating that paragraph: Let there be a set of features that describe a data point. Maybe you're looking at the weather. That set of features might include things like temperature, humidity, time of day, etc. So each data point might have one feature (if you're onl...
Machine learning curse of dimensionality explained? Translating that paragraph: Let there be a set of features that describe a data point. Maybe you're looking at the weather. That set of features might include things like temperature, humidity, time o
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Machine learning curse of dimensionality explained?
matty-d has already provided a very good answer, but I found another answer that explains this problem equally as well, from a Quora user Kevin Lacker: Let's say you have a straight line 100 yards long and you dropped a penny somewhere on it. It wouldn't be too hard to find. You walk along the line and it takes tw...
Machine learning curse of dimensionality explained?
matty-d has already provided a very good answer, but I found another answer that explains this problem equally as well, from a Quora user Kevin Lacker: Let's say you have a straight line 100 yards lo
Machine learning curse of dimensionality explained? matty-d has already provided a very good answer, but I found another answer that explains this problem equally as well, from a Quora user Kevin Lacker: Let's say you have a straight line 100 yards long and you dropped a penny somewhere on it. It wouldn't be too har...
Machine learning curse of dimensionality explained? matty-d has already provided a very good answer, but I found another answer that explains this problem equally as well, from a Quora user Kevin Lacker: Let's say you have a straight line 100 yards lo
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Machine learning curse of dimensionality explained?
That example can give some intuition of the problem, but is actually not a rigorous proof at all: that's only an example where many samples are needed to get a "good" space coverage. There could be (and there are indeed, e.g. hexagons in 2D already) much more efficient coverages than a regular grid... (the sophisticate...
Machine learning curse of dimensionality explained?
That example can give some intuition of the problem, but is actually not a rigorous proof at all: that's only an example where many samples are needed to get a "good" space coverage. There could be (a
Machine learning curse of dimensionality explained? That example can give some intuition of the problem, but is actually not a rigorous proof at all: that's only an example where many samples are needed to get a "good" space coverage. There could be (and there are indeed, e.g. hexagons in 2D already) much more efficien...
Machine learning curse of dimensionality explained? That example can give some intuition of the problem, but is actually not a rigorous proof at all: that's only an example where many samples are needed to get a "good" space coverage. There could be (a
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$t$-tests vs $z$-tests?
The names "$t$-test" and "$z$-test" are typically used to refer to the special case when $X$ is normal $\mbox{N}(\mu,\sigma^2)$, $\hat{b}=\bar{x}$ and $C=\mu_{0}$. You can however of course construct tests of "$t$-test type" in other settings as well (bootstrap comes to mind), using the same type of reasoning. Either w...
$t$-tests vs $z$-tests?
The names "$t$-test" and "$z$-test" are typically used to refer to the special case when $X$ is normal $\mbox{N}(\mu,\sigma^2)$, $\hat{b}=\bar{x}$ and $C=\mu_{0}$. You can however of course construct
$t$-tests vs $z$-tests? The names "$t$-test" and "$z$-test" are typically used to refer to the special case when $X$ is normal $\mbox{N}(\mu,\sigma^2)$, $\hat{b}=\bar{x}$ and $C=\mu_{0}$. You can however of course construct tests of "$t$-test type" in other settings as well (bootstrap comes to mind), using the same typ...
$t$-tests vs $z$-tests? The names "$t$-test" and "$z$-test" are typically used to refer to the special case when $X$ is normal $\mbox{N}(\mu,\sigma^2)$, $\hat{b}=\bar{x}$ and $C=\mu_{0}$. You can however of course construct
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Negative coefficient in ordered logistic regression
You're on the right track, but always have a look at the documentation of the software you're using to see what model is actually fit. Assume a situation with a categorical dependent variable $Y$ with ordered categories $1, \ldots, g, \ldots, k$ and predictors $X_{1}, \ldots, X_{j}, \ldots, X_{p}$. "In the wild", you c...
Negative coefficient in ordered logistic regression
You're on the right track, but always have a look at the documentation of the software you're using to see what model is actually fit. Assume a situation with a categorical dependent variable $Y$ with
Negative coefficient in ordered logistic regression You're on the right track, but always have a look at the documentation of the software you're using to see what model is actually fit. Assume a situation with a categorical dependent variable $Y$ with ordered categories $1, \ldots, g, \ldots, k$ and predictors $X_{1},...
Negative coefficient in ordered logistic regression You're on the right track, but always have a look at the documentation of the software you're using to see what model is actually fit. Assume a situation with a categorical dependent variable $Y$ with
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Principal component analysis "backwards": how much variance of the data is explained by a given linear combination of the variables?
If we start with the premise that all variables have been centred (standard practice in PCA), then the total variance in the data is just the sum of squares: $$T=\sum_{i}(A_{i}^{2}+B_{i}^{2}+C_{i}^{2}+D_{i}^{2}+E_{i}^{2}+F_{i}^{2})$$ This is equal to the trace of the covariance matrix of the variables, which equals the...
Principal component analysis "backwards": how much variance of the data is explained by a given line
If we start with the premise that all variables have been centred (standard practice in PCA), then the total variance in the data is just the sum of squares: $$T=\sum_{i}(A_{i}^{2}+B_{i}^{2}+C_{i}^{2}
Principal component analysis "backwards": how much variance of the data is explained by a given linear combination of the variables? If we start with the premise that all variables have been centred (standard practice in PCA), then the total variance in the data is just the sum of squares: $$T=\sum_{i}(A_{i}^{2}+B_{i}^...
Principal component analysis "backwards": how much variance of the data is explained by a given line If we start with the premise that all variables have been centred (standard practice in PCA), then the total variance in the data is just the sum of squares: $$T=\sum_{i}(A_{i}^{2}+B_{i}^{2}+C_{i}^{2}
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Principal component analysis "backwards": how much variance of the data is explained by a given linear combination of the variables?
Let's say I choose some linear combination of these variables -- e.g. $A+2B+5C$, could I work out how much variance in the data this describes? This question can be understood in two different ways, leading to two different answers. A linear combination corresponds to a vector, which in your example is $[1, 2, 5, 0, 0...
Principal component analysis "backwards": how much variance of the data is explained by a given line
Let's say I choose some linear combination of these variables -- e.g. $A+2B+5C$, could I work out how much variance in the data this describes? This question can be understood in two different ways,
Principal component analysis "backwards": how much variance of the data is explained by a given linear combination of the variables? Let's say I choose some linear combination of these variables -- e.g. $A+2B+5C$, could I work out how much variance in the data this describes? This question can be understood in two dif...
Principal component analysis "backwards": how much variance of the data is explained by a given line Let's say I choose some linear combination of these variables -- e.g. $A+2B+5C$, could I work out how much variance in the data this describes? This question can be understood in two different ways,
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Principal component analysis "backwards": how much variance of the data is explained by a given linear combination of the variables?
Let the total variance, $T$, in a data set of vectors be the sum of squared errors (SSE) between the vectors in the data set and the mean vector of the data set, $$T = \sum_{i} (x_i-\bar{x}) \cdot (x_i-\bar{x})$$ where $\bar{x}$ is the mean vector of the data set, $x_i$ is the ith vector in the data set, and $\cdot$ ...
Principal component analysis "backwards": how much variance of the data is explained by a given line
Let the total variance, $T$, in a data set of vectors be the sum of squared errors (SSE) between the vectors in the data set and the mean vector of the data set, $$T = \sum_{i} (x_i-\bar{x}) \cdot (x
Principal component analysis "backwards": how much variance of the data is explained by a given linear combination of the variables? Let the total variance, $T$, in a data set of vectors be the sum of squared errors (SSE) between the vectors in the data set and the mean vector of the data set, $$T = \sum_{i} (x_i-\bar...
Principal component analysis "backwards": how much variance of the data is explained by a given line Let the total variance, $T$, in a data set of vectors be the sum of squared errors (SSE) between the vectors in the data set and the mean vector of the data set, $$T = \sum_{i} (x_i-\bar{x}) \cdot (x
14,647
How does the power of a logistic regression and a t-test compare?
If I have computed correctly, logistic regression asymptotically has the same power as the t-test. To see this, write down its log likelihood and compute the expectation of its Hessian at its global maximum (its negative estimates the variance-covariance matrix of the ML solution). Don't bother with the usual logisti...
How does the power of a logistic regression and a t-test compare?
If I have computed correctly, logistic regression asymptotically has the same power as the t-test. To see this, write down its log likelihood and compute the expectation of its Hessian at its global
How does the power of a logistic regression and a t-test compare? If I have computed correctly, logistic regression asymptotically has the same power as the t-test. To see this, write down its log likelihood and compute the expectation of its Hessian at its global maximum (its negative estimates the variance-covarianc...
How does the power of a logistic regression and a t-test compare? If I have computed correctly, logistic regression asymptotically has the same power as the t-test. To see this, write down its log likelihood and compute the expectation of its Hessian at its global
14,648
How does the power of a logistic regression and a t-test compare?
Here is code in R that illustrates the simulation of whuber's answer. Feedback on improving my R code is more than welcome. N <- 900 # Total number data points m <- 30; # Size of draw per set n <- 30; # No of sets p_null <- 0.70; # Null hypothesis p_alternate <- 0.74 # Alternate hy...
How does the power of a logistic regression and a t-test compare?
Here is code in R that illustrates the simulation of whuber's answer. Feedback on improving my R code is more than welcome. N <- 900 # Total number data points m <- 30; # Size of
How does the power of a logistic regression and a t-test compare? Here is code in R that illustrates the simulation of whuber's answer. Feedback on improving my R code is more than welcome. N <- 900 # Total number data points m <- 30; # Size of draw per set n <- 30; # No of sets p_null...
How does the power of a logistic regression and a t-test compare? Here is code in R that illustrates the simulation of whuber's answer. Feedback on improving my R code is more than welcome. N <- 900 # Total number data points m <- 30; # Size of
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Good introduction into different kinds of entropy
Cover and Thomas's book Elements of Information Theory is a good source on entropy and its applications, although I don't know that it addresses exactly the issues you have in mind.
Good introduction into different kinds of entropy
Cover and Thomas's book Elements of Information Theory is a good source on entropy and its applications, although I don't know that it addresses exactly the issues you have in mind.
Good introduction into different kinds of entropy Cover and Thomas's book Elements of Information Theory is a good source on entropy and its applications, although I don't know that it addresses exactly the issues you have in mind.
Good introduction into different kinds of entropy Cover and Thomas's book Elements of Information Theory is a good source on entropy and its applications, although I don't know that it addresses exactly the issues you have in mind.
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Good introduction into different kinds of entropy
These lecture notes on information theory by O. Johnson contain a good introduction to different kinds of entropy.
Good introduction into different kinds of entropy
These lecture notes on information theory by O. Johnson contain a good introduction to different kinds of entropy.
Good introduction into different kinds of entropy These lecture notes on information theory by O. Johnson contain a good introduction to different kinds of entropy.
Good introduction into different kinds of entropy These lecture notes on information theory by O. Johnson contain a good introduction to different kinds of entropy.
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Good introduction into different kinds of entropy
If your interested in the mathematical statistic around entropy, you may consult this book http://www.renyi.hu/~csiszar/Publications/Information_Theory_and_Statistics:_A_Tutorial.pdf it is freely available !
Good introduction into different kinds of entropy
If your interested in the mathematical statistic around entropy, you may consult this book http://www.renyi.hu/~csiszar/Publications/Information_Theory_and_Statistics:_A_Tutorial.pdf it is freely ava
Good introduction into different kinds of entropy If your interested in the mathematical statistic around entropy, you may consult this book http://www.renyi.hu/~csiszar/Publications/Information_Theory_and_Statistics:_A_Tutorial.pdf it is freely available !
Good introduction into different kinds of entropy If your interested in the mathematical statistic around entropy, you may consult this book http://www.renyi.hu/~csiszar/Publications/Information_Theory_and_Statistics:_A_Tutorial.pdf it is freely ava
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Good introduction into different kinds of entropy
GrΓΌnwald and Dawid's paper Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory discuss generalisations of the traditional notion of entropy. Given a loss, its associated entropy function is the mapping from a distribution to the minimal achievable expected loss for that distribution. T...
Good introduction into different kinds of entropy
GrΓΌnwald and Dawid's paper Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory discuss generalisations of the traditional notion of entropy. Given a loss, its associa
Good introduction into different kinds of entropy GrΓΌnwald and Dawid's paper Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory discuss generalisations of the traditional notion of entropy. Given a loss, its associated entropy function is the mapping from a distribution to the minimal...
Good introduction into different kinds of entropy GrΓΌnwald and Dawid's paper Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory discuss generalisations of the traditional notion of entropy. Given a loss, its associa
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Good introduction into different kinds of entropy
The entropy is only one (as a concept) -- the amount of information needed to describe some system; there are only many its generalizations. Sample entropy is only some entropy-like descriptor used in heart rate analysis.
Good introduction into different kinds of entropy
The entropy is only one (as a concept) -- the amount of information needed to describe some system; there are only many its generalizations. Sample entropy is only some entropy-like descriptor used in
Good introduction into different kinds of entropy The entropy is only one (as a concept) -- the amount of information needed to describe some system; there are only many its generalizations. Sample entropy is only some entropy-like descriptor used in heart rate analysis.
Good introduction into different kinds of entropy The entropy is only one (as a concept) -- the amount of information needed to describe some system; there are only many its generalizations. Sample entropy is only some entropy-like descriptor used in
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Good introduction into different kinds of entropy
Jaynes shows how to derive Shannon's entropy from basic principles in his book. One idea is that if you approximate $n!$ by $n^n$, entropy is the rewriting of the following quantity $$\frac{1}{n}\log \frac{n!}{(n p_1)!\cdots (n p_d)!}$$ The quantity inside the log is the number of different length n observation sequen...
Good introduction into different kinds of entropy
Jaynes shows how to derive Shannon's entropy from basic principles in his book. One idea is that if you approximate $n!$ by $n^n$, entropy is the rewriting of the following quantity $$\frac{1}{n}\log
Good introduction into different kinds of entropy Jaynes shows how to derive Shannon's entropy from basic principles in his book. One idea is that if you approximate $n!$ by $n^n$, entropy is the rewriting of the following quantity $$\frac{1}{n}\log \frac{n!}{(n p_1)!\cdots (n p_d)!}$$ The quantity inside the log is t...
Good introduction into different kinds of entropy Jaynes shows how to derive Shannon's entropy from basic principles in his book. One idea is that if you approximate $n!$ by $n^n$, entropy is the rewriting of the following quantity $$\frac{1}{n}\log
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Does it make sense to use Logistic regression with binary outcome and predictor?
In this case you can collapse your data to $$ \begin{array}{c|cc} X \backslash Y & 0 & 1 \\ \hline 0 & S_{00} & S_{01} \\ 1 & S_{10} & S_{11} \end{array} $$ where $S_{ij}$ is the number of instances for $x = i$ and $y =j$ with $i,j \in \{0,1\}$. Suppose there are $n$ observations overall. If we fit the model $p_i = g^{...
Does it make sense to use Logistic regression with binary outcome and predictor?
In this case you can collapse your data to $$ \begin{array}{c|cc} X \backslash Y & 0 & 1 \\ \hline 0 & S_{00} & S_{01} \\ 1 & S_{10} & S_{11} \end{array} $$ where $S_{ij}$ is the number of instances f
Does it make sense to use Logistic regression with binary outcome and predictor? In this case you can collapse your data to $$ \begin{array}{c|cc} X \backslash Y & 0 & 1 \\ \hline 0 & S_{00} & S_{01} \\ 1 & S_{10} & S_{11} \end{array} $$ where $S_{ij}$ is the number of instances for $x = i$ and $y =j$ with $i,j \in \{0...
Does it make sense to use Logistic regression with binary outcome and predictor? In this case you can collapse your data to $$ \begin{array}{c|cc} X \backslash Y & 0 & 1 \\ \hline 0 & S_{00} & S_{01} \\ 1 & S_{10} & S_{11} \end{array} $$ where $S_{ij}$ is the number of instances f
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Does it make sense to use Logistic regression with binary outcome and predictor?
When you have more than one predictors and all the predictors are binary variables, you could fit a model using Logic Regression [1] (note it's "Logic" not "Logistic"). It's useful when you believe interaction effects among your predictors are prominent. There's an implementation in R (LogicReg package). [1] Ruczins...
Does it make sense to use Logistic regression with binary outcome and predictor?
When you have more than one predictors and all the predictors are binary variables, you could fit a model using Logic Regression [1] (note it's "Logic" not "Logistic"). It's useful when you believe in
Does it make sense to use Logistic regression with binary outcome and predictor? When you have more than one predictors and all the predictors are binary variables, you could fit a model using Logic Regression [1] (note it's "Logic" not "Logistic"). It's useful when you believe interaction effects among your predictors...
Does it make sense to use Logistic regression with binary outcome and predictor? When you have more than one predictors and all the predictors are binary variables, you could fit a model using Logic Regression [1] (note it's "Logic" not "Logistic"). It's useful when you believe in
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difference between convex and concave functions
A convex function has one minimum - a nice property, as an optimization algorithm won't get stuck in a local minimum that isn't a global minimum. Take $x^2 - 1$, for example: A non-convex function is wavy - has some 'valleys' (local minima) that aren't as deep as the overall deepest 'valley' (global minimum). Optimizat...
difference between convex and concave functions
A convex function has one minimum - a nice property, as an optimization algorithm won't get stuck in a local minimum that isn't a global minimum. Take $x^2 - 1$, for example: A non-convex function is
difference between convex and concave functions A convex function has one minimum - a nice property, as an optimization algorithm won't get stuck in a local minimum that isn't a global minimum. Take $x^2 - 1$, for example: A non-convex function is wavy - has some 'valleys' (local minima) that aren't as deep as the over...
difference between convex and concave functions A convex function has one minimum - a nice property, as an optimization algorithm won't get stuck in a local minimum that isn't a global minimum. Take $x^2 - 1$, for example: A non-convex function is
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difference between convex and concave functions
To define a convex function, you need a convex set $X$ as the domain and $\mathbb{R}$ as the codomain. A function is convex if it satisfies the following property: $$\forall x_1, x_2 \in X, \forall t \in [0,1], f(tx_1+(1-t)x_2) \le tf(x_1) +(1-t)f(x_2)$$ You should read through the wikipedia page of convex funciton. I...
difference between convex and concave functions
To define a convex function, you need a convex set $X$ as the domain and $\mathbb{R}$ as the codomain. A function is convex if it satisfies the following property: $$\forall x_1, x_2 \in X, \forall t
difference between convex and concave functions To define a convex function, you need a convex set $X$ as the domain and $\mathbb{R}$ as the codomain. A function is convex if it satisfies the following property: $$\forall x_1, x_2 \in X, \forall t \in [0,1], f(tx_1+(1-t)x_2) \le tf(x_1) +(1-t)f(x_2)$$ You should read ...
difference between convex and concave functions To define a convex function, you need a convex set $X$ as the domain and $\mathbb{R}$ as the codomain. A function is convex if it satisfies the following property: $$\forall x_1, x_2 \in X, \forall t
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Intuition behind the hazard rate
Let $X$ denote the time of death (or time of failure if you prefer a less morbid description). Suppose that $X$ is a continuous random variable whose density function $f(t)$ is nonzero only on $(0,\infty)$. Now, notice that it must be the case that $f(t)$ decays away to $0$ as $t \to \infty$ because if $f(t)$ does not...
Intuition behind the hazard rate
Let $X$ denote the time of death (or time of failure if you prefer a less morbid description). Suppose that $X$ is a continuous random variable whose density function $f(t)$ is nonzero only on $(0,\i
Intuition behind the hazard rate Let $X$ denote the time of death (or time of failure if you prefer a less morbid description). Suppose that $X$ is a continuous random variable whose density function $f(t)$ is nonzero only on $(0,\infty)$. Now, notice that it must be the case that $f(t)$ decays away to $0$ as $t \to \...
Intuition behind the hazard rate Let $X$ denote the time of death (or time of failure if you prefer a less morbid description). Suppose that $X$ is a continuous random variable whose density function $f(t)$ is nonzero only on $(0,\i
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Intuition behind the hazard rate
Imagine that you are interested in the incidence of (first) marriage for men. To look at the incidence of marriage at age 20, say, you would select a sample of people who are not married at that age and see if they get married within the next year (before they turn 21). The you could get a rough estimate for $$ P(\mat...
Intuition behind the hazard rate
Imagine that you are interested in the incidence of (first) marriage for men. To look at the incidence of marriage at age 20, say, you would select a sample of people who are not married at that age a
Intuition behind the hazard rate Imagine that you are interested in the incidence of (first) marriage for men. To look at the incidence of marriage at age 20, say, you would select a sample of people who are not married at that age and see if they get married within the next year (before they turn 21). The you could g...
Intuition behind the hazard rate Imagine that you are interested in the incidence of (first) marriage for men. To look at the incidence of marriage at age 20, say, you would select a sample of people who are not married at that age a
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Intuition behind the hazard rate
$f(x)$ is not the probability of death, but the probability density; the expected number of times you die within the next unit of time if the probability density remained constant during that unit of time. Notice there is a problem: your probability of dying when you already died before is rather problematic. So it mak...
Intuition behind the hazard rate
$f(x)$ is not the probability of death, but the probability density; the expected number of times you die within the next unit of time if the probability density remained constant during that unit of
Intuition behind the hazard rate $f(x)$ is not the probability of death, but the probability density; the expected number of times you die within the next unit of time if the probability density remained constant during that unit of time. Notice there is a problem: your probability of dying when you already died before...
Intuition behind the hazard rate $f(x)$ is not the probability of death, but the probability density; the expected number of times you die within the next unit of time if the probability density remained constant during that unit of
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Intuition behind the hazard rate
"Death of a person is a tragedy, deaths of millions is statistics" - Joseph Stalin Hazard rate is just a renormalization of the probability space that takes pallid impersonal statistics on input and converts it into your own chances to live another day. Suppose you're an average young man in the Wild West. You decide ...
Intuition behind the hazard rate
"Death of a person is a tragedy, deaths of millions is statistics" - Joseph Stalin Hazard rate is just a renormalization of the probability space that takes pallid impersonal statistics on input and
Intuition behind the hazard rate "Death of a person is a tragedy, deaths of millions is statistics" - Joseph Stalin Hazard rate is just a renormalization of the probability space that takes pallid impersonal statistics on input and converts it into your own chances to live another day. Suppose you're an average young ...
Intuition behind the hazard rate "Death of a person is a tragedy, deaths of millions is statistics" - Joseph Stalin Hazard rate is just a renormalization of the probability space that takes pallid impersonal statistics on input and
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What is "Targeted Maximum Likelihood Expectation"?
I agree that van der Laan has a tendency to invent new names for already existing ideas (e.g. the super-learner), but TMLE is not one of them as far as I know. It is actually a very clever idea, and I have seen nothing from the Machine Learning community which looks similar (although I might just be ignorant). The idea...
What is "Targeted Maximum Likelihood Expectation"?
I agree that van der Laan has a tendency to invent new names for already existing ideas (e.g. the super-learner), but TMLE is not one of them as far as I know. It is actually a very clever idea, and I
What is "Targeted Maximum Likelihood Expectation"? I agree that van der Laan has a tendency to invent new names for already existing ideas (e.g. the super-learner), but TMLE is not one of them as far as I know. It is actually a very clever idea, and I have seen nothing from the Machine Learning community which looks si...
What is "Targeted Maximum Likelihood Expectation"? I agree that van der Laan has a tendency to invent new names for already existing ideas (e.g. the super-learner), but TMLE is not one of them as far as I know. It is actually a very clever idea, and I
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What's the difference between multiple R and R squared?
Capital $R^2$ (as opposed to $r^2$) should generally be the multiple $R^2$ in a multiple regression model. In bivariate linear regression, there is no multiple $R$, and $R^2=r^2$. So one difference is applicability: "multiple $R$" implies multiple regressors, whereas "$R^2$" doesn't necessarily. Another simple differen...
What's the difference between multiple R and R squared?
Capital $R^2$ (as opposed to $r^2$) should generally be the multiple $R^2$ in a multiple regression model. In bivariate linear regression, there is no multiple $R$, and $R^2=r^2$. So one difference is
What's the difference between multiple R and R squared? Capital $R^2$ (as opposed to $r^2$) should generally be the multiple $R^2$ in a multiple regression model. In bivariate linear regression, there is no multiple $R$, and $R^2=r^2$. So one difference is applicability: "multiple $R$" implies multiple regressors, wher...
What's the difference between multiple R and R squared? Capital $R^2$ (as opposed to $r^2$) should generally be the multiple $R^2$ in a multiple regression model. In bivariate linear regression, there is no multiple $R$, and $R^2=r^2$. So one difference is
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What's the difference between multiple R and R squared?
Multiple R actually can be viewed as the correlation between response and the fitted values. As such it is always positive. Multiple R-squared is its squared version. Let me illustrate using a small example: set.seed(32) n <- 100 x1 <- runif(n) x2 <- runif(n) y <- 4 + x1 - 2*x2 + rnorm(n) fit <- lm(y ~ x1 + x2) summa...
What's the difference between multiple R and R squared?
Multiple R actually can be viewed as the correlation between response and the fitted values. As such it is always positive. Multiple R-squared is its squared version. Let me illustrate using a small
What's the difference between multiple R and R squared? Multiple R actually can be viewed as the correlation between response and the fitted values. As such it is always positive. Multiple R-squared is its squared version. Let me illustrate using a small example: set.seed(32) n <- 100 x1 <- runif(n) x2 <- runif(n) y <...
What's the difference between multiple R and R squared? Multiple R actually can be viewed as the correlation between response and the fitted values. As such it is always positive. Multiple R-squared is its squared version. Let me illustrate using a small
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What's the difference between multiple R and R squared?
I simply explain to my students that: the multiple R be thought of as the absolute value of the correlation coefficient (or the correlation coefficient without the negative sign)! The R-squared is simply the square of the multiple R. It can be through of as percentage of variation caused by the independent variable ...
What's the difference between multiple R and R squared?
I simply explain to my students that: the multiple R be thought of as the absolute value of the correlation coefficient (or the correlation coefficient without the negative sign)! The R-squared is
What's the difference between multiple R and R squared? I simply explain to my students that: the multiple R be thought of as the absolute value of the correlation coefficient (or the correlation coefficient without the negative sign)! The R-squared is simply the square of the multiple R. It can be through of as per...
What's the difference between multiple R and R squared? I simply explain to my students that: the multiple R be thought of as the absolute value of the correlation coefficient (or the correlation coefficient without the negative sign)! The R-squared is
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How do I find values not given in (interpolate in) statistical tables?
This answer is in two main parts: firstly, using linear interpolation, and secondly, using transformations for more accurate interpolation. The approaches discussed here are suitable for hand calculation when you have limited tables available, but if you're implementing a computer routine to produce p-values, there are...
How do I find values not given in (interpolate in) statistical tables?
This answer is in two main parts: firstly, using linear interpolation, and secondly, using transformations for more accurate interpolation. The approaches discussed here are suitable for hand calculat
How do I find values not given in (interpolate in) statistical tables? This answer is in two main parts: firstly, using linear interpolation, and secondly, using transformations for more accurate interpolation. The approaches discussed here are suitable for hand calculation when you have limited tables available, but i...
How do I find values not given in (interpolate in) statistical tables? This answer is in two main parts: firstly, using linear interpolation, and secondly, using transformations for more accurate interpolation. The approaches discussed here are suitable for hand calculat
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Random effect equal to 0 in generalized linear mixed model [duplicate]
With just three farms, there is no point in trying to pretend that you can fit a Gaussian distribution to three points. Analyze this simply as lm(response~as.factor(farm) + treat+other stuff), and don't bother with lmer; you won't be able to do much better than ANOVA, anyway. Generally, hitting exactly zero is not that...
Random effect equal to 0 in generalized linear mixed model [duplicate]
With just three farms, there is no point in trying to pretend that you can fit a Gaussian distribution to three points. Analyze this simply as lm(response~as.factor(farm) + treat+other stuff), and don
Random effect equal to 0 in generalized linear mixed model [duplicate] With just three farms, there is no point in trying to pretend that you can fit a Gaussian distribution to three points. Analyze this simply as lm(response~as.factor(farm) + treat+other stuff), and don't bother with lmer; you won't be able to do much...
Random effect equal to 0 in generalized linear mixed model [duplicate] With just three farms, there is no point in trying to pretend that you can fit a Gaussian distribution to three points. Analyze this simply as lm(response~as.factor(farm) + treat+other stuff), and don
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Random effect equal to 0 in generalized linear mixed model [duplicate]
Looks like there was probably no effect due to Farm built in from the experimental design; each farm has exactly half treated and half not. > xtabs(~treat+farm, territory) farm treat 1 2 3 0 14 12 10 1 14 12 10 It can also be instructive to fit farm as a fixed effect and see what happens; we see that t...
Random effect equal to 0 in generalized linear mixed model [duplicate]
Looks like there was probably no effect due to Farm built in from the experimental design; each farm has exactly half treated and half not. > xtabs(~treat+farm, territory) farm treat 1 2 3
Random effect equal to 0 in generalized linear mixed model [duplicate] Looks like there was probably no effect due to Farm built in from the experimental design; each farm has exactly half treated and half not. > xtabs(~treat+farm, territory) farm treat 1 2 3 0 14 12 10 1 14 12 10 It can also be instru...
Random effect equal to 0 in generalized linear mixed model [duplicate] Looks like there was probably no effect due to Farm built in from the experimental design; each farm has exactly half treated and half not. > xtabs(~treat+farm, territory) farm treat 1 2 3
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Why is regression about variance?
why would we care about "how much of the variance in the data is explained by the given regression model?" To answer this it is useful to think about exactly what it means for a certain percentage of the variance to be explained by the regression model. Let $Y_{1}, ..., Y_{n}$ be the outcome variable. The usual sample...
Why is regression about variance?
why would we care about "how much of the variance in the data is explained by the given regression model?" To answer this it is useful to think about exactly what it means for a certain percentage of
Why is regression about variance? why would we care about "how much of the variance in the data is explained by the given regression model?" To answer this it is useful to think about exactly what it means for a certain percentage of the variance to be explained by the regression model. Let $Y_{1}, ..., Y_{n}$ be the ...
Why is regression about variance? why would we care about "how much of the variance in the data is explained by the given regression model?" To answer this it is useful to think about exactly what it means for a certain percentage of
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Why is regression about variance?
I can't run with the big dogs of statistics who have answered before me, and perhaps my thinking is naive, but I look at it this way... Imagine you're in a car and you're going down the road and turning the wheel left and right and pressing the gas pedal and the brakes frantically. Yet the car is moving along smoothly,...
Why is regression about variance?
I can't run with the big dogs of statistics who have answered before me, and perhaps my thinking is naive, but I look at it this way... Imagine you're in a car and you're going down the road and turni
Why is regression about variance? I can't run with the big dogs of statistics who have answered before me, and perhaps my thinking is naive, but I look at it this way... Imagine you're in a car and you're going down the road and turning the wheel left and right and pressing the gas pedal and the brakes frantically. Yet...
Why is regression about variance? I can't run with the big dogs of statistics who have answered before me, and perhaps my thinking is naive, but I look at it this way... Imagine you're in a car and you're going down the road and turni
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How to get started with rating and ranking based on pairwise competition data?
Regarding "how to do it in R", the prefmod package http://cran.r-project.org/web/packages/prefmod/index.html is meant for preference analysis with paired comparisons, rankings and ratings. It fits Bradley-Terry models and pattern models with object and subject covariates. See my answer here How to fit Bradley–Terry–L...
How to get started with rating and ranking based on pairwise competition data?
Regarding "how to do it in R", the prefmod package http://cran.r-project.org/web/packages/prefmod/index.html is meant for preference analysis with paired comparisons, rankings and ratings. It fits B
How to get started with rating and ranking based on pairwise competition data? Regarding "how to do it in R", the prefmod package http://cran.r-project.org/web/packages/prefmod/index.html is meant for preference analysis with paired comparisons, rankings and ratings. It fits Bradley-Terry models and pattern models wi...
How to get started with rating and ranking based on pairwise competition data? Regarding "how to do it in R", the prefmod package http://cran.r-project.org/web/packages/prefmod/index.html is meant for preference analysis with paired comparisons, rankings and ratings. It fits B
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How to get started with rating and ranking based on pairwise competition data?
I just finished a pretty good book on that subject. It discusses ELO as well as many other ranking methods like Massey, Colley, and Keener's. Most of the methods in the book use sports matches as the example and use both win/loss and margin of victory as inputs.
How to get started with rating and ranking based on pairwise competition data?
I just finished a pretty good book on that subject. It discusses ELO as well as many other ranking methods like Massey, Colley, and Keener's. Most of the methods in the book use sports matches as the
How to get started with rating and ranking based on pairwise competition data? I just finished a pretty good book on that subject. It discusses ELO as well as many other ranking methods like Massey, Colley, and Keener's. Most of the methods in the book use sports matches as the example and use both win/loss and margin ...
How to get started with rating and ranking based on pairwise competition data? I just finished a pretty good book on that subject. It discusses ELO as well as many other ranking methods like Massey, Colley, and Keener's. Most of the methods in the book use sports matches as the
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How to get started with rating and ranking based on pairwise competition data?
Since asking this question, I've found I've had lots of success with the PlayerRatings package for R. It makes creating ELO/Glicko and the authors own method of performance ratings very easy.
How to get started with rating and ranking based on pairwise competition data?
Since asking this question, I've found I've had lots of success with the PlayerRatings package for R. It makes creating ELO/Glicko and the authors own method of performance ratings very easy.
How to get started with rating and ranking based on pairwise competition data? Since asking this question, I've found I've had lots of success with the PlayerRatings package for R. It makes creating ELO/Glicko and the authors own method of performance ratings very easy.
How to get started with rating and ranking based on pairwise competition data? Since asking this question, I've found I've had lots of success with the PlayerRatings package for R. It makes creating ELO/Glicko and the authors own method of performance ratings very easy.
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How to get started with rating and ranking based on pairwise competition data?
This book does not work with margins but provides the theory of rank teams based on paired comparisons. The Method of Paired Comparison by Herbert A. David http://www.amazon.com/Method-Paired-Comparisons-Statistical-Monograph/dp/0852640137/ref=sr_1_1?s=books&ie=UTF8&qid=1340424897&sr=1-1&keywords=The+method+of+paired+c...
How to get started with rating and ranking based on pairwise competition data?
This book does not work with margins but provides the theory of rank teams based on paired comparisons. The Method of Paired Comparison by Herbert A. David http://www.amazon.com/Method-Paired-Comparis
How to get started with rating and ranking based on pairwise competition data? This book does not work with margins but provides the theory of rank teams based on paired comparisons. The Method of Paired Comparison by Herbert A. David http://www.amazon.com/Method-Paired-Comparisons-Statistical-Monograph/dp/0852640137/r...
How to get started with rating and ranking based on pairwise competition data? This book does not work with margins but provides the theory of rank teams based on paired comparisons. The Method of Paired Comparison by Herbert A. David http://www.amazon.com/Method-Paired-Comparis
14,676
Clustering of mixed type data with R
This may come in late but try klaR (http://cran.r-project.org/web/packages/klaR/index.html) install.packages("klar") It uses the non-hierarchical k-modes algorithm, which is based on simple matching as a distance function, so the distance Ξ΄ between a variable m of two data points $x$ and $y$ is given by $$ \delta(x_m,...
Clustering of mixed type data with R
This may come in late but try klaR (http://cran.r-project.org/web/packages/klaR/index.html) install.packages("klar") It uses the non-hierarchical k-modes algorithm, which is based on simple matching
Clustering of mixed type data with R This may come in late but try klaR (http://cran.r-project.org/web/packages/klaR/index.html) install.packages("klar") It uses the non-hierarchical k-modes algorithm, which is based on simple matching as a distance function, so the distance Ξ΄ between a variable m of two data points $...
Clustering of mixed type data with R This may come in late but try klaR (http://cran.r-project.org/web/packages/klaR/index.html) install.packages("klar") It uses the non-hierarchical k-modes algorithm, which is based on simple matching
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Clustering of mixed type data with R
Another appealing way of handling variables of mixed types is to use the proximy/similarity matrix from Random Forests: http://cogns.northwestern.edu/cbmg/LiawAndWiener2002.pdf. This faciliates a unified way of equally treating all variables (nevertheless, be aware of the variable selection bias issue). On the other ha...
Clustering of mixed type data with R
Another appealing way of handling variables of mixed types is to use the proximy/similarity matrix from Random Forests: http://cogns.northwestern.edu/cbmg/LiawAndWiener2002.pdf. This faciliates a unif
Clustering of mixed type data with R Another appealing way of handling variables of mixed types is to use the proximy/similarity matrix from Random Forests: http://cogns.northwestern.edu/cbmg/LiawAndWiener2002.pdf. This faciliates a unified way of equally treating all variables (nevertheless, be aware of the variable s...
Clustering of mixed type data with R Another appealing way of handling variables of mixed types is to use the proximy/similarity matrix from Random Forests: http://cogns.northwestern.edu/cbmg/LiawAndWiener2002.pdf. This faciliates a unif
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Clustering of mixed type data with R
You might use multiple correspondence analysis to create continuous dimensions from the categorical variables and then use them with the numerical variables in a second step.
Clustering of mixed type data with R
You might use multiple correspondence analysis to create continuous dimensions from the categorical variables and then use them with the numerical variables in a second step.
Clustering of mixed type data with R You might use multiple correspondence analysis to create continuous dimensions from the categorical variables and then use them with the numerical variables in a second step.
Clustering of mixed type data with R You might use multiple correspondence analysis to create continuous dimensions from the categorical variables and then use them with the numerical variables in a second step.
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Clustering of mixed type data with R
Well, you certainly can. By making the categorical variables artificially numeric. Or using a distance-matrix based clustering (fpc can probably do that). The question you should first try to answer is: does it actually make sense?
Clustering of mixed type data with R
Well, you certainly can. By making the categorical variables artificially numeric. Or using a distance-matrix based clustering (fpc can probably do that). The question you should first try to answer i
Clustering of mixed type data with R Well, you certainly can. By making the categorical variables artificially numeric. Or using a distance-matrix based clustering (fpc can probably do that). The question you should first try to answer is: does it actually make sense?
Clustering of mixed type data with R Well, you certainly can. By making the categorical variables artificially numeric. Or using a distance-matrix based clustering (fpc can probably do that). The question you should first try to answer i
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Clustering of mixed type data with R
You could use the universal similarity coefficient of Gower (see Sneath & Sokal 1973, pp 135-136), which for two OTUs $j$ and $k$ is $$S_G = \frac{\sum_{i=1}^n{w_{i,j,k} s_{i,j,k}}}{\sum_{i=1}^n{w_{i,j,k}}}$$ for all characters $i$. The weight $w_{i,j,k}$ is either 1 or 0, depending on whether the the comparison is val...
Clustering of mixed type data with R
You could use the universal similarity coefficient of Gower (see Sneath & Sokal 1973, pp 135-136), which for two OTUs $j$ and $k$ is $$S_G = \frac{\sum_{i=1}^n{w_{i,j,k} s_{i,j,k}}}{\sum_{i=1}^n{w_{i,
Clustering of mixed type data with R You could use the universal similarity coefficient of Gower (see Sneath & Sokal 1973, pp 135-136), which for two OTUs $j$ and $k$ is $$S_G = \frac{\sum_{i=1}^n{w_{i,j,k} s_{i,j,k}}}{\sum_{i=1}^n{w_{i,j,k}}}$$ for all characters $i$. The weight $w_{i,j,k}$ is either 1 or 0, depending...
Clustering of mixed type data with R You could use the universal similarity coefficient of Gower (see Sneath & Sokal 1973, pp 135-136), which for two OTUs $j$ and $k$ is $$S_G = \frac{\sum_{i=1}^n{w_{i,j,k} s_{i,j,k}}}{\sum_{i=1}^n{w_{i,
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Clustering of mixed type data with R
If possible values of categorical variables are not too many, then you may think of creating binary variables out of those values. You can treat these binary variables as numeric variables and run your clustering. That's what I did for my project.
Clustering of mixed type data with R
If possible values of categorical variables are not too many, then you may think of creating binary variables out of those values. You can treat these binary variables as numeric variables and run yo
Clustering of mixed type data with R If possible values of categorical variables are not too many, then you may think of creating binary variables out of those values. You can treat these binary variables as numeric variables and run your clustering. That's what I did for my project.
Clustering of mixed type data with R If possible values of categorical variables are not too many, then you may think of creating binary variables out of those values. You can treat these binary variables as numeric variables and run yo
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Clustering of mixed type data with R
k-prototypes clustering might be better suited here. It combines k-modes and k-means and is able to cluster mixed numerical / categorical data. For R, use the Package 'clustMixType'. https://cran.r-project.org/web/packages/clustMixType/clustMixType.pdf
Clustering of mixed type data with R
k-prototypes clustering might be better suited here. It combines k-modes and k-means and is able to cluster mixed numerical / categorical data. For R, use the Package 'clustMixType'. https://cran.r-p
Clustering of mixed type data with R k-prototypes clustering might be better suited here. It combines k-modes and k-means and is able to cluster mixed numerical / categorical data. For R, use the Package 'clustMixType'. https://cran.r-project.org/web/packages/clustMixType/clustMixType.pdf
Clustering of mixed type data with R k-prototypes clustering might be better suited here. It combines k-modes and k-means and is able to cluster mixed numerical / categorical data. For R, use the Package 'clustMixType'. https://cran.r-p
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Clustering of mixed type data with R
VarSelLCM package offers Variable Selection for Model-Based Clustering of Mixed-Type Data Set with Missing Values On CRAN, and described more in paper. Advantage over some of the previous methods is that it offers some help in choice of the number of clusters and handles missing data. Nice shiny app provided is also ...
Clustering of mixed type data with R
VarSelLCM package offers Variable Selection for Model-Based Clustering of Mixed-Type Data Set with Missing Values On CRAN, and described more in paper. Advantage over some of the previous methods is
Clustering of mixed type data with R VarSelLCM package offers Variable Selection for Model-Based Clustering of Mixed-Type Data Set with Missing Values On CRAN, and described more in paper. Advantage over some of the previous methods is that it offers some help in choice of the number of clusters and handles missing d...
Clustering of mixed type data with R VarSelLCM package offers Variable Selection for Model-Based Clustering of Mixed-Type Data Set with Missing Values On CRAN, and described more in paper. Advantage over some of the previous methods is
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What is the difference between sample variance and sampling variance?
Sample variance refers to variation of observations (the data points) in a single sample. Sampling variance refers to variation of a particular statistic (e.g. the mean) calculated in sample, if to repeat the study (sample-creation/data-collection/statistic-calculation) many times. Due to central limit theorem, though,...
What is the difference between sample variance and sampling variance?
Sample variance refers to variation of observations (the data points) in a single sample. Sampling variance refers to variation of a particular statistic (e.g. the mean) calculated in sample, if to re
What is the difference between sample variance and sampling variance? Sample variance refers to variation of observations (the data points) in a single sample. Sampling variance refers to variation of a particular statistic (e.g. the mean) calculated in sample, if to repeat the study (sample-creation/data-collection/st...
What is the difference between sample variance and sampling variance? Sample variance refers to variation of observations (the data points) in a single sample. Sampling variance refers to variation of a particular statistic (e.g. the mean) calculated in sample, if to re
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What is the difference between sample variance and sampling variance?
The sample variance, $s^2$, is the variance of the sample, an estimate of the variance of the population from which the sample was drawn. "Sampling variance" I would interpret as "the variance that is due to sampling", for example of an estimator (like the mean). And so I would consider these two terms to be quite d...
What is the difference between sample variance and sampling variance?
The sample variance, $s^2$, is the variance of the sample, an estimate of the variance of the population from which the sample was drawn. "Sampling variance" I would interpret as "the variance that
What is the difference between sample variance and sampling variance? The sample variance, $s^2$, is the variance of the sample, an estimate of the variance of the population from which the sample was drawn. "Sampling variance" I would interpret as "the variance that is due to sampling", for example of an estimator (...
What is the difference between sample variance and sampling variance? The sample variance, $s^2$, is the variance of the sample, an estimate of the variance of the population from which the sample was drawn. "Sampling variance" I would interpret as "the variance that
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Draw integers independently & uniformly at random from 1 to $N$ using fair d6?
The set $\Omega(d,n)$ of distinct identifiable outcomes in $n$ independent rolls of a die with $d=6$ faces has $d^n$ elements. When the die is fair, that means each outcome of one roll has probability $1/d$ and independence means each of these outcomes will therefore have probability $(1/d)^n:$ that is, they have a un...
Draw integers independently & uniformly at random from 1 to $N$ using fair d6?
The set $\Omega(d,n)$ of distinct identifiable outcomes in $n$ independent rolls of a die with $d=6$ faces has $d^n$ elements. When the die is fair, that means each outcome of one roll has probabilit
Draw integers independently & uniformly at random from 1 to $N$ using fair d6? The set $\Omega(d,n)$ of distinct identifiable outcomes in $n$ independent rolls of a die with $d=6$ faces has $d^n$ elements. When the die is fair, that means each outcome of one roll has probability $1/d$ and independence means each of th...
Draw integers independently & uniformly at random from 1 to $N$ using fair d6? The set $\Omega(d,n)$ of distinct identifiable outcomes in $n$ independent rolls of a die with $d=6$ faces has $d^n$ elements. When the die is fair, that means each outcome of one roll has probabilit
14,687
Draw integers independently & uniformly at random from 1 to $N$ using fair d6?
For the case of $N=150$, rolling a d6 three times distinctly creates $6^3=216$ outcomes. The desired result can be tabulated in this way: Record a d6 three times sequentially. This produces results $a,b,c$. The result is uniform because all values of $a,b,c$ are equally likely (the dice are fair, and we are treating e...
Draw integers independently & uniformly at random from 1 to $N$ using fair d6?
For the case of $N=150$, rolling a d6 three times distinctly creates $6^3=216$ outcomes. The desired result can be tabulated in this way: Record a d6 three times sequentially. This produces results $
Draw integers independently & uniformly at random from 1 to $N$ using fair d6? For the case of $N=150$, rolling a d6 three times distinctly creates $6^3=216$ outcomes. The desired result can be tabulated in this way: Record a d6 three times sequentially. This produces results $a,b,c$. The result is uniform because all...
Draw integers independently & uniformly at random from 1 to $N$ using fair d6? For the case of $N=150$, rolling a d6 three times distinctly creates $6^3=216$ outcomes. The desired result can be tabulated in this way: Record a d6 three times sequentially. This produces results $
14,688
Draw integers independently & uniformly at random from 1 to $N$ using fair d6?
Here is an even simpler alternative to the answer by Sycorax for the case where $N=150$. Since $150 = 5 \times 5 \times 6$ you can perform the following procedure: Generating uniform random number from 1 to 150: Make three ordered rolls of 1D6 and denote these as $R_1, R_2, R_3$. If either of the first two rolls is ...
Draw integers independently & uniformly at random from 1 to $N$ using fair d6?
Here is an even simpler alternative to the answer by Sycorax for the case where $N=150$. Since $150 = 5 \times 5 \times 6$ you can perform the following procedure: Generating uniform random number f
Draw integers independently & uniformly at random from 1 to $N$ using fair d6? Here is an even simpler alternative to the answer by Sycorax for the case where $N=150$. Since $150 = 5 \times 5 \times 6$ you can perform the following procedure: Generating uniform random number from 1 to 150: Make three ordered rolls o...
Draw integers independently & uniformly at random from 1 to $N$ using fair d6? Here is an even simpler alternative to the answer by Sycorax for the case where $N=150$. Since $150 = 5 \times 5 \times 6$ you can perform the following procedure: Generating uniform random number f
14,689
Draw integers independently & uniformly at random from 1 to $N$ using fair d6?
As an illustration of an algorithm to choose uniformly between $150$ values using six-sided dice, try this which uses each roll to multiply the available values by $6$ and making each of the new values equally likely: After $0$ rolls, you have $1$ possibility, not enough to distinguish $150$ values After $1$ roll, you...
Draw integers independently & uniformly at random from 1 to $N$ using fair d6?
As an illustration of an algorithm to choose uniformly between $150$ values using six-sided dice, try this which uses each roll to multiply the available values by $6$ and making each of the new value
Draw integers independently & uniformly at random from 1 to $N$ using fair d6? As an illustration of an algorithm to choose uniformly between $150$ values using six-sided dice, try this which uses each roll to multiply the available values by $6$ and making each of the new values equally likely: After $0$ rolls, you h...
Draw integers independently & uniformly at random from 1 to $N$ using fair d6? As an illustration of an algorithm to choose uniformly between $150$ values using six-sided dice, try this which uses each roll to multiply the available values by $6$ and making each of the new value
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How can the central limit theorem hold for distributions which have limits on the random variable?
This is an excellent question, since it shows that you are thinking about the intuitive aspects of the theorems you are learning. That puts you ahead of most students who learn the CLT. Here I will try to supply you with an explanation for how it is possible for the CLT to hold for random variables with restricted su...
How can the central limit theorem hold for distributions which have limits on the random variable?
This is an excellent question, since it shows that you are thinking about the intuitive aspects of the theorems you are learning. That puts you ahead of most students who learn the CLT. Here I will
How can the central limit theorem hold for distributions which have limits on the random variable? This is an excellent question, since it shows that you are thinking about the intuitive aspects of the theorems you are learning. That puts you ahead of most students who learn the CLT. Here I will try to supply you wit...
How can the central limit theorem hold for distributions which have limits on the random variable? This is an excellent question, since it shows that you are thinking about the intuitive aspects of the theorems you are learning. That puts you ahead of most students who learn the CLT. Here I will
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How can the central limit theorem hold for distributions which have limits on the random variable?
Your source of confusion stems from two sources: 1) The CLT applies to the normalized sample means, i.e.: $Z_n=\frac{S_n/n-\mu}{\sigma/\sqrt{n}}=\frac{S_n-n\mu}{\sigma\sqrt{n}}$, which is centered around 0, hence admits negative values with positive probability. As an extreme example, if $n=1$ then $\frac{X_1-\mu}{\sig...
How can the central limit theorem hold for distributions which have limits on the random variable?
Your source of confusion stems from two sources: 1) The CLT applies to the normalized sample means, i.e.: $Z_n=\frac{S_n/n-\mu}{\sigma/\sqrt{n}}=\frac{S_n-n\mu}{\sigma\sqrt{n}}$, which is centered aro
How can the central limit theorem hold for distributions which have limits on the random variable? Your source of confusion stems from two sources: 1) The CLT applies to the normalized sample means, i.e.: $Z_n=\frac{S_n/n-\mu}{\sigma/\sqrt{n}}=\frac{S_n-n\mu}{\sigma\sqrt{n}}$, which is centered around 0, hence admits n...
How can the central limit theorem hold for distributions which have limits on the random variable? Your source of confusion stems from two sources: 1) The CLT applies to the normalized sample means, i.e.: $Z_n=\frac{S_n/n-\mu}{\sigma/\sqrt{n}}=\frac{S_n-n\mu}{\sigma\sqrt{n}}$, which is centered aro
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Understanding which features were most important for logistic regression
The first thing to note is that you don't use logistic regression as a classifier. The fact that $Y$ is binary has absolutely nothing to do with using this maximum likelihood method to actually classify observations. Once you get past that, concentrate on the gold standard information measure which is a by-product of...
Understanding which features were most important for logistic regression
The first thing to note is that you don't use logistic regression as a classifier. The fact that $Y$ is binary has absolutely nothing to do with using this maximum likelihood method to actually class
Understanding which features were most important for logistic regression The first thing to note is that you don't use logistic regression as a classifier. The fact that $Y$ is binary has absolutely nothing to do with using this maximum likelihood method to actually classify observations. Once you get past that, conc...
Understanding which features were most important for logistic regression The first thing to note is that you don't use logistic regression as a classifier. The fact that $Y$ is binary has absolutely nothing to do with using this maximum likelihood method to actually class
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Understanding which features were most important for logistic regression
The short answer is that is that there isn't a single, "right" way to answer this question. For the best review of the issues see Ulrike Groemping's papers, e.g., Estimators of Relative Importance in Linear Regression Based on Variance Decomposition. The options she discusses range from simple heuristics to sophisticat...
Understanding which features were most important for logistic regression
The short answer is that is that there isn't a single, "right" way to answer this question. For the best review of the issues see Ulrike Groemping's papers, e.g., Estimators of Relative Importance in
Understanding which features were most important for logistic regression The short answer is that is that there isn't a single, "right" way to answer this question. For the best review of the issues see Ulrike Groemping's papers, e.g., Estimators of Relative Importance in Linear Regression Based on Variance Decompositi...
Understanding which features were most important for logistic regression The short answer is that is that there isn't a single, "right" way to answer this question. For the best review of the issues see Ulrike Groemping's papers, e.g., Estimators of Relative Importance in
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Understanding which features were most important for logistic regression
A fairly robust way of doing this would be to try fitting the model N times where N is the number of features. Each time use N-1 of the features and leave one feature out. Then you can use your favourite validation metric to measure how much the inclusion or exclusion of each feature affects the performance of the mode...
Understanding which features were most important for logistic regression
A fairly robust way of doing this would be to try fitting the model N times where N is the number of features. Each time use N-1 of the features and leave one feature out. Then you can use your favour
Understanding which features were most important for logistic regression A fairly robust way of doing this would be to try fitting the model N times where N is the number of features. Each time use N-1 of the features and leave one feature out. Then you can use your favourite validation metric to measure how much the i...
Understanding which features were most important for logistic regression A fairly robust way of doing this would be to try fitting the model N times where N is the number of features. Each time use N-1 of the features and leave one feature out. Then you can use your favour
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Understanding which features were most important for logistic regression
You are correct in your observation that merely looking at the size of the estimated coefficient $|\hat{\beta_j}|$ is not very meaningful for the reason mentioned. But a simple adjustment is to multiply the coefficient estimate by the estimated standard deviation of the predictor $|\hat{\beta_j}| \hat{\sigma}_j$ and u...
Understanding which features were most important for logistic regression
You are correct in your observation that merely looking at the size of the estimated coefficient $|\hat{\beta_j}|$ is not very meaningful for the reason mentioned. But a simple adjustment is to multi
Understanding which features were most important for logistic regression You are correct in your observation that merely looking at the size of the estimated coefficient $|\hat{\beta_j}|$ is not very meaningful for the reason mentioned. But a simple adjustment is to multiply the coefficient estimate by the estimated s...
Understanding which features were most important for logistic regression You are correct in your observation that merely looking at the size of the estimated coefficient $|\hat{\beta_j}|$ is not very meaningful for the reason mentioned. But a simple adjustment is to multi
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Understanding which features were most important for logistic regression
You are right about why you should not use the coefficients as a measure of relevance, but you absolutelly can if you divide them by their standard error! If you have estimated the model with R, then it is already done for you! You can even remove the least important features from the model and see how it works. A more...
Understanding which features were most important for logistic regression
You are right about why you should not use the coefficients as a measure of relevance, but you absolutelly can if you divide them by their standard error! If you have estimated the model with R, then
Understanding which features were most important for logistic regression You are right about why you should not use the coefficients as a measure of relevance, but you absolutelly can if you divide them by their standard error! If you have estimated the model with R, then it is already done for you! You can even remove...
Understanding which features were most important for logistic regression You are right about why you should not use the coefficients as a measure of relevance, but you absolutelly can if you divide them by their standard error! If you have estimated the model with R, then
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Rand index calculation
I was pondering about the same, and I solved it like this. Suppose you have a co-occurrence matrix/contingency table where the rows are the ground truth clusters, and the columns are the clusters found by the clustering algorithm. So, for the example in the book, it would look like: | 1 | 2 | 3 --+---+---+--- x | 5 |...
Rand index calculation
I was pondering about the same, and I solved it like this. Suppose you have a co-occurrence matrix/contingency table where the rows are the ground truth clusters, and the columns are the clusters foun
Rand index calculation I was pondering about the same, and I solved it like this. Suppose you have a co-occurrence matrix/contingency table where the rows are the ground truth clusters, and the columns are the clusters found by the clustering algorithm. So, for the example in the book, it would look like: | 1 | 2 | 3...
Rand index calculation I was pondering about the same, and I solved it like this. Suppose you have a co-occurrence matrix/contingency table where the rows are the ground truth clusters, and the columns are the clusters foun
14,698
Rand index calculation
After having studied the other answers in this thread, here is my Python implementation, which takes arrays as inputs, sklearn-style: import numpy as np from scipy.misc import comb def rand_index_score(clusters, classes): tp_plus_fp = comb(np.bincount(clusters), 2).sum() tp_plus_fn = comb(np.bincount(classes)...
Rand index calculation
After having studied the other answers in this thread, here is my Python implementation, which takes arrays as inputs, sklearn-style: import numpy as np from scipy.misc import comb def rand_index_sco
Rand index calculation After having studied the other answers in this thread, here is my Python implementation, which takes arrays as inputs, sklearn-style: import numpy as np from scipy.misc import comb def rand_index_score(clusters, classes): tp_plus_fp = comb(np.bincount(clusters), 2).sum() tp_plus_fn = co...
Rand index calculation After having studied the other answers in this thread, here is my Python implementation, which takes arrays as inputs, sklearn-style: import numpy as np from scipy.misc import comb def rand_index_sco
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Rand index calculation
I am not quite sure myself, but this is how I did the TN value: TN=(7 2) (10 2) (4 2) (7 2) – Cluster 1 – test says β€˜x’, so count those that are NOT x (and are correctly clustered in clusters 2 & 3) i.e. 4 β€˜o’s + 3 β€˜d’s (diamonds) =(7 2) (10 2) – Cluster 2, count those that are NOT β€˜o’s and correctly clustered...
Rand index calculation
I am not quite sure myself, but this is how I did the TN value: TN=(7 2) (10 2) (4 2) (7 2) – Cluster 1 – test says β€˜x’, so count those that are NOT x (and are correctly clustered in clusters 2 &
Rand index calculation I am not quite sure myself, but this is how I did the TN value: TN=(7 2) (10 2) (4 2) (7 2) – Cluster 1 – test says β€˜x’, so count those that are NOT x (and are correctly clustered in clusters 2 & 3) i.e. 4 β€˜o’s + 3 β€˜d’s (diamonds) =(7 2) (10 2) – Cluster 2, count those that are NOT β€˜o’s ...
Rand index calculation I am not quite sure myself, but this is how I did the TN value: TN=(7 2) (10 2) (4 2) (7 2) – Cluster 1 – test says β€˜x’, so count those that are NOT x (and are correctly clustered in clusters 2 &
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Rand index calculation
Taking the example of another question: | 1 | 2 | 3 --+---+---+--- x | 5 | 1 | 2 --+---+---+--- o | 1 | 4 | 0 --+---+---+--- β—Š | 0 | 1 | 3 The reasonable answer for FN: FN = (c(8,2)-c(5,2)-c(2,2))+(c(5,2)-c(4,2))+(c(4,2)-c(3,2))=24 Explanation: (c(8,2)-c(5,2)-c(2,2)) choose 2 from 8 for 'x'(a) the combinatio...
Rand index calculation
Taking the example of another question: | 1 | 2 | 3 --+---+---+--- x | 5 | 1 | 2 --+---+---+--- o | 1 | 4 | 0 --+---+---+--- β—Š | 0 | 1 | 3 The reasonable answer for FN: FN = (c(8,2)-c(5,2)-c(2,2))
Rand index calculation Taking the example of another question: | 1 | 2 | 3 --+---+---+--- x | 5 | 1 | 2 --+---+---+--- o | 1 | 4 | 0 --+---+---+--- β—Š | 0 | 1 | 3 The reasonable answer for FN: FN = (c(8,2)-c(5,2)-c(2,2))+(c(5,2)-c(4,2))+(c(4,2)-c(3,2))=24 Explanation: (c(8,2)-c(5,2)-c(2,2)) choose 2 from 8 fo...
Rand index calculation Taking the example of another question: | 1 | 2 | 3 --+---+---+--- x | 5 | 1 | 2 --+---+---+--- o | 1 | 4 | 0 --+---+---+--- β—Š | 0 | 1 | 3 The reasonable answer for FN: FN = (c(8,2)-c(5,2)-c(2,2))