idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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601 | Intuitive explanation for dividing by $n-1$ when calculating standard deviation? | Generally using "n" in the denominator gives smaller values than the population variance which is what we want to estimate. This especially happens if the small samples are taken. In the language of statistics, we say that the sample variance provides a “biased” estimate of the population variance and needs to be made ... | Intuitive explanation for dividing by $n-1$ when calculating standard deviation? | Generally using "n" in the denominator gives smaller values than the population variance which is what we want to estimate. This especially happens if the small samples are taken. In the language of s | Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
Generally using "n" in the denominator gives smaller values than the population variance which is what we want to estimate. This especially happens if the small samples are taken. In the language of statistics, we say that the sample varia... | Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
Generally using "n" in the denominator gives smaller values than the population variance which is what we want to estimate. This especially happens if the small samples are taken. In the language of s |
602 | Intuitive explanation for dividing by $n-1$ when calculating standard deviation? | I think it's worth pointing out the connection to Bayesian estimation. Suppose you assume your data is Gaussian, and so you measure the mean $\mu$ and variance $\sigma^2$ of a sample of $n$ points. You want to draw conclusions about the population. The Bayesian approach would be to evaluate the posterior predictive ... | Intuitive explanation for dividing by $n-1$ when calculating standard deviation? | I think it's worth pointing out the connection to Bayesian estimation. Suppose you assume your data is Gaussian, and so you measure the mean $\mu$ and variance $\sigma^2$ of a sample of $n$ points. | Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
I think it's worth pointing out the connection to Bayesian estimation. Suppose you assume your data is Gaussian, and so you measure the mean $\mu$ and variance $\sigma^2$ of a sample of $n$ points. You want to draw conclusions about the ... | Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
I think it's worth pointing out the connection to Bayesian estimation. Suppose you assume your data is Gaussian, and so you measure the mean $\mu$ and variance $\sigma^2$ of a sample of $n$ points. |
603 | Intuitive explanation for dividing by $n-1$ when calculating standard deviation? | I'm jumping VERY late into this, but would like to offer an answer that is possibly more intuitive than others, albeit incomplete.
As others asserted, the population mean ($\mu$) and the sample mean ($\overline{X}$) are going to differ (where the larger the sample size the smaller the difference).
Let $e$ be the differ... | Intuitive explanation for dividing by $n-1$ when calculating standard deviation? | I'm jumping VERY late into this, but would like to offer an answer that is possibly more intuitive than others, albeit incomplete.
As others asserted, the population mean ($\mu$) and the sample mean ( | Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
I'm jumping VERY late into this, but would like to offer an answer that is possibly more intuitive than others, albeit incomplete.
As others asserted, the population mean ($\mu$) and the sample mean ($\overline{X}$) are going to differ (wh... | Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
I'm jumping VERY late into this, but would like to offer an answer that is possibly more intuitive than others, albeit incomplete.
As others asserted, the population mean ($\mu$) and the sample mean ( |
604 | Intuitive explanation for dividing by $n-1$ when calculating standard deviation? | Here's a very good overview and full proof
In the more general case, note that the sample mean is not the same as the population mean. One's sample observations are naturally going to be closer on average to the sample mean than the population mean, resulting in the average $(x−\bar{x})^2$ value underestimating the av... | Intuitive explanation for dividing by $n-1$ when calculating standard deviation? | Here's a very good overview and full proof
In the more general case, note that the sample mean is not the same as the population mean. One's sample observations are naturally going to be closer on av | Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
Here's a very good overview and full proof
In the more general case, note that the sample mean is not the same as the population mean. One's sample observations are naturally going to be closer on average to the sample mean than the popul... | Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
Here's a very good overview and full proof
In the more general case, note that the sample mean is not the same as the population mean. One's sample observations are naturally going to be closer on av |
605 | Intuitive explanation for dividing by $n-1$ when calculating standard deviation? | My goodness it's getting complicated! I thought the simple answer was... if you have all the data points you can use "n" but if you have a "sample" then, assuming it's a random sample, you've got more sample points from inside the standard deviation than from outside (the definition of standard deviation). You just ... | Intuitive explanation for dividing by $n-1$ when calculating standard deviation? | My goodness it's getting complicated! I thought the simple answer was... if you have all the data points you can use "n" but if you have a "sample" then, assuming it's a random sample, you've got mo | Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
My goodness it's getting complicated! I thought the simple answer was... if you have all the data points you can use "n" but if you have a "sample" then, assuming it's a random sample, you've got more sample points from inside the standa... | Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
My goodness it's getting complicated! I thought the simple answer was... if you have all the data points you can use "n" but if you have a "sample" then, assuming it's a random sample, you've got mo |
606 | Why is accuracy not the best measure for assessing classification models? | Most of the other answers focus on the example of unbalanced classes. Yes, this is important. However, I argue that accuracy is problematic even with balanced classes.
Frank Harrell has written about this on his blog: Classification vs. Prediction and Damage Caused by Classification Accuracy and Other Discontinuous Imp... | Why is accuracy not the best measure for assessing classification models? | Most of the other answers focus on the example of unbalanced classes. Yes, this is important. However, I argue that accuracy is problematic even with balanced classes.
Frank Harrell has written about | Why is accuracy not the best measure for assessing classification models?
Most of the other answers focus on the example of unbalanced classes. Yes, this is important. However, I argue that accuracy is problematic even with balanced classes.
Frank Harrell has written about this on his blog: Classification vs. Predictio... | Why is accuracy not the best measure for assessing classification models?
Most of the other answers focus on the example of unbalanced classes. Yes, this is important. However, I argue that accuracy is problematic even with balanced classes.
Frank Harrell has written about |
607 | Why is accuracy not the best measure for assessing classification models? | When we use accuracy, we assign equal cost to false positives and false negatives. When that data set is imbalanced - say it has 99% of instances in one class and only 1 % in the other - there is a great way to lower the cost. Predict that every instance belongs to the majority class, get accuracy of 99% and go home ea... | Why is accuracy not the best measure for assessing classification models? | When we use accuracy, we assign equal cost to false positives and false negatives. When that data set is imbalanced - say it has 99% of instances in one class and only 1 % in the other - there is a gr | Why is accuracy not the best measure for assessing classification models?
When we use accuracy, we assign equal cost to false positives and false negatives. When that data set is imbalanced - say it has 99% of instances in one class and only 1 % in the other - there is a great way to lower the cost. Predict that every ... | Why is accuracy not the best measure for assessing classification models?
When we use accuracy, we assign equal cost to false positives and false negatives. When that data set is imbalanced - say it has 99% of instances in one class and only 1 % in the other - there is a gr |
608 | Why is accuracy not the best measure for assessing classification models? | The problem with accuracy
Standard accuracy is defined as the ratio of correct classifications to the number of classifications done.
\begin{align*}
accuracy := \frac{\text{correct classifications}}{\text{number of classifications}}
\end{align*}
It is thus an overall measure over all classes and as we'll shortly see it... | Why is accuracy not the best measure for assessing classification models? | The problem with accuracy
Standard accuracy is defined as the ratio of correct classifications to the number of classifications done.
\begin{align*}
accuracy := \frac{\text{correct classifications}}{\ | Why is accuracy not the best measure for assessing classification models?
The problem with accuracy
Standard accuracy is defined as the ratio of correct classifications to the number of classifications done.
\begin{align*}
accuracy := \frac{\text{correct classifications}}{\text{number of classifications}}
\end{align*}
... | Why is accuracy not the best measure for assessing classification models?
The problem with accuracy
Standard accuracy is defined as the ratio of correct classifications to the number of classifications done.
\begin{align*}
accuracy := \frac{\text{correct classifications}}{\ |
609 | Why is accuracy not the best measure for assessing classification models? | Here is a somewhat adversarial counter-example, where accuracy is better than a proper scoring rule, based on @Benoit_Sanchez's neat thought experiment,
You own an egg shop and each egg you sell generates a net revenue of 2
dollars. Each customer who enters the shop may either buy an egg or
leave without buying any. F... | Why is accuracy not the best measure for assessing classification models? | Here is a somewhat adversarial counter-example, where accuracy is better than a proper scoring rule, based on @Benoit_Sanchez's neat thought experiment,
You own an egg shop and each egg you sell gene | Why is accuracy not the best measure for assessing classification models?
Here is a somewhat adversarial counter-example, where accuracy is better than a proper scoring rule, based on @Benoit_Sanchez's neat thought experiment,
You own an egg shop and each egg you sell generates a net revenue of 2
dollars. Each custome... | Why is accuracy not the best measure for assessing classification models?
Here is a somewhat adversarial counter-example, where accuracy is better than a proper scoring rule, based on @Benoit_Sanchez's neat thought experiment,
You own an egg shop and each egg you sell gene |
610 | Why is accuracy not the best measure for assessing classification models? | Imbalanced classes in your dataset
To be short: imagine, 99% of one class (say apples) and 1% of another class is in your data set (say bananas). My super duper algorithm gets an astonishing 99% accuracy for this data set, check it out:
return "it's an apple"
He will be right 99% of the time and therefore gets a 99% ac... | Why is accuracy not the best measure for assessing classification models? | Imbalanced classes in your dataset
To be short: imagine, 99% of one class (say apples) and 1% of another class is in your data set (say bananas). My super duper algorithm gets an astonishing 99% accur | Why is accuracy not the best measure for assessing classification models?
Imbalanced classes in your dataset
To be short: imagine, 99% of one class (say apples) and 1% of another class is in your data set (say bananas). My super duper algorithm gets an astonishing 99% accuracy for this data set, check it out:
return "i... | Why is accuracy not the best measure for assessing classification models?
Imbalanced classes in your dataset
To be short: imagine, 99% of one class (say apples) and 1% of another class is in your data set (say bananas). My super duper algorithm gets an astonishing 99% accur |
611 | Why is accuracy not the best measure for assessing classification models? | DaL answer is just exactly this. I'll illustrate it with a very simple example about... selling eggs.
You own an egg shop and each egg you sell generates a net revenue of $2$ dollars. Each customer who enters the shop may either buy an egg or leave without buying any. For some customers you can decide to make a discoun... | Why is accuracy not the best measure for assessing classification models? | DaL answer is just exactly this. I'll illustrate it with a very simple example about... selling eggs.
You own an egg shop and each egg you sell generates a net revenue of $2$ dollars. Each customer wh | Why is accuracy not the best measure for assessing classification models?
DaL answer is just exactly this. I'll illustrate it with a very simple example about... selling eggs.
You own an egg shop and each egg you sell generates a net revenue of $2$ dollars. Each customer who enters the shop may either buy an egg or lea... | Why is accuracy not the best measure for assessing classification models?
DaL answer is just exactly this. I'll illustrate it with a very simple example about... selling eggs.
You own an egg shop and each egg you sell generates a net revenue of $2$ dollars. Each customer wh |
612 | Why is accuracy not the best measure for assessing classification models? | After reading through all the answers above, here is an appeal to common sense. Optimality is a flexible term and always needs to be qualified; in other words, saying a model or algorithm is "optimal" is meaningless, especially in a scientific sense.
Whenever anyone says they are scientifically optimizing something, I... | Why is accuracy not the best measure for assessing classification models? | After reading through all the answers above, here is an appeal to common sense. Optimality is a flexible term and always needs to be qualified; in other words, saying a model or algorithm is "optimal | Why is accuracy not the best measure for assessing classification models?
After reading through all the answers above, here is an appeal to common sense. Optimality is a flexible term and always needs to be qualified; in other words, saying a model or algorithm is "optimal" is meaningless, especially in a scientific s... | Why is accuracy not the best measure for assessing classification models?
After reading through all the answers above, here is an appeal to common sense. Optimality is a flexible term and always needs to be qualified; in other words, saying a model or algorithm is "optimal |
613 | Why is accuracy not the best measure for assessing classification models? | I wrote a whole blog post on the matter:
https://blog.ephorie.de/zeror-the-simplest-possible-classifier-or-why-high-accuracy-can-be-misleading
ZeroR, the simplest possible classifier, just takes the majority class as the prediction. With highly imbalanced data you will get a very high accuracy, yet if your minority cla... | Why is accuracy not the best measure for assessing classification models? | I wrote a whole blog post on the matter:
https://blog.ephorie.de/zeror-the-simplest-possible-classifier-or-why-high-accuracy-can-be-misleading
ZeroR, the simplest possible classifier, just takes the m | Why is accuracy not the best measure for assessing classification models?
I wrote a whole blog post on the matter:
https://blog.ephorie.de/zeror-the-simplest-possible-classifier-or-why-high-accuracy-can-be-misleading
ZeroR, the simplest possible classifier, just takes the majority class as the prediction. With highly i... | Why is accuracy not the best measure for assessing classification models?
I wrote a whole blog post on the matter:
https://blog.ephorie.de/zeror-the-simplest-possible-classifier-or-why-high-accuracy-can-be-misleading
ZeroR, the simplest possible classifier, just takes the m |
614 | Why is accuracy not the best measure for assessing classification models? | Classification accuracy is the number of correct predictions divided by the total number of predictions.
Accuracy can be misleading. For example, in a problem where there is a large class imbalance, a model can predict the value of the majority class for all predictions and achieve a high classification accuracy. So, f... | Why is accuracy not the best measure for assessing classification models? | Classification accuracy is the number of correct predictions divided by the total number of predictions.
Accuracy can be misleading. For example, in a problem where there is a large class imbalance, a | Why is accuracy not the best measure for assessing classification models?
Classification accuracy is the number of correct predictions divided by the total number of predictions.
Accuracy can be misleading. For example, in a problem where there is a large class imbalance, a model can predict the value of the majority c... | Why is accuracy not the best measure for assessing classification models?
Classification accuracy is the number of correct predictions divided by the total number of predictions.
Accuracy can be misleading. For example, in a problem where there is a large class imbalance, a |
615 | Why is accuracy not the best measure for assessing classification models? | You may view accuracy as the $R^2$ of classification: an initially appealing metric with which to compare models, that falls short under detailed examination.
In both cases overfitting can be a major problem. Just as in the case of a high $R^2$ might mean that you are modelling the noise rather than the signal, a high ... | Why is accuracy not the best measure for assessing classification models? | You may view accuracy as the $R^2$ of classification: an initially appealing metric with which to compare models, that falls short under detailed examination.
In both cases overfitting can be a major | Why is accuracy not the best measure for assessing classification models?
You may view accuracy as the $R^2$ of classification: an initially appealing metric with which to compare models, that falls short under detailed examination.
In both cases overfitting can be a major problem. Just as in the case of a high $R^2$ m... | Why is accuracy not the best measure for assessing classification models?
You may view accuracy as the $R^2$ of classification: an initially appealing metric with which to compare models, that falls short under detailed examination.
In both cases overfitting can be a major |
616 | What are the advantages of ReLU over sigmoid function in deep neural networks? | Two additional major benefits of ReLUs are sparsity and a reduced likelihood of vanishing gradient. But first recall the definition of a ReLU is $h = \max(0, a)$ where $a = Wx + b$.
One major benefit is the reduced likelihood of the gradient to vanish. This arises when $a > 0$. In this regime the gradient has a constan... | What are the advantages of ReLU over sigmoid function in deep neural networks? | Two additional major benefits of ReLUs are sparsity and a reduced likelihood of vanishing gradient. But first recall the definition of a ReLU is $h = \max(0, a)$ where $a = Wx + b$.
One major benefit | What are the advantages of ReLU over sigmoid function in deep neural networks?
Two additional major benefits of ReLUs are sparsity and a reduced likelihood of vanishing gradient. But first recall the definition of a ReLU is $h = \max(0, a)$ where $a = Wx + b$.
One major benefit is the reduced likelihood of the gradient... | What are the advantages of ReLU over sigmoid function in deep neural networks?
Two additional major benefits of ReLUs are sparsity and a reduced likelihood of vanishing gradient. But first recall the definition of a ReLU is $h = \max(0, a)$ where $a = Wx + b$.
One major benefit |
617 | What are the advantages of ReLU over sigmoid function in deep neural networks? | Advantage:
Sigmoid: not blowing up activation
Relu : not vanishing gradient
Relu : More computationally efficient to compute than Sigmoid like
functions since Relu just needs to pick max(0,$x$) and not perform
expensive exponential operations as in Sigmoids
Relu : In practice, networks with R... | What are the advantages of ReLU over sigmoid function in deep neural networks? | Advantage:
Sigmoid: not blowing up activation
Relu : not vanishing gradient
Relu : More computationally efficient to compute than Sigmoid like
functions since Relu just needs to pick m | What are the advantages of ReLU over sigmoid function in deep neural networks?
Advantage:
Sigmoid: not blowing up activation
Relu : not vanishing gradient
Relu : More computationally efficient to compute than Sigmoid like
functions since Relu just needs to pick max(0,$x$) and not perform
expens... | What are the advantages of ReLU over sigmoid function in deep neural networks?
Advantage:
Sigmoid: not blowing up activation
Relu : not vanishing gradient
Relu : More computationally efficient to compute than Sigmoid like
functions since Relu just needs to pick m |
618 | What are the advantages of ReLU over sigmoid function in deep neural networks? | Just complementing the other answers:
Vanishing Gradients
The other answers are right to point out that the bigger the input (in absolute value) the smaller the gradient of the sigmoid function. But, probably an even more important effect is that the derivative of the sigmoid function is ALWAYS smaller than one. In fa... | What are the advantages of ReLU over sigmoid function in deep neural networks? | Just complementing the other answers:
Vanishing Gradients
The other answers are right to point out that the bigger the input (in absolute value) the smaller the gradient of the sigmoid function. But, | What are the advantages of ReLU over sigmoid function in deep neural networks?
Just complementing the other answers:
Vanishing Gradients
The other answers are right to point out that the bigger the input (in absolute value) the smaller the gradient of the sigmoid function. But, probably an even more important effect i... | What are the advantages of ReLU over sigmoid function in deep neural networks?
Just complementing the other answers:
Vanishing Gradients
The other answers are right to point out that the bigger the input (in absolute value) the smaller the gradient of the sigmoid function. But, |
619 | What are the advantages of ReLU over sigmoid function in deep neural networks? | An advantage to ReLU other than avoiding vanishing gradients problem is that it has much lower run time. max(0,a) runs much faster than any sigmoid function (logistic function for example = 1/(1+e^(-a)) which uses an exponent which is computational slow when done often). This is true for both feed forward and back prop... | What are the advantages of ReLU over sigmoid function in deep neural networks? | An advantage to ReLU other than avoiding vanishing gradients problem is that it has much lower run time. max(0,a) runs much faster than any sigmoid function (logistic function for example = 1/(1+e^(-a | What are the advantages of ReLU over sigmoid function in deep neural networks?
An advantage to ReLU other than avoiding vanishing gradients problem is that it has much lower run time. max(0,a) runs much faster than any sigmoid function (logistic function for example = 1/(1+e^(-a)) which uses an exponent which is comput... | What are the advantages of ReLU over sigmoid function in deep neural networks?
An advantage to ReLU other than avoiding vanishing gradients problem is that it has much lower run time. max(0,a) runs much faster than any sigmoid function (logistic function for example = 1/(1+e^(-a |
620 | What are the advantages of ReLU over sigmoid function in deep neural networks? | The main reason why ReLu is used is because it is simple, fast, and empirically it seems to work well.
Empirically, early papers observed that training a deep network with ReLu tended to converge much more quickly and reliably than training a deep network with sigmoid activation. In the early days, people were able to... | What are the advantages of ReLU over sigmoid function in deep neural networks? | The main reason why ReLu is used is because it is simple, fast, and empirically it seems to work well.
Empirically, early papers observed that training a deep network with ReLu tended to converge much | What are the advantages of ReLU over sigmoid function in deep neural networks?
The main reason why ReLu is used is because it is simple, fast, and empirically it seems to work well.
Empirically, early papers observed that training a deep network with ReLu tended to converge much more quickly and reliably than training ... | What are the advantages of ReLU over sigmoid function in deep neural networks?
The main reason why ReLu is used is because it is simple, fast, and empirically it seems to work well.
Empirically, early papers observed that training a deep network with ReLu tended to converge much |
621 | What are the advantages of ReLU over sigmoid function in deep neural networks? | Main benefit is that the derivative of ReLu is either 0 or 1, so multiplying by it won't cause weights that are further away from the end result of the loss function to suffer from the vanishing gradient problem: | What are the advantages of ReLU over sigmoid function in deep neural networks? | Main benefit is that the derivative of ReLu is either 0 or 1, so multiplying by it won't cause weights that are further away from the end result of the loss function to suffer from the vanishing gradi | What are the advantages of ReLU over sigmoid function in deep neural networks?
Main benefit is that the derivative of ReLu is either 0 or 1, so multiplying by it won't cause weights that are further away from the end result of the loss function to suffer from the vanishing gradient problem: | What are the advantages of ReLU over sigmoid function in deep neural networks?
Main benefit is that the derivative of ReLu is either 0 or 1, so multiplying by it won't cause weights that are further away from the end result of the loss function to suffer from the vanishing gradi |
622 | What are the advantages of ReLU over sigmoid function in deep neural networks? | ReLu does not have the vanishing gradient problem. Vanishing gradients lead to very small changes in the weights proportional to the partial derivative of the error function. The gradient is multiplied n times in back propagation to get the gradients of lower layers. The effect of multiplying the gradient n times makes... | What are the advantages of ReLU over sigmoid function in deep neural networks? | ReLu does not have the vanishing gradient problem. Vanishing gradients lead to very small changes in the weights proportional to the partial derivative of the error function. The gradient is multiplie | What are the advantages of ReLU over sigmoid function in deep neural networks?
ReLu does not have the vanishing gradient problem. Vanishing gradients lead to very small changes in the weights proportional to the partial derivative of the error function. The gradient is multiplied n times in back propagation to get the ... | What are the advantages of ReLU over sigmoid function in deep neural networks?
ReLu does not have the vanishing gradient problem. Vanishing gradients lead to very small changes in the weights proportional to the partial derivative of the error function. The gradient is multiplie |
623 | What are the advantages of ReLU over sigmoid function in deep neural networks? | I read all the answers and still feel that I need to write a new one.
Let us consider a linear activation function g(z)=z, which is different from Relu(z) only in the region z<0.
If all activation functions used in a network is g(z), then the network is equivalent to a simple single layer linear network,
which we know ... | What are the advantages of ReLU over sigmoid function in deep neural networks? | I read all the answers and still feel that I need to write a new one.
Let us consider a linear activation function g(z)=z, which is different from Relu(z) only in the region z<0.
If all activation fun | What are the advantages of ReLU over sigmoid function in deep neural networks?
I read all the answers and still feel that I need to write a new one.
Let us consider a linear activation function g(z)=z, which is different from Relu(z) only in the region z<0.
If all activation functions used in a network is g(z), then th... | What are the advantages of ReLU over sigmoid function in deep neural networks?
I read all the answers and still feel that I need to write a new one.
Let us consider a linear activation function g(z)=z, which is different from Relu(z) only in the region z<0.
If all activation fun |
624 | Which "mean" to use and when? | This answer may have a slightly more mathematical bent than you were looking for.
The important thing to recognize is that all of these means are simply the arithmetic mean in disguise.
The important characteristic in identifying which (if any!) of the three common means (arithmetic, geometric or harmonic) is the "righ... | Which "mean" to use and when? | This answer may have a slightly more mathematical bent than you were looking for.
The important thing to recognize is that all of these means are simply the arithmetic mean in disguise.
The important | Which "mean" to use and when?
This answer may have a slightly more mathematical bent than you were looking for.
The important thing to recognize is that all of these means are simply the arithmetic mean in disguise.
The important characteristic in identifying which (if any!) of the three common means (arithmetic, geome... | Which "mean" to use and when?
This answer may have a slightly more mathematical bent than you were looking for.
The important thing to recognize is that all of these means are simply the arithmetic mean in disguise.
The important |
625 | Which "mean" to use and when? | Expanding on @Brandon 's excellent comment (which I think should be promoted to answer):
The geometric mean should be used when you are interested in multiplicative differences. Brandon notes that geometric mean should be used when the ranges are different. This is usually correct. The reason is that we want to equaliz... | Which "mean" to use and when? | Expanding on @Brandon 's excellent comment (which I think should be promoted to answer):
The geometric mean should be used when you are interested in multiplicative differences. Brandon notes that geo | Which "mean" to use and when?
Expanding on @Brandon 's excellent comment (which I think should be promoted to answer):
The geometric mean should be used when you are interested in multiplicative differences. Brandon notes that geometric mean should be used when the ranges are different. This is usually correct. The rea... | Which "mean" to use and when?
Expanding on @Brandon 's excellent comment (which I think should be promoted to answer):
The geometric mean should be used when you are interested in multiplicative differences. Brandon notes that geo |
626 | Which "mean" to use and when? | I'll try to boil it down to 3-4 rules of thumb and provide some more examples of the Pythagorean means.
The relationship between the 3 means is HM < GM < AM for non-negative data with some variation. They will be equal if and only if there's no variation at all in sample data.
For data in levels, use the AM. Prices ... | Which "mean" to use and when? | I'll try to boil it down to 3-4 rules of thumb and provide some more examples of the Pythagorean means.
The relationship between the 3 means is HM < GM < AM for non-negative data with some variatio | Which "mean" to use and when?
I'll try to boil it down to 3-4 rules of thumb and provide some more examples of the Pythagorean means.
The relationship between the 3 means is HM < GM < AM for non-negative data with some variation. They will be equal if and only if there's no variation at all in sample data.
For data ... | Which "mean" to use and when?
I'll try to boil it down to 3-4 rules of thumb and provide some more examples of the Pythagorean means.
The relationship between the 3 means is HM < GM < AM for non-negative data with some variatio |
627 | Which "mean" to use and when? | A possible answer to your question ("how do I decide which mean is the most appropriate to use in a given context?") is the definition of mean as given by the Italian mathematician Oscar Chisini.
How to Compute a Mean? The Chisini Approach and Its Applications is a paper with a more detailed explanation and some exampl... | Which "mean" to use and when? | A possible answer to your question ("how do I decide which mean is the most appropriate to use in a given context?") is the definition of mean as given by the Italian mathematician Oscar Chisini.
How | Which "mean" to use and when?
A possible answer to your question ("how do I decide which mean is the most appropriate to use in a given context?") is the definition of mean as given by the Italian mathematician Oscar Chisini.
How to Compute a Mean? The Chisini Approach and Its Applications is a paper with a more detail... | Which "mean" to use and when?
A possible answer to your question ("how do I decide which mean is the most appropriate to use in a given context?") is the definition of mean as given by the Italian mathematician Oscar Chisini.
How |
628 | Which "mean" to use and when? | I think a simple way to answer the question would be:
If the mathematical structure is xy = k (an inverse relationship between variables) and you're looking for an average, then you need to use the harmonic mean--which amounts to a weighted arithmetic mean--consider
Harmonic average = 2ab/(a+b) = a(b/a+b) + b(a/(a+b)... | Which "mean" to use and when? | I think a simple way to answer the question would be:
If the mathematical structure is xy = k (an inverse relationship between variables) and you're looking for an average, then you need to use the h | Which "mean" to use and when?
I think a simple way to answer the question would be:
If the mathematical structure is xy = k (an inverse relationship between variables) and you're looking for an average, then you need to use the harmonic mean--which amounts to a weighted arithmetic mean--consider
Harmonic average = 2a... | Which "mean" to use and when?
I think a simple way to answer the question would be:
If the mathematical structure is xy = k (an inverse relationship between variables) and you're looking for an average, then you need to use the h |
629 | What is the difference between data mining, statistics, machine learning and AI? | There is considerable overlap among these, but some distinctions can be made. Of necessity, I will have to over-simplify some things or give short-shrift to others, but I will do my best to give some sense of these areas.
Firstly, Artificial Intelligence is fairly distinct from the rest. AI is the study of how to c... | What is the difference between data mining, statistics, machine learning and AI? | There is considerable overlap among these, but some distinctions can be made. Of necessity, I will have to over-simplify some things or give short-shrift to others, but I will do my best to give some | What is the difference between data mining, statistics, machine learning and AI?
There is considerable overlap among these, but some distinctions can be made. Of necessity, I will have to over-simplify some things or give short-shrift to others, but I will do my best to give some sense of these areas.
Firstly, Artif... | What is the difference between data mining, statistics, machine learning and AI?
There is considerable overlap among these, but some distinctions can be made. Of necessity, I will have to over-simplify some things or give short-shrift to others, but I will do my best to give some |
630 | What is the difference between data mining, statistics, machine learning and AI? | Many of the other answers have covered the main points but you asked for a hierarchy if any exists and the way I see it, although they are each disciplines in their own right, there is hierarchy no one seems to have mentioned yet since each builds upon the previous one.
Statistics is just about the numbers, and quanti... | What is the difference between data mining, statistics, machine learning and AI? | Many of the other answers have covered the main points but you asked for a hierarchy if any exists and the way I see it, although they are each disciplines in their own right, there is hierarchy no on | What is the difference between data mining, statistics, machine learning and AI?
Many of the other answers have covered the main points but you asked for a hierarchy if any exists and the way I see it, although they are each disciplines in their own right, there is hierarchy no one seems to have mentioned yet since eac... | What is the difference between data mining, statistics, machine learning and AI?
Many of the other answers have covered the main points but you asked for a hierarchy if any exists and the way I see it, although they are each disciplines in their own right, there is hierarchy no on |
631 | What is the difference between data mining, statistics, machine learning and AI? | Statistics is concerned with probabilistic models, specifically inference on these models using data.
Machine Learning is concerned with predicting a particular outcome given some data. Almost any reasonable machine learning method can be formulated as a formal probabilistic model, so in this sense machine learning is ... | What is the difference between data mining, statistics, machine learning and AI? | Statistics is concerned with probabilistic models, specifically inference on these models using data.
Machine Learning is concerned with predicting a particular outcome given some data. Almost any rea | What is the difference between data mining, statistics, machine learning and AI?
Statistics is concerned with probabilistic models, specifically inference on these models using data.
Machine Learning is concerned with predicting a particular outcome given some data. Almost any reasonable machine learning method can be ... | What is the difference between data mining, statistics, machine learning and AI?
Statistics is concerned with probabilistic models, specifically inference on these models using data.
Machine Learning is concerned with predicting a particular outcome given some data. Almost any rea |
632 | What is the difference between data mining, statistics, machine learning and AI? | We can say that they are all related, but they are all different things.
Although you can have things in common among them, such as that in statistics and data mining you use clustering methods.
Let me try to briefly define each:
Statistics is a very old discipline mainly based on classical mathematical methods, whi... | What is the difference between data mining, statistics, machine learning and AI? | We can say that they are all related, but they are all different things.
Although you can have things in common among them, such as that in statistics and data mining you use clustering methods.
Let m | What is the difference between data mining, statistics, machine learning and AI?
We can say that they are all related, but they are all different things.
Although you can have things in common among them, such as that in statistics and data mining you use clustering methods.
Let me try to briefly define each:
Statis... | What is the difference between data mining, statistics, machine learning and AI?
We can say that they are all related, but they are all different things.
Although you can have things in common among them, such as that in statistics and data mining you use clustering methods.
Let m |
633 | What is the difference between data mining, statistics, machine learning and AI? | I'm most familiar with the machine-learning - data mining axis - so I'll concentrate on that:
Machine learning tends to be interested in inference in non-standard situations, for instance non-i.i.d. data, active learning, semi-supervised learning, learning with structured data (for instance strings or graphs). ML also... | What is the difference between data mining, statistics, machine learning and AI? | I'm most familiar with the machine-learning - data mining axis - so I'll concentrate on that:
Machine learning tends to be interested in inference in non-standard situations, for instance non-i.i.d. d | What is the difference between data mining, statistics, machine learning and AI?
I'm most familiar with the machine-learning - data mining axis - so I'll concentrate on that:
Machine learning tends to be interested in inference in non-standard situations, for instance non-i.i.d. data, active learning, semi-supervised l... | What is the difference between data mining, statistics, machine learning and AI?
I'm most familiar with the machine-learning - data mining axis - so I'll concentrate on that:
Machine learning tends to be interested in inference in non-standard situations, for instance non-i.i.d. d |
634 | What is the difference between data mining, statistics, machine learning and AI? | Here is my take at it. Let's start with the two very broad categories:
anything that even just pretends to be smart is artificial intelligence (including ML and DM).
anything that summarizes data is statistics, although you usually only apply this to methods that pay attention to the validity of the results (often use... | What is the difference between data mining, statistics, machine learning and AI? | Here is my take at it. Let's start with the two very broad categories:
anything that even just pretends to be smart is artificial intelligence (including ML and DM).
anything that summarizes data is | What is the difference between data mining, statistics, machine learning and AI?
Here is my take at it. Let's start with the two very broad categories:
anything that even just pretends to be smart is artificial intelligence (including ML and DM).
anything that summarizes data is statistics, although you usually only a... | What is the difference between data mining, statistics, machine learning and AI?
Here is my take at it. Let's start with the two very broad categories:
anything that even just pretends to be smart is artificial intelligence (including ML and DM).
anything that summarizes data is |
635 | What is the difference between data mining, statistics, machine learning and AI? | I'd add some observations to what's been said...
AI is a very broad term for anything that has to do with machines doing reasoning-like or sentient-appearing activities, ranging from planning a task or cooperating with other entities, to learning to operate limbs to walk. A pithy definition is that AI is anything compu... | What is the difference between data mining, statistics, machine learning and AI? | I'd add some observations to what's been said...
AI is a very broad term for anything that has to do with machines doing reasoning-like or sentient-appearing activities, ranging from planning a task o | What is the difference between data mining, statistics, machine learning and AI?
I'd add some observations to what's been said...
AI is a very broad term for anything that has to do with machines doing reasoning-like or sentient-appearing activities, ranging from planning a task or cooperating with other entities, to l... | What is the difference between data mining, statistics, machine learning and AI?
I'd add some observations to what's been said...
AI is a very broad term for anything that has to do with machines doing reasoning-like or sentient-appearing activities, ranging from planning a task o |
636 | What is the difference between data mining, statistics, machine learning and AI? | Sadly, the difference between these areas is largely where they're taught: statistics is based in maths depts, ai, machine learning in computer science depts, and data mining is more applied (used by business or marketing depts, developed by software companies).
Firstly AI (although it could mean any intelligent syste... | What is the difference between data mining, statistics, machine learning and AI? | Sadly, the difference between these areas is largely where they're taught: statistics is based in maths depts, ai, machine learning in computer science depts, and data mining is more applied (used by | What is the difference between data mining, statistics, machine learning and AI?
Sadly, the difference between these areas is largely where they're taught: statistics is based in maths depts, ai, machine learning in computer science depts, and data mining is more applied (used by business or marketing depts, developed ... | What is the difference between data mining, statistics, machine learning and AI?
Sadly, the difference between these areas is largely where they're taught: statistics is based in maths depts, ai, machine learning in computer science depts, and data mining is more applied (used by |
637 | What is the difference between data mining, statistics, machine learning and AI? | Data mining is about discovering hidden patterns or unknown knowledge, which can be used
for decision making by people.
Machine learning is about learning a model to classify new objects. | What is the difference between data mining, statistics, machine learning and AI? | Data mining is about discovering hidden patterns or unknown knowledge, which can be used
for decision making by people.
Machine learning is about learning a model to classify new objects. | What is the difference between data mining, statistics, machine learning and AI?
Data mining is about discovering hidden patterns or unknown knowledge, which can be used
for decision making by people.
Machine learning is about learning a model to classify new objects. | What is the difference between data mining, statistics, machine learning and AI?
Data mining is about discovering hidden patterns or unknown knowledge, which can be used
for decision making by people.
Machine learning is about learning a model to classify new objects. |
638 | What is the difference between data mining, statistics, machine learning and AI? | In my opinion, Artificial Intelligence could be considered as the "superset" of fields such as Machine Learning, Data Mining, Pattern Recognition etc.
Statistics, is a field of mathematics that includes all the mathematical models, techniques and theorems that are being used in AI.
Machine Learning is a field of AI th... | What is the difference between data mining, statistics, machine learning and AI? | In my opinion, Artificial Intelligence could be considered as the "superset" of fields such as Machine Learning, Data Mining, Pattern Recognition etc.
Statistics, is a field of mathematics that inclu | What is the difference between data mining, statistics, machine learning and AI?
In my opinion, Artificial Intelligence could be considered as the "superset" of fields such as Machine Learning, Data Mining, Pattern Recognition etc.
Statistics, is a field of mathematics that includes all the mathematical models, techni... | What is the difference between data mining, statistics, machine learning and AI?
In my opinion, Artificial Intelligence could be considered as the "superset" of fields such as Machine Learning, Data Mining, Pattern Recognition etc.
Statistics, is a field of mathematics that inclu |
639 | What is the difference between data mining, statistics, machine learning and AI? | How about: teaching machines to learn
Recognise meaningful patterns in data : data mining
Predict outcome from known patterns : ML
Find new features to remap raw data : AI
This bird brain really needs simple definitions. | What is the difference between data mining, statistics, machine learning and AI? | How about: teaching machines to learn
Recognise meaningful patterns in data : data mining
Predict outcome from known patterns : ML
Find new features to remap raw data : AI
This bird brain really needs | What is the difference between data mining, statistics, machine learning and AI?
How about: teaching machines to learn
Recognise meaningful patterns in data : data mining
Predict outcome from known patterns : ML
Find new features to remap raw data : AI
This bird brain really needs simple definitions. | What is the difference between data mining, statistics, machine learning and AI?
How about: teaching machines to learn
Recognise meaningful patterns in data : data mining
Predict outcome from known patterns : ML
Find new features to remap raw data : AI
This bird brain really needs |
640 | What is the difference between data mining, statistics, machine learning and AI? | Often data mining tries to "predict" some future data, or "explaining" why something happens.
Statistics are more used to validate hypothesis in my eyes. But this is a subjective discussion.
One obvious difference between statisticians and data miners can be found in the type of summary statistics they look at.
Stat... | What is the difference between data mining, statistics, machine learning and AI? | Often data mining tries to "predict" some future data, or "explaining" why something happens.
Statistics are more used to validate hypothesis in my eyes. But this is a subjective discussion.
One obv | What is the difference between data mining, statistics, machine learning and AI?
Often data mining tries to "predict" some future data, or "explaining" why something happens.
Statistics are more used to validate hypothesis in my eyes. But this is a subjective discussion.
One obvious difference between statisticians a... | What is the difference between data mining, statistics, machine learning and AI?
Often data mining tries to "predict" some future data, or "explaining" why something happens.
Statistics are more used to validate hypothesis in my eyes. But this is a subjective discussion.
One obv |
641 | What is the difference between data mining, statistics, machine learning and AI? | With all due respect to former answers, I believe that a huge part of the answer is still missing and it is in front of our eyes. Let me try to have a go at it:
In data mining, just like the name sounds, you mine data. Now mining means extracting knowledge from it, but also in general that usually means you are calcula... | What is the difference between data mining, statistics, machine learning and AI? | With all due respect to former answers, I believe that a huge part of the answer is still missing and it is in front of our eyes. Let me try to have a go at it:
In data mining, just like the name soun | What is the difference between data mining, statistics, machine learning and AI?
With all due respect to former answers, I believe that a huge part of the answer is still missing and it is in front of our eyes. Let me try to have a go at it:
In data mining, just like the name sounds, you mine data. Now mining means ext... | What is the difference between data mining, statistics, machine learning and AI?
With all due respect to former answers, I believe that a huge part of the answer is still missing and it is in front of our eyes. Let me try to have a go at it:
In data mining, just like the name soun |
642 | R's lmer cheat sheet | What's the difference between (~1 +....) and (1 | ...) and (0 | ...) etc.?
Say you have variable V1 predicted by categorical variable V2, which is treated as a random effect, and continuous variable V3, which is treated as a linear fixed effect. Using lmer syntax, simplest model (M1) is:
V1 ~ (1|V2) + V3
This model w... | R's lmer cheat sheet | What's the difference between (~1 +....) and (1 | ...) and (0 | ...) etc.?
Say you have variable V1 predicted by categorical variable V2, which is treated as a random effect, and continuous variable | R's lmer cheat sheet
What's the difference between (~1 +....) and (1 | ...) and (0 | ...) etc.?
Say you have variable V1 predicted by categorical variable V2, which is treated as a random effect, and continuous variable V3, which is treated as a linear fixed effect. Using lmer syntax, simplest model (M1) is:
V1 ~ (1|V... | R's lmer cheat sheet
What's the difference between (~1 +....) and (1 | ...) and (0 | ...) etc.?
Say you have variable V1 predicted by categorical variable V2, which is treated as a random effect, and continuous variable |
643 | R's lmer cheat sheet | The general trick is, as mentioned in another answer, is that the formula follows the form dependent ~ independent | grouping. The groupingis generally a random factor, you can include fixed factors without any grouping and you can have additional random factors without any fixed factor (an intercept-only model). A + ... | R's lmer cheat sheet | The general trick is, as mentioned in another answer, is that the formula follows the form dependent ~ independent | grouping. The groupingis generally a random factor, you can include fixed factors w | R's lmer cheat sheet
The general trick is, as mentioned in another answer, is that the formula follows the form dependent ~ independent | grouping. The groupingis generally a random factor, you can include fixed factors without any grouping and you can have additional random factors without any fixed factor (an interce... | R's lmer cheat sheet
The general trick is, as mentioned in another answer, is that the formula follows the form dependent ~ independent | grouping. The groupingis generally a random factor, you can include fixed factors w |
644 | R's lmer cheat sheet | The | symbol indicates a grouping factor in mixed methods.
As per Pinheiro & Bates:
...The formula also designates a response and, when available, a primary covariate. It is given as
response ~ primary | grouping
where response is an expression for the response, primary is an expression for the primary covariate, and... | R's lmer cheat sheet | The | symbol indicates a grouping factor in mixed methods.
As per Pinheiro & Bates:
...The formula also designates a response and, when available, a primary covariate. It is given as
response ~ prima | R's lmer cheat sheet
The | symbol indicates a grouping factor in mixed methods.
As per Pinheiro & Bates:
...The formula also designates a response and, when available, a primary covariate. It is given as
response ~ primary | grouping
where response is an expression for the response, primary is an expression for the p... | R's lmer cheat sheet
The | symbol indicates a grouping factor in mixed methods.
As per Pinheiro & Bates:
...The formula also designates a response and, when available, a primary covariate. It is given as
response ~ prima |
645 | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables? | Although a PCA applied on binary data would yield results comparable to those obtained from a Multiple Correspondence Analysis (factor scores and eigenvalues are linearly related), there are more appropriate techniques to deal with mixed data types, namely Multiple Factor Analysis for mixed data available in the FactoM... | Can principal component analysis be applied to datasets containing a mix of continuous and categoric | Although a PCA applied on binary data would yield results comparable to those obtained from a Multiple Correspondence Analysis (factor scores and eigenvalues are linearly related), there are more appr | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables?
Although a PCA applied on binary data would yield results comparable to those obtained from a Multiple Correspondence Analysis (factor scores and eigenvalues are linearly related), there are more appropriat... | Can principal component analysis be applied to datasets containing a mix of continuous and categoric
Although a PCA applied on binary data would yield results comparable to those obtained from a Multiple Correspondence Analysis (factor scores and eigenvalues are linearly related), there are more appr |
646 | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables? | A Google search "pca for discrete variables" gives this nice overview by S. Kolenikov (@StasK) and G. Angeles. To add to chl answer, the PC analysis is really analysis of eigenvectors of covariance matrix. So the problem is how to calculate the "correct" covariance matrix. One of the approaches is to use
polychoric cor... | Can principal component analysis be applied to datasets containing a mix of continuous and categoric | A Google search "pca for discrete variables" gives this nice overview by S. Kolenikov (@StasK) and G. Angeles. To add to chl answer, the PC analysis is really analysis of eigenvectors of covariance ma | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables?
A Google search "pca for discrete variables" gives this nice overview by S. Kolenikov (@StasK) and G. Angeles. To add to chl answer, the PC analysis is really analysis of eigenvectors of covariance matrix. ... | Can principal component analysis be applied to datasets containing a mix of continuous and categoric
A Google search "pca for discrete variables" gives this nice overview by S. Kolenikov (@StasK) and G. Angeles. To add to chl answer, the PC analysis is really analysis of eigenvectors of covariance ma |
647 | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables? | I would suggest having a look at Linting & Kooij, 2012 "Non linear principal component analysis with CATPCA: a tutorial", Journal of Personality Assessment; 94(1).
Abstract
This article is set up as a tutorial for nonlinear principal components analysis (NLPCA), systematically guiding the reader through the process of... | Can principal component analysis be applied to datasets containing a mix of continuous and categoric | I would suggest having a look at Linting & Kooij, 2012 "Non linear principal component analysis with CATPCA: a tutorial", Journal of Personality Assessment; 94(1).
Abstract
This article is set up as | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables?
I would suggest having a look at Linting & Kooij, 2012 "Non linear principal component analysis with CATPCA: a tutorial", Journal of Personality Assessment; 94(1).
Abstract
This article is set up as a tuto... | Can principal component analysis be applied to datasets containing a mix of continuous and categoric
I would suggest having a look at Linting & Kooij, 2012 "Non linear principal component analysis with CATPCA: a tutorial", Journal of Personality Assessment; 94(1).
Abstract
This article is set up as |
648 | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables? | Continuing on what @Martin F commented, recently I came across with the nonlinear PCAs. I was looking into Nonlinear PCAs as a possible alternative when a continuous variable approaches distribution of an ordinal variable as the data gets sparser (it happens in genetics a lot of times when the minor allele frequency of... | Can principal component analysis be applied to datasets containing a mix of continuous and categoric | Continuing on what @Martin F commented, recently I came across with the nonlinear PCAs. I was looking into Nonlinear PCAs as a possible alternative when a continuous variable approaches distribution o | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables?
Continuing on what @Martin F commented, recently I came across with the nonlinear PCAs. I was looking into Nonlinear PCAs as a possible alternative when a continuous variable approaches distribution of an o... | Can principal component analysis be applied to datasets containing a mix of continuous and categoric
Continuing on what @Martin F commented, recently I came across with the nonlinear PCAs. I was looking into Nonlinear PCAs as a possible alternative when a continuous variable approaches distribution o |
649 | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables? | PCAmixdata #Rstats package:
Implements principal component analysis, orthogonal rotation and multiple factor analysis for a mixture of quantitative and qualitative variables.
Example from vignette shows results for both continuous and categorical output | Can principal component analysis be applied to datasets containing a mix of continuous and categoric | PCAmixdata #Rstats package:
Implements principal component analysis, orthogonal rotation and multiple factor analysis for a mixture of quantitative and qualitative variables.
Example from vignette | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables?
PCAmixdata #Rstats package:
Implements principal component analysis, orthogonal rotation and multiple factor analysis for a mixture of quantitative and qualitative variables.
Example from vignette shows ... | Can principal component analysis be applied to datasets containing a mix of continuous and categoric
PCAmixdata #Rstats package:
Implements principal component analysis, orthogonal rotation and multiple factor analysis for a mixture of quantitative and qualitative variables.
Example from vignette |
650 | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables? | There is a recently developed approach to such problems: Generalized Low Rank Models.
One of papers that use this technique is even called PCA on a Data Frame.
PCA can be posed like this:
For $n$ x $m$ matrix $M$
find $n$ x $k$ matrix $\hat{X}$ and $k$ x $m$ matrix $\hat{Y}$ (this encodes rank $k$ e constraint implic... | Can principal component analysis be applied to datasets containing a mix of continuous and categoric | There is a recently developed approach to such problems: Generalized Low Rank Models.
One of papers that use this technique is even called PCA on a Data Frame.
PCA can be posed like this:
For $n$ x $ | Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables?
There is a recently developed approach to such problems: Generalized Low Rank Models.
One of papers that use this technique is even called PCA on a Data Frame.
PCA can be posed like this:
For $n$ x $m$ mat... | Can principal component analysis be applied to datasets containing a mix of continuous and categoric
There is a recently developed approach to such problems: Generalized Low Rank Models.
One of papers that use this technique is even called PCA on a Data Frame.
PCA can be posed like this:
For $n$ x $ |
651 | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? | I always hesitate to jump into a thread with as many excellent responses as this, but it strikes me that few of the answers provide any reason to prefer the logarithm to some other transformation that "squashes" the data, such as a root or reciprocal.
Before getting to that, let's recapitulate the wisdom in the existin... | In linear regression, when is it appropriate to use the log of an independent variable instead of th | I always hesitate to jump into a thread with as many excellent responses as this, but it strikes me that few of the answers provide any reason to prefer the logarithm to some other transformation that | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?
I always hesitate to jump into a thread with as many excellent responses as this, but it strikes me that few of the answers provide any reason to prefer the logarithm to some other transformation that "s... | In linear regression, when is it appropriate to use the log of an independent variable instead of th
I always hesitate to jump into a thread with as many excellent responses as this, but it strikes me that few of the answers provide any reason to prefer the logarithm to some other transformation that |
652 | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? | I always tell students there are three reasons to transform a variable by taking the natural logarithm. The reason for logging the variable will determine whether you want to log the independent variable(s), dependent or both. To be clear throughout I'm talking about taking the natural logarithm.
Firstly, to improve m... | In linear regression, when is it appropriate to use the log of an independent variable instead of th | I always tell students there are three reasons to transform a variable by taking the natural logarithm. The reason for logging the variable will determine whether you want to log the independent varia | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?
I always tell students there are three reasons to transform a variable by taking the natural logarithm. The reason for logging the variable will determine whether you want to log the independent variable... | In linear regression, when is it appropriate to use the log of an independent variable instead of th
I always tell students there are three reasons to transform a variable by taking the natural logarithm. The reason for logging the variable will determine whether you want to log the independent varia |
653 | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? | For more on whuber's excellent point about reasons to prefer the logarithm to some other transformations such as a root or reciprocal, but focussing on the unique interpretability of the regression coefficients resulting from log-transformation compared to other transformations, see:
Oliver N. Keene. The log transforma... | In linear regression, when is it appropriate to use the log of an independent variable instead of th | For more on whuber's excellent point about reasons to prefer the logarithm to some other transformations such as a root or reciprocal, but focussing on the unique interpretability of the regression co | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?
For more on whuber's excellent point about reasons to prefer the logarithm to some other transformations such as a root or reciprocal, but focussing on the unique interpretability of the regression coeff... | In linear regression, when is it appropriate to use the log of an independent variable instead of th
For more on whuber's excellent point about reasons to prefer the logarithm to some other transformations such as a root or reciprocal, but focussing on the unique interpretability of the regression co |
654 | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? | One typically takes the log of an input variable to scale it and change the distribution (e.g. to make it normally distributed). It cannot be done blindly however; you need to be careful when making any scaling to ensure that the results are still interpretable.
This is discussed in most introductory statistics text... | In linear regression, when is it appropriate to use the log of an independent variable instead of th | One typically takes the log of an input variable to scale it and change the distribution (e.g. to make it normally distributed). It cannot be done blindly however; you need to be careful when making | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?
One typically takes the log of an input variable to scale it and change the distribution (e.g. to make it normally distributed). It cannot be done blindly however; you need to be careful when making any... | In linear regression, when is it appropriate to use the log of an independent variable instead of th
One typically takes the log of an input variable to scale it and change the distribution (e.g. to make it normally distributed). It cannot be done blindly however; you need to be careful when making |
655 | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? | You tend to take logs of the data when there is a problem with the residuals. For example, if you plot the residuals against a particular covariate and observe an increasing/decreasing pattern (a funnel shape), then a transformation may be appropriate. Non-random residuals usually indicate that your model assumptions a... | In linear regression, when is it appropriate to use the log of an independent variable instead of th | You tend to take logs of the data when there is a problem with the residuals. For example, if you plot the residuals against a particular covariate and observe an increasing/decreasing pattern (a funn | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?
You tend to take logs of the data when there is a problem with the residuals. For example, if you plot the residuals against a particular covariate and observe an increasing/decreasing pattern (a funnel ... | In linear regression, when is it appropriate to use the log of an independent variable instead of th
You tend to take logs of the data when there is a problem with the residuals. For example, if you plot the residuals against a particular covariate and observe an increasing/decreasing pattern (a funn |
656 | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? | Transformation of an independent variable $X$ is one occasion where one can just be empirical without distorting inference as long as one is honest about the number of degrees of freedom in play. One way is to use regression splines for continuous $X$ not already known to act linearly. To me it's not a question of lo... | In linear regression, when is it appropriate to use the log of an independent variable instead of th | Transformation of an independent variable $X$ is one occasion where one can just be empirical without distorting inference as long as one is honest about the number of degrees of freedom in play. One | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?
Transformation of an independent variable $X$ is one occasion where one can just be empirical without distorting inference as long as one is honest about the number of degrees of freedom in play. One wa... | In linear regression, when is it appropriate to use the log of an independent variable instead of th
Transformation of an independent variable $X$ is one occasion where one can just be empirical without distorting inference as long as one is honest about the number of degrees of freedom in play. One |
657 | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? | I would like to respond to user1690130's question that was left as a comment to the first answer on Oct 26 '12 and reads as follows: "What about variables like population density in a region or the child-teacher ratio for each school district or the number of homicides per 1000 in the population? I have seen professors... | In linear regression, when is it appropriate to use the log of an independent variable instead of th | I would like to respond to user1690130's question that was left as a comment to the first answer on Oct 26 '12 and reads as follows: "What about variables like population density in a region or the ch | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?
I would like to respond to user1690130's question that was left as a comment to the first answer on Oct 26 '12 and reads as follows: "What about variables like population density in a region or the child... | In linear regression, when is it appropriate to use the log of an independent variable instead of th
I would like to respond to user1690130's question that was left as a comment to the first answer on Oct 26 '12 and reads as follows: "What about variables like population density in a region or the ch |
658 | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? | Shane's point that taking the log to deal with bad data is well taken. As is Colin's regarding the importance of normal residuals. In practice I find that usually you can get normal residuals if the input and output variables are also relatively normal. In practice this means eyeballing the distribution of the trans... | In linear regression, when is it appropriate to use the log of an independent variable instead of th | Shane's point that taking the log to deal with bad data is well taken. As is Colin's regarding the importance of normal residuals. In practice I find that usually you can get normal residuals if the | In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?
Shane's point that taking the log to deal with bad data is well taken. As is Colin's regarding the importance of normal residuals. In practice I find that usually you can get normal residuals if the in... | In linear regression, when is it appropriate to use the log of an independent variable instead of th
Shane's point that taking the log to deal with bad data is well taken. As is Colin's regarding the importance of normal residuals. In practice I find that usually you can get normal residuals if the |
659 | What does the hidden layer in a neural network compute? | Three sentence version:
Each layer can apply any function you want to the previous layer (usually a linear transformation followed by a squashing nonlinearity).
The hidden layers' job is to transform the inputs into something that the output layer can use.
The output layer transforms the hidden layer activations into... | What does the hidden layer in a neural network compute? | Three sentence version:
Each layer can apply any function you want to the previous layer (usually a linear transformation followed by a squashing nonlinearity).
The hidden layers' job is to transfor | What does the hidden layer in a neural network compute?
Three sentence version:
Each layer can apply any function you want to the previous layer (usually a linear transformation followed by a squashing nonlinearity).
The hidden layers' job is to transform the inputs into something that the output layer can use.
The o... | What does the hidden layer in a neural network compute?
Three sentence version:
Each layer can apply any function you want to the previous layer (usually a linear transformation followed by a squashing nonlinearity).
The hidden layers' job is to transfor |
660 | What does the hidden layer in a neural network compute? | I'm going to describe my view of this in two steps: The input-to-hidden step and the hidden-to-output step. I'll do the hidden-to-output step first because it seems less interesting (to me).
Hidden-to-Output
The output of the hidden layer could be different things, but for now let's suppose that they come out of sigmoi... | What does the hidden layer in a neural network compute? | I'm going to describe my view of this in two steps: The input-to-hidden step and the hidden-to-output step. I'll do the hidden-to-output step first because it seems less interesting (to me).
Hidden-to | What does the hidden layer in a neural network compute?
I'm going to describe my view of this in two steps: The input-to-hidden step and the hidden-to-output step. I'll do the hidden-to-output step first because it seems less interesting (to me).
Hidden-to-Output
The output of the hidden layer could be different things... | What does the hidden layer in a neural network compute?
I'm going to describe my view of this in two steps: The input-to-hidden step and the hidden-to-output step. I'll do the hidden-to-output step first because it seems less interesting (to me).
Hidden-to |
661 | What does the hidden layer in a neural network compute? | I'll try to add to the intuitive operational description...
A good intuitive way to think about a neural network is to think about what a linear regression model attempts to do. A linear regression will take some inputs and come up with a linear model which takes each input value times some model optimal weighting coe... | What does the hidden layer in a neural network compute? | I'll try to add to the intuitive operational description...
A good intuitive way to think about a neural network is to think about what a linear regression model attempts to do. A linear regression w | What does the hidden layer in a neural network compute?
I'll try to add to the intuitive operational description...
A good intuitive way to think about a neural network is to think about what a linear regression model attempts to do. A linear regression will take some inputs and come up with a linear model which takes... | What does the hidden layer in a neural network compute?
I'll try to add to the intuitive operational description...
A good intuitive way to think about a neural network is to think about what a linear regression model attempts to do. A linear regression w |
662 | What does the hidden layer in a neural network compute? | Let us take the case of classification. What the output layer is trying to do is estimate the conditional probability that your sample belongs to a given class, i.e. how likely is for that sample to belong to a given class. In geometrical terms, combining layers in a non-linear fashion via the threshold functions allow... | What does the hidden layer in a neural network compute? | Let us take the case of classification. What the output layer is trying to do is estimate the conditional probability that your sample belongs to a given class, i.e. how likely is for that sample to b | What does the hidden layer in a neural network compute?
Let us take the case of classification. What the output layer is trying to do is estimate the conditional probability that your sample belongs to a given class, i.e. how likely is for that sample to belong to a given class. In geometrical terms, combining layers i... | What does the hidden layer in a neural network compute?
Let us take the case of classification. What the output layer is trying to do is estimate the conditional probability that your sample belongs to a given class, i.e. how likely is for that sample to b |
663 | Generative vs. discriminative | The fundamental difference between discriminative models and generative models is:
Discriminative models learn the (hard or soft) boundary between classes
Generative models model the distribution of individual classes
To answer your direct questions:
SVMs (Support Vector Machines) and DTs (Decision Trees) are discri... | Generative vs. discriminative | The fundamental difference between discriminative models and generative models is:
Discriminative models learn the (hard or soft) boundary between classes
Generative models model the distribution of | Generative vs. discriminative
The fundamental difference between discriminative models and generative models is:
Discriminative models learn the (hard or soft) boundary between classes
Generative models model the distribution of individual classes
To answer your direct questions:
SVMs (Support Vector Machines) and D... | Generative vs. discriminative
The fundamental difference between discriminative models and generative models is:
Discriminative models learn the (hard or soft) boundary between classes
Generative models model the distribution of |
664 | Generative vs. discriminative | (hamner's answer is great, so just cross-posting my answer from MetaOptimize for completeness.)
I think of generative algorithms as providing a model of how the data is actually generated (I think of them as giving you a model of both $P(X|Y)$ and $P(Y)$, rather than of $P(X, Y)$, though I guess it's equivalent), and d... | Generative vs. discriminative | (hamner's answer is great, so just cross-posting my answer from MetaOptimize for completeness.)
I think of generative algorithms as providing a model of how the data is actually generated (I think of | Generative vs. discriminative
(hamner's answer is great, so just cross-posting my answer from MetaOptimize for completeness.)
I think of generative algorithms as providing a model of how the data is actually generated (I think of them as giving you a model of both $P(X|Y)$ and $P(Y)$, rather than of $P(X, Y)$, though I... | Generative vs. discriminative
(hamner's answer is great, so just cross-posting my answer from MetaOptimize for completeness.)
I think of generative algorithms as providing a model of how the data is actually generated (I think of |
665 | Generative vs. discriminative | As an additional point to the above answers, when the aim of algorithm is only to classify, then discriminative approach may be better and less expensive than generative approach, as following the generative approach to model input distribution can result in requiring too much training data to model complexities in dis... | Generative vs. discriminative | As an additional point to the above answers, when the aim of algorithm is only to classify, then discriminative approach may be better and less expensive than generative approach, as following the gen | Generative vs. discriminative
As an additional point to the above answers, when the aim of algorithm is only to classify, then discriminative approach may be better and less expensive than generative approach, as following the generative approach to model input distribution can result in requiring too much training dat... | Generative vs. discriminative
As an additional point to the above answers, when the aim of algorithm is only to classify, then discriminative approach may be better and less expensive than generative approach, as following the gen |
666 | PCA on correlation or covariance? | You tend to use the covariance matrix when the variable scales are similar and the correlation matrix when variables are on different scales.
Using the correlation matrix is equivalent to standardizing each of the variables (to mean 0 and standard deviation 1). In general, PCA with and without standardizing will give d... | PCA on correlation or covariance? | You tend to use the covariance matrix when the variable scales are similar and the correlation matrix when variables are on different scales.
Using the correlation matrix is equivalent to standardizin | PCA on correlation or covariance?
You tend to use the covariance matrix when the variable scales are similar and the correlation matrix when variables are on different scales.
Using the correlation matrix is equivalent to standardizing each of the variables (to mean 0 and standard deviation 1). In general, PCA with and... | PCA on correlation or covariance?
You tend to use the covariance matrix when the variable scales are similar and the correlation matrix when variables are on different scales.
Using the correlation matrix is equivalent to standardizin |
667 | PCA on correlation or covariance? | Bernard Flury, in his excellent book introducing multivariate analysis, described this as an anti-property of principal components. It's actually worse than choosing between correlation or covariance. If you changed the units (e.g. US style gallons, inches etc. and EU style litres, centimetres) you will get substan... | PCA on correlation or covariance? | Bernard Flury, in his excellent book introducing multivariate analysis, described this as an anti-property of principal components. It's actually worse than choosing between correlation or covarianc | PCA on correlation or covariance?
Bernard Flury, in his excellent book introducing multivariate analysis, described this as an anti-property of principal components. It's actually worse than choosing between correlation or covariance. If you changed the units (e.g. US style gallons, inches etc. and EU style litres,... | PCA on correlation or covariance?
Bernard Flury, in his excellent book introducing multivariate analysis, described this as an anti-property of principal components. It's actually worse than choosing between correlation or covarianc |
668 | PCA on correlation or covariance? | UNTRANSFORMED (RAW) DATA: If you have variables with widely varying scales for raw, untransformed data, that is, caloric intake per day, gene expression, ELISA/Luminex in units of ug/dl, ng/dl, based on several orders of magnitude of protein expression, then use correlation as an input to PCA. However, if all of your ... | PCA on correlation or covariance? | UNTRANSFORMED (RAW) DATA: If you have variables with widely varying scales for raw, untransformed data, that is, caloric intake per day, gene expression, ELISA/Luminex in units of ug/dl, ng/dl, based | PCA on correlation or covariance?
UNTRANSFORMED (RAW) DATA: If you have variables with widely varying scales for raw, untransformed data, that is, caloric intake per day, gene expression, ELISA/Luminex in units of ug/dl, ng/dl, based on several orders of magnitude of protein expression, then use correlation as an input... | PCA on correlation or covariance?
UNTRANSFORMED (RAW) DATA: If you have variables with widely varying scales for raw, untransformed data, that is, caloric intake per day, gene expression, ELISA/Luminex in units of ug/dl, ng/dl, based |
669 | PCA on correlation or covariance? | A common answer is to suggest that covariance is used when variables are on the same scale, and correlation when their scales are different. However, this is only true when scale of the variables isn't a factor. Otherwise, why would anyone ever do covariance PCA? It would be safer to always perform correlation PCA.
Ima... | PCA on correlation or covariance? | A common answer is to suggest that covariance is used when variables are on the same scale, and correlation when their scales are different. However, this is only true when scale of the variables isn' | PCA on correlation or covariance?
A common answer is to suggest that covariance is used when variables are on the same scale, and correlation when their scales are different. However, this is only true when scale of the variables isn't a factor. Otherwise, why would anyone ever do covariance PCA? It would be safer to a... | PCA on correlation or covariance?
A common answer is to suggest that covariance is used when variables are on the same scale, and correlation when their scales are different. However, this is only true when scale of the variables isn' |
670 | PCA on correlation or covariance? | I personally find it very valuable to discuss these options in light of the maximum-likelihood principal component analysis model (MLPCA) [1,2]. In MLPCA one applies a scaling (or even a rotation) such that the measurement errors in the measured variables are independent and distributed according to the standard normal... | PCA on correlation or covariance? | I personally find it very valuable to discuss these options in light of the maximum-likelihood principal component analysis model (MLPCA) [1,2]. In MLPCA one applies a scaling (or even a rotation) suc | PCA on correlation or covariance?
I personally find it very valuable to discuss these options in light of the maximum-likelihood principal component analysis model (MLPCA) [1,2]. In MLPCA one applies a scaling (or even a rotation) such that the measurement errors in the measured variables are independent and distribute... | PCA on correlation or covariance?
I personally find it very valuable to discuss these options in light of the maximum-likelihood principal component analysis model (MLPCA) [1,2]. In MLPCA one applies a scaling (or even a rotation) suc |
671 | PCA on correlation or covariance? | Straight and simple: if the scales are similar use cov-PCA, if not, use corr-PCA; otherwise, you better have a defense for not. If in doubt, use an F-test for the equality of the variances (ANOVA). If it fails the F-test, use corr; otherwise, use cov. | PCA on correlation or covariance? | Straight and simple: if the scales are similar use cov-PCA, if not, use corr-PCA; otherwise, you better have a defense for not. If in doubt, use an F-test for the equality of the variances (ANOVA). If | PCA on correlation or covariance?
Straight and simple: if the scales are similar use cov-PCA, if not, use corr-PCA; otherwise, you better have a defense for not. If in doubt, use an F-test for the equality of the variances (ANOVA). If it fails the F-test, use corr; otherwise, use cov. | PCA on correlation or covariance?
Straight and simple: if the scales are similar use cov-PCA, if not, use corr-PCA; otherwise, you better have a defense for not. If in doubt, use an F-test for the equality of the variances (ANOVA). If |
672 | PCA on correlation or covariance? | The arguments based on scale (for variables expressed in the same physical units) seem rather weak. Imagine a set of (dimensionless) variables whose standard deviations vary between 0.001 and 0.1. Compared to a standardized value of 1, these both seem to be 'small' and comparable levels of fluctuations. However, when y... | PCA on correlation or covariance? | The arguments based on scale (for variables expressed in the same physical units) seem rather weak. Imagine a set of (dimensionless) variables whose standard deviations vary between 0.001 and 0.1. Com | PCA on correlation or covariance?
The arguments based on scale (for variables expressed in the same physical units) seem rather weak. Imagine a set of (dimensionless) variables whose standard deviations vary between 0.001 and 0.1. Compared to a standardized value of 1, these both seem to be 'small' and comparable level... | PCA on correlation or covariance?
The arguments based on scale (for variables expressed in the same physical units) seem rather weak. Imagine a set of (dimensionless) variables whose standard deviations vary between 0.001 and 0.1. Com |
673 | How exactly does one “control for other variables”? | There are many ways to control for variables.
The easiest, and one you came up with, is to stratify your data so you have sub-groups with similar characteristics - there are then methods to pool those results together to get a single "answer". This works if you have a very small number of variables you want to control ... | How exactly does one “control for other variables”? | There are many ways to control for variables.
The easiest, and one you came up with, is to stratify your data so you have sub-groups with similar characteristics - there are then methods to pool those | How exactly does one “control for other variables”?
There are many ways to control for variables.
The easiest, and one you came up with, is to stratify your data so you have sub-groups with similar characteristics - there are then methods to pool those results together to get a single "answer". This works if you have a... | How exactly does one “control for other variables”?
There are many ways to control for variables.
The easiest, and one you came up with, is to stratify your data so you have sub-groups with similar characteristics - there are then methods to pool those |
674 | How exactly does one “control for other variables”? | Introduction
I like @EpiGrad's answer (+1) but let me take a different perspective. In the following I am referring to this PDF document: "Multiple Regression Analysis: Estimation", which has a section on "A 'Partialling Out' Interpretation of Multiple Regression" (p. 83f.). Unfortunately, I have no idea who is the aut... | How exactly does one “control for other variables”? | Introduction
I like @EpiGrad's answer (+1) but let me take a different perspective. In the following I am referring to this PDF document: "Multiple Regression Analysis: Estimation", which has a sectio | How exactly does one “control for other variables”?
Introduction
I like @EpiGrad's answer (+1) but let me take a different perspective. In the following I am referring to this PDF document: "Multiple Regression Analysis: Estimation", which has a section on "A 'Partialling Out' Interpretation of Multiple Regression" (p.... | How exactly does one “control for other variables”?
Introduction
I like @EpiGrad's answer (+1) but let me take a different perspective. In the following I am referring to this PDF document: "Multiple Regression Analysis: Estimation", which has a sectio |
675 | How exactly does one “control for other variables”? | Of course some math will be involved, but it's not much: Euclid would have understood it well. All you really need to know is how to add and rescale vectors. Although this goes by the name of "linear algebra" nowadays, you only need to visualize it in two dimensions. This enables us to avoid the matrix machinery of ... | How exactly does one “control for other variables”? | Of course some math will be involved, but it's not much: Euclid would have understood it well. All you really need to know is how to add and rescale vectors. Although this goes by the name of "linea | How exactly does one “control for other variables”?
Of course some math will be involved, but it's not much: Euclid would have understood it well. All you really need to know is how to add and rescale vectors. Although this goes by the name of "linear algebra" nowadays, you only need to visualize it in two dimensions... | How exactly does one “control for other variables”?
Of course some math will be involved, but it's not much: Euclid would have understood it well. All you really need to know is how to add and rescale vectors. Although this goes by the name of "linea |
676 | How exactly does one “control for other variables”? | There is an excellent discussion so far of covariate adjustment as a means of "controlling for other variables". But I think that is only part of the story. In fact, there are many (other) design, model, and machine learning based strategies to address the impact of a number of possible confounding variables. This is a... | How exactly does one “control for other variables”? | There is an excellent discussion so far of covariate adjustment as a means of "controlling for other variables". But I think that is only part of the story. In fact, there are many (other) design, mod | How exactly does one “control for other variables”?
There is an excellent discussion so far of covariate adjustment as a means of "controlling for other variables". But I think that is only part of the story. In fact, there are many (other) design, model, and machine learning based strategies to address the impact of a... | How exactly does one “control for other variables”?
There is an excellent discussion so far of covariate adjustment as a means of "controlling for other variables". But I think that is only part of the story. In fact, there are many (other) design, mod |
677 | How exactly does one “control for other variables”? | The software doesn't literally control for variables. If you're familiar with matrix notation of regression $Y=X\beta+\varepsilon$, then you may remember that least squares solution is $b=(X^TX)^{-1}X^TY$. So, the software evaluates this expression numerically using computational linear algebra methods. | How exactly does one “control for other variables”? | The software doesn't literally control for variables. If you're familiar with matrix notation of regression $Y=X\beta+\varepsilon$, then you may remember that least squares solution is $b=(X^TX)^{-1}X | How exactly does one “control for other variables”?
The software doesn't literally control for variables. If you're familiar with matrix notation of regression $Y=X\beta+\varepsilon$, then you may remember that least squares solution is $b=(X^TX)^{-1}X^TY$. So, the software evaluates this expression numerically using c... | How exactly does one “control for other variables”?
The software doesn't literally control for variables. If you're familiar with matrix notation of regression $Y=X\beta+\varepsilon$, then you may remember that least squares solution is $b=(X^TX)^{-1}X |
678 | When should I use lasso vs ridge? | Keep in mind that ridge regression can't zero out coefficients; thus, you either end up including all the coefficients in the model, or none of them. In contrast, the LASSO does both parameter shrinkage and variable selection automatically. If some of your covariates are highly correlated, you may want to look at the E... | When should I use lasso vs ridge? | Keep in mind that ridge regression can't zero out coefficients; thus, you either end up including all the coefficients in the model, or none of them. In contrast, the LASSO does both parameter shrinka | When should I use lasso vs ridge?
Keep in mind that ridge regression can't zero out coefficients; thus, you either end up including all the coefficients in the model, or none of them. In contrast, the LASSO does both parameter shrinkage and variable selection automatically. If some of your covariates are highly correla... | When should I use lasso vs ridge?
Keep in mind that ridge regression can't zero out coefficients; thus, you either end up including all the coefficients in the model, or none of them. In contrast, the LASSO does both parameter shrinka |
679 | When should I use lasso vs ridge? | Ridge or lasso are forms of regularized linear regressions. The regularization can also be interpreted as prior in a maximum a posteriori estimation method. Under this interpretation, the ridge and the lasso make different assumptions on the class of linear transformation they infer to relate input and output data. ... | When should I use lasso vs ridge? | Ridge or lasso are forms of regularized linear regressions. The regularization can also be interpreted as prior in a maximum a posteriori estimation method. Under this interpretation, the ridge and | When should I use lasso vs ridge?
Ridge or lasso are forms of regularized linear regressions. The regularization can also be interpreted as prior in a maximum a posteriori estimation method. Under this interpretation, the ridge and the lasso make different assumptions on the class of linear transformation they infer ... | When should I use lasso vs ridge?
Ridge or lasso are forms of regularized linear regressions. The regularization can also be interpreted as prior in a maximum a posteriori estimation method. Under this interpretation, the ridge and |
680 | When should I use lasso vs ridge? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Generally, when you have many small/medium sized effec... | When should I use lasso vs ridge? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| When should I use lasso vs ridge?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Generally, when you ... | When should I use lasso vs ridge?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
681 | How to deal with perfect separation in logistic regression? | A solution to this is to utilize a form of penalized regression. In fact, this is the original reason some of the penalized regression forms were developed (although they turned out to have other interesting properties.
Install and load package glmnet in R and you're mostly ready to go. One of the less user-friendly as... | How to deal with perfect separation in logistic regression? | A solution to this is to utilize a form of penalized regression. In fact, this is the original reason some of the penalized regression forms were developed (although they turned out to have other inte | How to deal with perfect separation in logistic regression?
A solution to this is to utilize a form of penalized regression. In fact, this is the original reason some of the penalized regression forms were developed (although they turned out to have other interesting properties.
Install and load package glmnet in R and... | How to deal with perfect separation in logistic regression?
A solution to this is to utilize a form of penalized regression. In fact, this is the original reason some of the penalized regression forms were developed (although they turned out to have other inte |
682 | How to deal with perfect separation in logistic regression? | You've several options:
Remove some of the bias.
(a) By penalizing the likelihood as per @Nick's suggestion. Package logistf in R or the FIRTH option in SAS's PROC LOGISTIC implement the method proposed in Firth (1993), "Bias reduction of maximum likelihood estimates", Biometrika, 80,1.; which removes the first-order ... | How to deal with perfect separation in logistic regression? | You've several options:
Remove some of the bias.
(a) By penalizing the likelihood as per @Nick's suggestion. Package logistf in R or the FIRTH option in SAS's PROC LOGISTIC implement the method propo | How to deal with perfect separation in logistic regression?
You've several options:
Remove some of the bias.
(a) By penalizing the likelihood as per @Nick's suggestion. Package logistf in R or the FIRTH option in SAS's PROC LOGISTIC implement the method proposed in Firth (1993), "Bias reduction of maximum likelihood e... | How to deal with perfect separation in logistic regression?
You've several options:
Remove some of the bias.
(a) By penalizing the likelihood as per @Nick's suggestion. Package logistf in R or the FIRTH option in SAS's PROC LOGISTIC implement the method propo |
683 | How to deal with perfect separation in logistic regression? | This is an expansion of Scortchi and Manoel's answers, but since you seem to use R I thought I'd supply some code. :)
I believe the easiest and most straightforward solution to your problem is to use a Bayesian analysis with non-informative prior assumptions as proposed by Gelman et al (2008). As Scortchi mentions, Gel... | How to deal with perfect separation in logistic regression? | This is an expansion of Scortchi and Manoel's answers, but since you seem to use R I thought I'd supply some code. :)
I believe the easiest and most straightforward solution to your problem is to use | How to deal with perfect separation in logistic regression?
This is an expansion of Scortchi and Manoel's answers, but since you seem to use R I thought I'd supply some code. :)
I believe the easiest and most straightforward solution to your problem is to use a Bayesian analysis with non-informative prior assumptions a... | How to deal with perfect separation in logistic regression?
This is an expansion of Scortchi and Manoel's answers, but since you seem to use R I thought I'd supply some code. :)
I believe the easiest and most straightforward solution to your problem is to use |
684 | How to deal with perfect separation in logistic regression? | One of the most thorough explanations of "quasi-complete separation" issues in maximum likelihood is Paul Allison's paper. He's writing about SAS software, but the issues he addresses are generalizable to any software:
Complete separation occurs whenever a linear function of x can generate perfect predictions of y
Qu... | How to deal with perfect separation in logistic regression? | One of the most thorough explanations of "quasi-complete separation" issues in maximum likelihood is Paul Allison's paper. He's writing about SAS software, but the issues he addresses are generalizabl | How to deal with perfect separation in logistic regression?
One of the most thorough explanations of "quasi-complete separation" issues in maximum likelihood is Paul Allison's paper. He's writing about SAS software, but the issues he addresses are generalizable to any software:
Complete separation occurs whenever a l... | How to deal with perfect separation in logistic regression?
One of the most thorough explanations of "quasi-complete separation" issues in maximum likelihood is Paul Allison's paper. He's writing about SAS software, but the issues he addresses are generalizabl |
685 | How to deal with perfect separation in logistic regression? | The original question is miscast and many of the answers are problematic. The fact that a maximum likelihood estimate is $\infty$ when there is perfect separation is only a problem because we continue to use Wald statistics (i.e., we use the information matrix and standard errors) for inference. An $\infty$ $\beta$ g... | How to deal with perfect separation in logistic regression? | The original question is miscast and many of the answers are problematic. The fact that a maximum likelihood estimate is $\infty$ when there is perfect separation is only a problem because we continu | How to deal with perfect separation in logistic regression?
The original question is miscast and many of the answers are problematic. The fact that a maximum likelihood estimate is $\infty$ when there is perfect separation is only a problem because we continue to use Wald statistics (i.e., we use the information matri... | How to deal with perfect separation in logistic regression?
The original question is miscast and many of the answers are problematic. The fact that a maximum likelihood estimate is $\infty$ when there is perfect separation is only a problem because we continu |
686 | How to deal with perfect separation in logistic regression? | For logistic models for inference, it's important to first underscore that there is no error here. The warning in R is correctly informing you that the maximum likelihood estimator lies on the boundary of the parameter space. The odds ratio of $\infty$ is strongly suggestive of an association. The only issue is that tw... | How to deal with perfect separation in logistic regression? | For logistic models for inference, it's important to first underscore that there is no error here. The warning in R is correctly informing you that the maximum likelihood estimator lies on the boundar | How to deal with perfect separation in logistic regression?
For logistic models for inference, it's important to first underscore that there is no error here. The warning in R is correctly informing you that the maximum likelihood estimator lies on the boundary of the parameter space. The odds ratio of $\infty$ is stro... | How to deal with perfect separation in logistic regression?
For logistic models for inference, it's important to first underscore that there is no error here. The warning in R is correctly informing you that the maximum likelihood estimator lies on the boundar |
687 | How to deal with perfect separation in logistic regression? | Be careful with this warning message from R. Take a look at this blog post by Andrew Gelman, and you will see that it is not always a problem of perfect separation, but sometimes a bug with glm. It seems that if the starting values are too far from the maximum-likelihood estimate, it blows up. So, check first with othe... | How to deal with perfect separation in logistic regression? | Be careful with this warning message from R. Take a look at this blog post by Andrew Gelman, and you will see that it is not always a problem of perfect separation, but sometimes a bug with glm. It se | How to deal with perfect separation in logistic regression?
Be careful with this warning message from R. Take a look at this blog post by Andrew Gelman, and you will see that it is not always a problem of perfect separation, but sometimes a bug with glm. It seems that if the starting values are too far from the maximum... | How to deal with perfect separation in logistic regression?
Be careful with this warning message from R. Take a look at this blog post by Andrew Gelman, and you will see that it is not always a problem of perfect separation, but sometimes a bug with glm. It se |
688 | How to deal with perfect separation in logistic regression? | I am not sure that I agree with the statements in your question.
I think that warning message means, for some of the observed X level in your data, the fitted probability is numerically 0 or 1. In other words, at the resolution, it shows as 0 or 1.
You can run predict(yourmodel,yourdata,type='response') and you will fi... | How to deal with perfect separation in logistic regression? | I am not sure that I agree with the statements in your question.
I think that warning message means, for some of the observed X level in your data, the fitted probability is numerically 0 or 1. In oth | How to deal with perfect separation in logistic regression?
I am not sure that I agree with the statements in your question.
I think that warning message means, for some of the observed X level in your data, the fitted probability is numerically 0 or 1. In other words, at the resolution, it shows as 0 or 1.
You can run... | How to deal with perfect separation in logistic regression?
I am not sure that I agree with the statements in your question.
I think that warning message means, for some of the observed X level in your data, the fitted probability is numerically 0 or 1. In oth |
689 | How to deal with perfect separation in logistic regression? | This is a discussion from some points in Scortchi's answers. It is important and needs to be carefully handled. :)
I highly recommend Re-cast the model if you have this warning. Double-check the correlation between all predictors to see if there are any very high correlated pairs, if so, remove one from that pair. In ... | How to deal with perfect separation in logistic regression? | This is a discussion from some points in Scortchi's answers. It is important and needs to be carefully handled. :)
I highly recommend Re-cast the model if you have this warning. Double-check the corr | How to deal with perfect separation in logistic regression?
This is a discussion from some points in Scortchi's answers. It is important and needs to be carefully handled. :)
I highly recommend Re-cast the model if you have this warning. Double-check the correlation between all predictors to see if there are any very ... | How to deal with perfect separation in logistic regression?
This is a discussion from some points in Scortchi's answers. It is important and needs to be carefully handled. :)
I highly recommend Re-cast the model if you have this warning. Double-check the corr |
690 | How to deal with perfect separation in logistic regression? | I understand this is an old post, however I will still proceed with answering this as I have struggled days with it and it can help others.
Complete separation happens when your selected variables to fit the model can very accurately differentiate between 0’s and 1’s or yes and no. Our whole approach of data science is... | How to deal with perfect separation in logistic regression? | I understand this is an old post, however I will still proceed with answering this as I have struggled days with it and it can help others.
Complete separation happens when your selected variables to | How to deal with perfect separation in logistic regression?
I understand this is an old post, however I will still proceed with answering this as I have struggled days with it and it can help others.
Complete separation happens when your selected variables to fit the model can very accurately differentiate between 0’s ... | How to deal with perfect separation in logistic regression?
I understand this is an old post, however I will still proceed with answering this as I have struggled days with it and it can help others.
Complete separation happens when your selected variables to |
691 | What intuitive explanation is there for the central limit theorem? | I apologize in advance for the length of this post: it is with some trepidation that I let it out in public at all, because it takes some time and attention to read through and undoubtedly has typographic errors and expository lapses. But here it is for those who are interested in the fascinating topic, offered in the... | What intuitive explanation is there for the central limit theorem? | I apologize in advance for the length of this post: it is with some trepidation that I let it out in public at all, because it takes some time and attention to read through and undoubtedly has typogra | What intuitive explanation is there for the central limit theorem?
I apologize in advance for the length of this post: it is with some trepidation that I let it out in public at all, because it takes some time and attention to read through and undoubtedly has typographic errors and expository lapses. But here it is fo... | What intuitive explanation is there for the central limit theorem?
I apologize in advance for the length of this post: it is with some trepidation that I let it out in public at all, because it takes some time and attention to read through and undoubtedly has typogra |
692 | What intuitive explanation is there for the central limit theorem? | The nicest animation I know:
http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html
The simplest words I have read: http://elonen.iki.fi/articles/centrallimit/index.en.html
If you sum the results of these ten
throws, what you get is likely to be
closer to 30-40 than the maximum, 60
(all sixes) or on the other ... | What intuitive explanation is there for the central limit theorem? | The nicest animation I know:
http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html
The simplest words I have read: http://elonen.iki.fi/articles/centrallimit/index.en.html
If you sum the results o | What intuitive explanation is there for the central limit theorem?
The nicest animation I know:
http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html
The simplest words I have read: http://elonen.iki.fi/articles/centrallimit/index.en.html
If you sum the results of these ten
throws, what you get is likely to be
... | What intuitive explanation is there for the central limit theorem?
The nicest animation I know:
http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html
The simplest words I have read: http://elonen.iki.fi/articles/centrallimit/index.en.html
If you sum the results o |
693 | What intuitive explanation is there for the central limit theorem? | An observation concerning the CLT may be the following. When you have a sum
$$
S = X_1 + X_2 + \ldots + X_n
$$
of a lot of random components, if one is "smaller than usual" then this is mostly compensated for by some of the other components being "larger than usual". In other words, negative deviations and positive de... | What intuitive explanation is there for the central limit theorem? | An observation concerning the CLT may be the following. When you have a sum
$$
S = X_1 + X_2 + \ldots + X_n
$$
of a lot of random components, if one is "smaller than usual" then this is mostly compen | What intuitive explanation is there for the central limit theorem?
An observation concerning the CLT may be the following. When you have a sum
$$
S = X_1 + X_2 + \ldots + X_n
$$
of a lot of random components, if one is "smaller than usual" then this is mostly compensated for by some of the other components being "larg... | What intuitive explanation is there for the central limit theorem?
An observation concerning the CLT may be the following. When you have a sum
$$
S = X_1 + X_2 + \ldots + X_n
$$
of a lot of random components, if one is "smaller than usual" then this is mostly compen |
694 | What intuitive explanation is there for the central limit theorem? | Intuition is a tricky thing. It's even trickier with theory in our hands tied behind our back.
The CLT is all about sums of tiny, independent disturbances. "Sums" in the sense of the sample mean, "tiny" in the sense of finite variance (of the population), and "disturbances" in the sense of plus/minus around a central... | What intuitive explanation is there for the central limit theorem? | Intuition is a tricky thing. It's even trickier with theory in our hands tied behind our back.
The CLT is all about sums of tiny, independent disturbances. "Sums" in the sense of the sample mean, "t | What intuitive explanation is there for the central limit theorem?
Intuition is a tricky thing. It's even trickier with theory in our hands tied behind our back.
The CLT is all about sums of tiny, independent disturbances. "Sums" in the sense of the sample mean, "tiny" in the sense of finite variance (of the populati... | What intuitive explanation is there for the central limit theorem?
Intuition is a tricky thing. It's even trickier with theory in our hands tied behind our back.
The CLT is all about sums of tiny, independent disturbances. "Sums" in the sense of the sample mean, "t |
695 | What intuitive explanation is there for the central limit theorem? | This answer hopes to give an intuitive meaning of the central limit theorem, using simple calculus techniques (Taylor expansion of order 3).
Here is the outline:
What the CLT says
An intuitive proof of the CLT using simple calculus
Why the normal distribution?
We will mention the normal distribution at the very end; ... | What intuitive explanation is there for the central limit theorem? | This answer hopes to give an intuitive meaning of the central limit theorem, using simple calculus techniques (Taylor expansion of order 3).
Here is the outline:
What the CLT says
An intuitive proof | What intuitive explanation is there for the central limit theorem?
This answer hopes to give an intuitive meaning of the central limit theorem, using simple calculus techniques (Taylor expansion of order 3).
Here is the outline:
What the CLT says
An intuitive proof of the CLT using simple calculus
Why the normal distr... | What intuitive explanation is there for the central limit theorem?
This answer hopes to give an intuitive meaning of the central limit theorem, using simple calculus techniques (Taylor expansion of order 3).
Here is the outline:
What the CLT says
An intuitive proof |
696 | What intuitive explanation is there for the central limit theorem? | Why the $\sqrt{n}$ instead of $n$? What's this weird version of an average?
If you have a bunch of perpendicular vectors $x_1, \dotsc, x_n$ of length $\ell$, then
$ \frac{x_1 + \dotsb + x_n}{\sqrt{n}}$ is again of length $\ell.$ You have to normalize by $\sqrt{n}$ to keep the sum at the same scale.
There is a deep conn... | What intuitive explanation is there for the central limit theorem? | Why the $\sqrt{n}$ instead of $n$? What's this weird version of an average?
If you have a bunch of perpendicular vectors $x_1, \dotsc, x_n$ of length $\ell$, then
$ \frac{x_1 + \dotsb + x_n}{\sqrt{n}} | What intuitive explanation is there for the central limit theorem?
Why the $\sqrt{n}$ instead of $n$? What's this weird version of an average?
If you have a bunch of perpendicular vectors $x_1, \dotsc, x_n$ of length $\ell$, then
$ \frac{x_1 + \dotsb + x_n}{\sqrt{n}}$ is again of length $\ell.$ You have to normalize by... | What intuitive explanation is there for the central limit theorem?
Why the $\sqrt{n}$ instead of $n$? What's this weird version of an average?
If you have a bunch of perpendicular vectors $x_1, \dotsc, x_n$ of length $\ell$, then
$ \frac{x_1 + \dotsb + x_n}{\sqrt{n}} |
697 | What intuitive explanation is there for the central limit theorem? | I gave up on trying to come up with an intuitive version and came up with some simulations. I have one that presents a simulation of a Quincunx and some others that do things like show how even a skewed raw reaction time distribution will become normal if you collect enough RT's per subject. I think they help but the... | What intuitive explanation is there for the central limit theorem? | I gave up on trying to come up with an intuitive version and came up with some simulations. I have one that presents a simulation of a Quincunx and some others that do things like show how even a ske | What intuitive explanation is there for the central limit theorem?
I gave up on trying to come up with an intuitive version and came up with some simulations. I have one that presents a simulation of a Quincunx and some others that do things like show how even a skewed raw reaction time distribution will become normal... | What intuitive explanation is there for the central limit theorem?
I gave up on trying to come up with an intuitive version and came up with some simulations. I have one that presents a simulation of a Quincunx and some others that do things like show how even a ske |
698 | What intuitive explanation is there for the central limit theorem? | What follows is perhaps the most intuitive explanation I have come across for the CLT.
Consider a standard six-sided die. Every time you roll that die, an integer value results between 1 and 6, with equal probability. So, if you were to roll that die many, many times and then plot the frequency with which the different... | What intuitive explanation is there for the central limit theorem? | What follows is perhaps the most intuitive explanation I have come across for the CLT.
Consider a standard six-sided die. Every time you roll that die, an integer value results between 1 and 6, with e | What intuitive explanation is there for the central limit theorem?
What follows is perhaps the most intuitive explanation I have come across for the CLT.
Consider a standard six-sided die. Every time you roll that die, an integer value results between 1 and 6, with equal probability. So, if you were to roll that die ma... | What intuitive explanation is there for the central limit theorem?
What follows is perhaps the most intuitive explanation I have come across for the CLT.
Consider a standard six-sided die. Every time you roll that die, an integer value results between 1 and 6, with e |
699 | What does 1x1 convolution mean in a neural network? | Suppose that I have a conv layer which outputs an $(N, F, H, W)$ shaped tensor where:
$N$ is the batch size
$F$ is the number of convolutional filters
$H, W$ are the spatial dimensions
Suppose the input is fed into a conv layer with $F_1$ 1x1 filters, zero padding and stride 1. Then the output of this 1x1 conv layer ... | What does 1x1 convolution mean in a neural network? | Suppose that I have a conv layer which outputs an $(N, F, H, W)$ shaped tensor where:
$N$ is the batch size
$F$ is the number of convolutional filters
$H, W$ are the spatial dimensions
Suppose the i | What does 1x1 convolution mean in a neural network?
Suppose that I have a conv layer which outputs an $(N, F, H, W)$ shaped tensor where:
$N$ is the batch size
$F$ is the number of convolutional filters
$H, W$ are the spatial dimensions
Suppose the input is fed into a conv layer with $F_1$ 1x1 filters, zero padding a... | What does 1x1 convolution mean in a neural network?
Suppose that I have a conv layer which outputs an $(N, F, H, W)$ shaped tensor where:
$N$ is the batch size
$F$ is the number of convolutional filters
$H, W$ are the spatial dimensions
Suppose the i |
700 | What does 1x1 convolution mean in a neural network? | A 1x1 convolution simply maps an input pixel with all it's channels to an output pixel, not looking at anything around itself. It is often used to reduce the number of depth channels, since it is often very slow to multiply volumes with extremely large depths.
input (256 depth) -> 1x1 convolution (64 depth) -> 4x4 conv... | What does 1x1 convolution mean in a neural network? | A 1x1 convolution simply maps an input pixel with all it's channels to an output pixel, not looking at anything around itself. It is often used to reduce the number of depth channels, since it is ofte | What does 1x1 convolution mean in a neural network?
A 1x1 convolution simply maps an input pixel with all it's channels to an output pixel, not looking at anything around itself. It is often used to reduce the number of depth channels, since it is often very slow to multiply volumes with extremely large depths.
input (... | What does 1x1 convolution mean in a neural network?
A 1x1 convolution simply maps an input pixel with all it's channels to an output pixel, not looking at anything around itself. It is often used to reduce the number of depth channels, since it is ofte |
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