idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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4,701 | Help me understand the quantile (inverse CDF) function | All this may sound complicated at first, but it is essentially about something very simple.
By cumulative distribution function we denote the function that returns probabilities of $X$ being smaller than or equal to some value $x$,
$$ \Pr(X \le x) = F(x).$$
This function takes as input $x$ and returns values from the $... | Help me understand the quantile (inverse CDF) function | All this may sound complicated at first, but it is essentially about something very simple.
By cumulative distribution function we denote the function that returns probabilities of $X$ being smaller t | Help me understand the quantile (inverse CDF) function
All this may sound complicated at first, but it is essentially about something very simple.
By cumulative distribution function we denote the function that returns probabilities of $X$ being smaller than or equal to some value $x$,
$$ \Pr(X \le x) = F(x).$$
This fu... | Help me understand the quantile (inverse CDF) function
All this may sound complicated at first, but it is essentially about something very simple.
By cumulative distribution function we denote the function that returns probabilities of $X$ being smaller t |
4,702 | Help me understand the quantile (inverse CDF) function | Tim had a very thorough answer. Good job!
I'd like to add one more remark. Not every monotonically increasing function has an inverse function. Actually only strictly monotonically increasing/decreasing functions have inverse functions.
For monotonically increasing cdf which are not strictly monotonically increasing,... | Help me understand the quantile (inverse CDF) function | Tim had a very thorough answer. Good job!
I'd like to add one more remark. Not every monotonically increasing function has an inverse function. Actually only strictly monotonically increasing/decreasi | Help me understand the quantile (inverse CDF) function
Tim had a very thorough answer. Good job!
I'd like to add one more remark. Not every monotonically increasing function has an inverse function. Actually only strictly monotonically increasing/decreasing functions have inverse functions.
For monotonically increasi... | Help me understand the quantile (inverse CDF) function
Tim had a very thorough answer. Good job!
I'd like to add one more remark. Not every monotonically increasing function has an inverse function. Actually only strictly monotonically increasing/decreasi |
4,703 | Help me understand the quantile (inverse CDF) function | Chapter 2 of the book "Statistical Distributions" by Forbes, Evans, Hastings, and Peacock has a concise
summary with consistent notation.
A quantile is any possible value (e.g. in context of a random draw)
of a variable, that is, a variate.
The authors give an example of a sample space of tossing 2 coins
as the set {HH... | Help me understand the quantile (inverse CDF) function | Chapter 2 of the book "Statistical Distributions" by Forbes, Evans, Hastings, and Peacock has a concise
summary with consistent notation.
A quantile is any possible value (e.g. in context of a random | Help me understand the quantile (inverse CDF) function
Chapter 2 of the book "Statistical Distributions" by Forbes, Evans, Hastings, and Peacock has a concise
summary with consistent notation.
A quantile is any possible value (e.g. in context of a random draw)
of a variable, that is, a variate.
The authors give an exam... | Help me understand the quantile (inverse CDF) function
Chapter 2 of the book "Statistical Distributions" by Forbes, Evans, Hastings, and Peacock has a concise
summary with consistent notation.
A quantile is any possible value (e.g. in context of a random |
4,704 | Why downsample? | Most classification models in fact don't yield a binary decision, but rather a continuous decision value (for instance, logistic regression models output a probability, SVMs output a signed distance to the hyperplane, ...). Using the decision values we can rank test samples, from 'almost certainly positive' to 'almost ... | Why downsample? | Most classification models in fact don't yield a binary decision, but rather a continuous decision value (for instance, logistic regression models output a probability, SVMs output a signed distance t | Why downsample?
Most classification models in fact don't yield a binary decision, but rather a continuous decision value (for instance, logistic regression models output a probability, SVMs output a signed distance to the hyperplane, ...). Using the decision values we can rank test samples, from 'almost certainly posit... | Why downsample?
Most classification models in fact don't yield a binary decision, but rather a continuous decision value (for instance, logistic regression models output a probability, SVMs output a signed distance t |
4,705 | Why downsample? | The real problem here is your choice of metric: % accuracy is a poor measure of a model's success on an un-balanced dataset (for the exactly reason you mention: it's trivial to achieve 99% accuracy in this case).
Balancing your dataset before fitting the model is a bad solution as it biases your model and (even worse) ... | Why downsample? | The real problem here is your choice of metric: % accuracy is a poor measure of a model's success on an un-balanced dataset (for the exactly reason you mention: it's trivial to achieve 99% accuracy in | Why downsample?
The real problem here is your choice of metric: % accuracy is a poor measure of a model's success on an un-balanced dataset (for the exactly reason you mention: it's trivial to achieve 99% accuracy in this case).
Balancing your dataset before fitting the model is a bad solution as it biases your model a... | Why downsample?
The real problem here is your choice of metric: % accuracy is a poor measure of a model's success on an un-balanced dataset (for the exactly reason you mention: it's trivial to achieve 99% accuracy in |
4,706 | Why downsample? | As always @Marc Claesen as a great answer.
I'd just add that the key concept that seems to be missing is the concept of a cost function. In any model you have an implicit or explicit cost of false negatives to false positives (FN/FP). For the unbalanced data described one is often willing to have a 5:1 or 10:1 ratio. ... | Why downsample? | As always @Marc Claesen as a great answer.
I'd just add that the key concept that seems to be missing is the concept of a cost function. In any model you have an implicit or explicit cost of false ne | Why downsample?
As always @Marc Claesen as a great answer.
I'd just add that the key concept that seems to be missing is the concept of a cost function. In any model you have an implicit or explicit cost of false negatives to false positives (FN/FP). For the unbalanced data described one is often willing to have a 5:1... | Why downsample?
As always @Marc Claesen as a great answer.
I'd just add that the key concept that seems to be missing is the concept of a cost function. In any model you have an implicit or explicit cost of false ne |
4,707 | Why downsample? | Answering Jessica's question directly - one reason for downsampling is when you're working with a large dataset and facing memory limits on your computer or simply want to reduce processing time. Downsampling (i.e., taking a random sample without replacement) from the negative cases reduces the dataset to a more manage... | Why downsample? | Answering Jessica's question directly - one reason for downsampling is when you're working with a large dataset and facing memory limits on your computer or simply want to reduce processing time. Down | Why downsample?
Answering Jessica's question directly - one reason for downsampling is when you're working with a large dataset and facing memory limits on your computer or simply want to reduce processing time. Downsampling (i.e., taking a random sample without replacement) from the negative cases reduces the dataset ... | Why downsample?
Answering Jessica's question directly - one reason for downsampling is when you're working with a large dataset and facing memory limits on your computer or simply want to reduce processing time. Down |
4,708 | Why downsample? | Of course classifying everything as 'not spam' allows you to say that, given 100 mails, it classifies correctly 99 of them, but it also classifies as 'not spam' the only one labelled as spam (100% False Positive).
It turns out that the metric you choose to evaluate the algorithm is not adapt.
This video exemplifies the... | Why downsample? | Of course classifying everything as 'not spam' allows you to say that, given 100 mails, it classifies correctly 99 of them, but it also classifies as 'not spam' the only one labelled as spam (100% Fal | Why downsample?
Of course classifying everything as 'not spam' allows you to say that, given 100 mails, it classifies correctly 99 of them, but it also classifies as 'not spam' the only one labelled as spam (100% False Positive).
It turns out that the metric you choose to evaluate the algorithm is not adapt.
This video... | Why downsample?
Of course classifying everything as 'not spam' allows you to say that, given 100 mails, it classifies correctly 99 of them, but it also classifies as 'not spam' the only one labelled as spam (100% Fal |
4,709 | Why downsample? | I would not go for either downsampling or upsampling as both tricks the learning algorithm, however, if the data was imbalanced the accuracy measure becomes invalid or uninformative, therefore, it is better to use precision and recall measures, both depends mainly on the TP (the correctly classified spams in your case)... | Why downsample? | I would not go for either downsampling or upsampling as both tricks the learning algorithm, however, if the data was imbalanced the accuracy measure becomes invalid or uninformative, therefore, it is | Why downsample?
I would not go for either downsampling or upsampling as both tricks the learning algorithm, however, if the data was imbalanced the accuracy measure becomes invalid or uninformative, therefore, it is better to use precision and recall measures, both depends mainly on the TP (the correctly classified spa... | Why downsample?
I would not go for either downsampling or upsampling as both tricks the learning algorithm, however, if the data was imbalanced the accuracy measure becomes invalid or uninformative, therefore, it is |
4,710 | Machine Learning using Python | About the scikit-learn option: 100k (sparse) features and 10k samples is reasonably small enough to fit in memory hence perfectly doable with scikit-learn (same size as the 20 newsgroups dataset).
Here is a tutorial I gave at PyCon 2011 with a chapter on text classification with exercises and solutions:
http://scikit-... | Machine Learning using Python | About the scikit-learn option: 100k (sparse) features and 10k samples is reasonably small enough to fit in memory hence perfectly doable with scikit-learn (same size as the 20 newsgroups dataset).
Her | Machine Learning using Python
About the scikit-learn option: 100k (sparse) features and 10k samples is reasonably small enough to fit in memory hence perfectly doable with scikit-learn (same size as the 20 newsgroups dataset).
Here is a tutorial I gave at PyCon 2011 with a chapter on text classification with exercises ... | Machine Learning using Python
About the scikit-learn option: 100k (sparse) features and 10k samples is reasonably small enough to fit in memory hence perfectly doable with scikit-learn (same size as the 20 newsgroups dataset).
Her |
4,711 | Machine Learning using Python | In terms of working with text, have a look at NLTK. Very, very well supported & documented (there's even a book online, or in paper if you prefer) and will do the preprocesing you require. You might find Gensim useful as well; the emphasis is on vector space modeling and it's got scalable implementations of LSI and LDA... | Machine Learning using Python | In terms of working with text, have a look at NLTK. Very, very well supported & documented (there's even a book online, or in paper if you prefer) and will do the preprocesing you require. You might f | Machine Learning using Python
In terms of working with text, have a look at NLTK. Very, very well supported & documented (there's even a book online, or in paper if you prefer) and will do the preprocesing you require. You might find Gensim useful as well; the emphasis is on vector space modeling and it's got scalable ... | Machine Learning using Python
In terms of working with text, have a look at NLTK. Very, very well supported & documented (there's even a book online, or in paper if you prefer) and will do the preprocesing you require. You might f |
4,712 | Machine Learning using Python | Python has a wide range of ML libraries (check out mloss.org as well). However, I always have the feeling that it's more of use for ml researchers than for ml practitioners.
Numpy/SciPy and matplotlib are excellent tools for scientific work with Python. If you are not afraid to hack in most of the math formulas yoursel... | Machine Learning using Python | Python has a wide range of ML libraries (check out mloss.org as well). However, I always have the feeling that it's more of use for ml researchers than for ml practitioners.
Numpy/SciPy and matplotlib | Machine Learning using Python
Python has a wide range of ML libraries (check out mloss.org as well). However, I always have the feeling that it's more of use for ml researchers than for ml practitioners.
Numpy/SciPy and matplotlib are excellent tools for scientific work with Python. If you are not afraid to hack in mos... | Machine Learning using Python
Python has a wide range of ML libraries (check out mloss.org as well). However, I always have the feeling that it's more of use for ml researchers than for ml practitioners.
Numpy/SciPy and matplotlib |
4,713 | Machine Learning using Python | Let me suggest Orange
comprehensive
Yes
scalable (100k features, 10k examples)
Yes
well supported libraries for doing ML in Python out there?
Yes
library that has a good collection of classifiers, feature selection methods (Information Gain, Chi-Sqaured etc.),
All of these work out of box in Orange
and text... | Machine Learning using Python | Let me suggest Orange
comprehensive
Yes
scalable (100k features, 10k examples)
Yes
well supported libraries for doing ML in Python out there?
Yes
library that has a good collection of classif | Machine Learning using Python
Let me suggest Orange
comprehensive
Yes
scalable (100k features, 10k examples)
Yes
well supported libraries for doing ML in Python out there?
Yes
library that has a good collection of classifiers, feature selection methods (Information Gain, Chi-Sqaured etc.),
All of these work ... | Machine Learning using Python
Let me suggest Orange
comprehensive
Yes
scalable (100k features, 10k examples)
Yes
well supported libraries for doing ML in Python out there?
Yes
library that has a good collection of classif |
4,714 | Machine Learning using Python | Not sure if this is particularly useful, but there's a guide for programmers to learn statistics in Python available online. http://www.greenteapress.com/thinkstats/
It seems pretty good from my brief scan, and it appears to talk about some machine learning methods, so it might be a good place to start. | Machine Learning using Python | Not sure if this is particularly useful, but there's a guide for programmers to learn statistics in Python available online. http://www.greenteapress.com/thinkstats/
It seems pretty good from my brief | Machine Learning using Python
Not sure if this is particularly useful, but there's a guide for programmers to learn statistics in Python available online. http://www.greenteapress.com/thinkstats/
It seems pretty good from my brief scan, and it appears to talk about some machine learning methods, so it might be a good p... | Machine Learning using Python
Not sure if this is particularly useful, but there's a guide for programmers to learn statistics in Python available online. http://www.greenteapress.com/thinkstats/
It seems pretty good from my brief |
4,715 | Machine Learning using Python | Check out libsvm. | Machine Learning using Python | Check out libsvm. | Machine Learning using Python
Check out libsvm. | Machine Learning using Python
Check out libsvm. |
4,716 | Machine Learning using Python | SHOGUN (将軍) is a large scale machine learning toolbox, which seems promising. | Machine Learning using Python | SHOGUN (将軍) is a large scale machine learning toolbox, which seems promising. | Machine Learning using Python
SHOGUN (将軍) is a large scale machine learning toolbox, which seems promising. | Machine Learning using Python
SHOGUN (将軍) is a large scale machine learning toolbox, which seems promising. |
4,717 | Machine Learning using Python | 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.
open source python ml library
PySpark MLlib https://s... | Machine Learning using Python | 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.
| Machine Learning using Python
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.
open source python ml li... | Machine Learning using Python
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.
|
4,718 | Machine Learning using Python | As @ogrisel highlighted, scikit-learn is one of the best machine learning packages out there for Python. It is well suited for data-sets as small as 100k (sparse) features and 10k samples, and even for marginally bigger data-sets that may contains over 200k rows. Basically, any dataset that fits in the memory.
But, if ... | Machine Learning using Python | As @ogrisel highlighted, scikit-learn is one of the best machine learning packages out there for Python. It is well suited for data-sets as small as 100k (sparse) features and 10k samples, and even fo | Machine Learning using Python
As @ogrisel highlighted, scikit-learn is one of the best machine learning packages out there for Python. It is well suited for data-sets as small as 100k (sparse) features and 10k samples, and even for marginally bigger data-sets that may contains over 200k rows. Basically, any dataset tha... | Machine Learning using Python
As @ogrisel highlighted, scikit-learn is one of the best machine learning packages out there for Python. It is well suited for data-sets as small as 100k (sparse) features and 10k samples, and even fo |
4,719 | Machine Learning using Python | I don't know if your are still looking for some advice (you made this question 5 months ago...). I just started this book and so far is pretty well:
https://www.amazon.com.mx/dp/1491962291/ref=cm_cr_ryp_prd_ttl_sol_3
The author shows code, examples and explains some theory and math "behind the scenes" of ML algorithms.... | Machine Learning using Python | I don't know if your are still looking for some advice (you made this question 5 months ago...). I just started this book and so far is pretty well:
https://www.amazon.com.mx/dp/1491962291/ref=cm_cr_r | Machine Learning using Python
I don't know if your are still looking for some advice (you made this question 5 months ago...). I just started this book and so far is pretty well:
https://www.amazon.com.mx/dp/1491962291/ref=cm_cr_ryp_prd_ttl_sol_3
The author shows code, examples and explains some theory and math "behind... | Machine Learning using Python
I don't know if your are still looking for some advice (you made this question 5 months ago...). I just started this book and so far is pretty well:
https://www.amazon.com.mx/dp/1491962291/ref=cm_cr_r |
4,720 | Prediction in Cox regression | Following Cox model, the estimated hazard for individual $i$ with covariate vector $x_i$ has the form
$$\hat{h}_i(t) = \hat{h}_0(t) \exp(x_i' \hat{\beta}),$$
where $\hat{\beta}$ is found by maximising the partial likelihood, while $\hat{h}_0$ follows from the Nelson-Aalen estimator,
$$
\hat{h}_0(t_i) = \frac{d_i}{\sum_... | Prediction in Cox regression | Following Cox model, the estimated hazard for individual $i$ with covariate vector $x_i$ has the form
$$\hat{h}_i(t) = \hat{h}_0(t) \exp(x_i' \hat{\beta}),$$
where $\hat{\beta}$ is found by maximising | Prediction in Cox regression
Following Cox model, the estimated hazard for individual $i$ with covariate vector $x_i$ has the form
$$\hat{h}_i(t) = \hat{h}_0(t) \exp(x_i' \hat{\beta}),$$
where $\hat{\beta}$ is found by maximising the partial likelihood, while $\hat{h}_0$ follows from the Nelson-Aalen estimator,
$$
\hat... | Prediction in Cox regression
Following Cox model, the estimated hazard for individual $i$ with covariate vector $x_i$ has the form
$$\hat{h}_i(t) = \hat{h}_0(t) \exp(x_i' \hat{\beta}),$$
where $\hat{\beta}$ is found by maximising |
4,721 | Prediction in Cox regression | Maybe you would also like to try something like this? Fit a Cox proportional hazards model and use it to get the predicted Survival curve for a new instance.
Taken out of the help file for the survfit.coxph in R (I just added the lines part)
# fit a Cox proportional hazards model and plot the
# predicted survival for... | Prediction in Cox regression | Maybe you would also like to try something like this? Fit a Cox proportional hazards model and use it to get the predicted Survival curve for a new instance.
Taken out of the help file for the survfit | Prediction in Cox regression
Maybe you would also like to try something like this? Fit a Cox proportional hazards model and use it to get the predicted Survival curve for a new instance.
Taken out of the help file for the survfit.coxph in R (I just added the lines part)
# fit a Cox proportional hazards model and plot t... | Prediction in Cox regression
Maybe you would also like to try something like this? Fit a Cox proportional hazards model and use it to get the predicted Survival curve for a new instance.
Taken out of the help file for the survfit |
4,722 | Prediction in Cox regression | The function predictSurvProb in the pec package can give you absolute risk estimates for new data based on an existing cox model if you use R.
The mathematical details I cannot explain.
EDIT: The function provides survival probabilities, which I have so far taken as 1-(Event probability).
EDIT 2:
One can do without the... | Prediction in Cox regression | The function predictSurvProb in the pec package can give you absolute risk estimates for new data based on an existing cox model if you use R.
The mathematical details I cannot explain.
EDIT: The func | Prediction in Cox regression
The function predictSurvProb in the pec package can give you absolute risk estimates for new data based on an existing cox model if you use R.
The mathematical details I cannot explain.
EDIT: The function provides survival probabilities, which I have so far taken as 1-(Event probability).
E... | Prediction in Cox regression
The function predictSurvProb in the pec package can give you absolute risk estimates for new data based on an existing cox model if you use R.
The mathematical details I cannot explain.
EDIT: The func |
4,723 | Prediction in Cox regression | The basehaz function of survival packages provides the baseline hazard at the event time points. From that you can work your way up the math that ocram provides and include the ORs of your coxph estimates. | Prediction in Cox regression | The basehaz function of survival packages provides the baseline hazard at the event time points. From that you can work your way up the math that ocram provides and include the ORs of your coxph estim | Prediction in Cox regression
The basehaz function of survival packages provides the baseline hazard at the event time points. From that you can work your way up the math that ocram provides and include the ORs of your coxph estimates. | Prediction in Cox regression
The basehaz function of survival packages provides the baseline hazard at the event time points. From that you can work your way up the math that ocram provides and include the ORs of your coxph estim |
4,724 | Prediction in Cox regression | The whole point of the Cox model is the proportional hazard's assumption and the use of the partial likelhood. The partial likelihood has the baseline hazard function eliminated. So you do not need to specify one. That is the beauty of it! | Prediction in Cox regression | The whole point of the Cox model is the proportional hazard's assumption and the use of the partial likelhood. The partial likelihood has the baseline hazard function eliminated. So you do not need | Prediction in Cox regression
The whole point of the Cox model is the proportional hazard's assumption and the use of the partial likelhood. The partial likelihood has the baseline hazard function eliminated. So you do not need to specify one. That is the beauty of it! | Prediction in Cox regression
The whole point of the Cox model is the proportional hazard's assumption and the use of the partial likelhood. The partial likelihood has the baseline hazard function eliminated. So you do not need |
4,725 | Class imbalance in Supervised Machine Learning | There are many frameworks and approaches. This is a recurrent issue.
Examples:
Undersampling. Select a subsample of the sets of zeros such that it's size matches the set of ones. There is an obvious loss of information, unless you use a more complex framework (for a instance, I would split the first set on 9 smaller, ... | Class imbalance in Supervised Machine Learning | There are many frameworks and approaches. This is a recurrent issue.
Examples:
Undersampling. Select a subsample of the sets of zeros such that it's size matches the set of ones. There is an obvious | Class imbalance in Supervised Machine Learning
There are many frameworks and approaches. This is a recurrent issue.
Examples:
Undersampling. Select a subsample of the sets of zeros such that it's size matches the set of ones. There is an obvious loss of information, unless you use a more complex framework (for a insta... | Class imbalance in Supervised Machine Learning
There are many frameworks and approaches. This is a recurrent issue.
Examples:
Undersampling. Select a subsample of the sets of zeros such that it's size matches the set of ones. There is an obvious |
4,726 | Class imbalance in Supervised Machine Learning | This heavily depends on the learning method. Most general purpose approaches have one (or several) ways to deal with this. A common fix is to assign a higher misclassification penalty on the minority class, forcing the classifier to recognize them (SVM, logistic regression, neural networks, ...).
Changing sampling is ... | Class imbalance in Supervised Machine Learning | This heavily depends on the learning method. Most general purpose approaches have one (or several) ways to deal with this. A common fix is to assign a higher misclassification penalty on the minority | Class imbalance in Supervised Machine Learning
This heavily depends on the learning method. Most general purpose approaches have one (or several) ways to deal with this. A common fix is to assign a higher misclassification penalty on the minority class, forcing the classifier to recognize them (SVM, logistic regression... | Class imbalance in Supervised Machine Learning
This heavily depends on the learning method. Most general purpose approaches have one (or several) ways to deal with this. A common fix is to assign a higher misclassification penalty on the minority |
4,727 | Class imbalance in Supervised Machine Learning | Often problem is not the frequency but absolute amount of cases in the minority class. If you do not have enought variation in the target when compared against variation in the features, then it might mean that algorithm cannot classify things very accurately.
One thing is that misclassification penalty could be used... | Class imbalance in Supervised Machine Learning | Often problem is not the frequency but absolute amount of cases in the minority class. If you do not have enought variation in the target when compared against variation in the features, then it might | Class imbalance in Supervised Machine Learning
Often problem is not the frequency but absolute amount of cases in the minority class. If you do not have enought variation in the target when compared against variation in the features, then it might mean that algorithm cannot classify things very accurately.
One thing ... | Class imbalance in Supervised Machine Learning
Often problem is not the frequency but absolute amount of cases in the minority class. If you do not have enought variation in the target when compared against variation in the features, then it might |
4,728 | Class imbalance in Supervised Machine Learning | Add two trick:
1. use CDF , count the frequency in your training data or use very large validation (if your test set will not change, but the validation set must have same distribution with training set), then sort your prediction, and get first X%(your count the frequency before) for the one class and the others are e... | Class imbalance in Supervised Machine Learning | Add two trick:
1. use CDF , count the frequency in your training data or use very large validation (if your test set will not change, but the validation set must have same distribution with training s | Class imbalance in Supervised Machine Learning
Add two trick:
1. use CDF , count the frequency in your training data or use very large validation (if your test set will not change, but the validation set must have same distribution with training set), then sort your prediction, and get first X%(your count the frequency... | Class imbalance in Supervised Machine Learning
Add two trick:
1. use CDF , count the frequency in your training data or use very large validation (if your test set will not change, but the validation set must have same distribution with training s |
4,729 | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regression when we don't have to? | In Econometrics, we would say that non-normality violates the conditions of the Classical Normal Linear Regression Model, while heteroskedasticity violates both the assumptions of the CNLR and of the Classical Linear Regression Model.
But those that say "...violates OLS" are also justified: the name Ordinary Least-Sq... | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regre | In Econometrics, we would say that non-normality violates the conditions of the Classical Normal Linear Regression Model, while heteroskedasticity violates both the assumptions of the CNLR and of the | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regression when we don't have to?
In Econometrics, we would say that non-normality violates the conditions of the Classical Normal Linear Regression Model, while heteroskedasticity violates both the assumptions of the CNLR an... | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regre
In Econometrics, we would say that non-normality violates the conditions of the Classical Normal Linear Regression Model, while heteroskedasticity violates both the assumptions of the CNLR and of the |
4,730 | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regression when we don't have to? | If we had time in the class where we first introduce regression models to discuss bootstrapping and the other techniques that you mentioned (including all their assumptions, pitfalls, etc.), then I would agree with you that it is not necessary to talk about normality and homoscedasticity assumptions. But in truth, whe... | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regre | If we had time in the class where we first introduce regression models to discuss bootstrapping and the other techniques that you mentioned (including all their assumptions, pitfalls, etc.), then I wo | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regression when we don't have to?
If we had time in the class where we first introduce regression models to discuss bootstrapping and the other techniques that you mentioned (including all their assumptions, pitfalls, etc.), ... | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regre
If we had time in the class where we first introduce regression models to discuss bootstrapping and the other techniques that you mentioned (including all their assumptions, pitfalls, etc.), then I wo |
4,731 | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regression when we don't have to? | 1) rarely do people only want to estimate. Usually inference - CIs, PIs, tests - is the aim, or at least part of it (even if sometimes it's done relatively informally)
2) Things like the Gauss Markov theorem isn't necessarily much help -- if the distribution is sufficiently far from normal, a linear estimator is not mu... | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regre | 1) rarely do people only want to estimate. Usually inference - CIs, PIs, tests - is the aim, or at least part of it (even if sometimes it's done relatively informally)
2) Things like the Gauss Markov | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regression when we don't have to?
1) rarely do people only want to estimate. Usually inference - CIs, PIs, tests - is the aim, or at least part of it (even if sometimes it's done relatively informally)
2) Things like the Gaus... | Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regre
1) rarely do people only want to estimate. Usually inference - CIs, PIs, tests - is the aim, or at least part of it (even if sometimes it's done relatively informally)
2) Things like the Gauss Markov |
4,732 | What is the difference between NaN and NA? | ?is.nan
?is.na
?NA
?NaN
Should answer your question.
But, in short:
NaN means $\frac {0} {0}$ -- Stands for Not a Number
NA is generally interpreted as a missing value and has various forms - NA_integer_, NA_real_, etc.
Therefore, NaN $\neq$ NA and there is a need for NaN and NA. | What is the difference between NaN and NA? | ?is.nan
?is.na
?NA
?NaN
Should answer your question.
But, in short:
NaN means $\frac {0} {0}$ -- Stands for Not a Number
NA is generally interpreted as a missing value and has various forms - NA_int | What is the difference between NaN and NA?
?is.nan
?is.na
?NA
?NaN
Should answer your question.
But, in short:
NaN means $\frac {0} {0}$ -- Stands for Not a Number
NA is generally interpreted as a missing value and has various forms - NA_integer_, NA_real_, etc.
Therefore, NaN $\neq$ NA and there is a need for NaN an... | What is the difference between NaN and NA?
?is.nan
?is.na
?NA
?NaN
Should answer your question.
But, in short:
NaN means $\frac {0} {0}$ -- Stands for Not a Number
NA is generally interpreted as a missing value and has various forms - NA_int |
4,733 | What is the difference between NaN and NA? | NA is for missing data. NaN, as J.M. said is for arithmetic purpose. NaN is usually the product of some arithmetic operation, such as 0/0. NA usually is declared in advance, or is a product of operation when you try to access something that is not there:
> a <- c(1,2)
> a[3]
[1] NA | What is the difference between NaN and NA? | NA is for missing data. NaN, as J.M. said is for arithmetic purpose. NaN is usually the product of some arithmetic operation, such as 0/0. NA usually is declared in advance, or is a product of operati | What is the difference between NaN and NA?
NA is for missing data. NaN, as J.M. said is for arithmetic purpose. NaN is usually the product of some arithmetic operation, such as 0/0. NA usually is declared in advance, or is a product of operation when you try to access something that is not there:
> a <- c(1,2)
> a[3]... | What is the difference between NaN and NA?
NA is for missing data. NaN, as J.M. said is for arithmetic purpose. NaN is usually the product of some arithmetic operation, such as 0/0. NA usually is declared in advance, or is a product of operati |
4,734 | What is the difference between NaN and NA? | I think of NA standing for 'Not Available', while NaN is 'Not a Number', although this is more mnemonic than explanation. By the way, I know of no language other than R (perhaps Splus?) that has both. Matlab, for example, has only NaN. | What is the difference between NaN and NA? | I think of NA standing for 'Not Available', while NaN is 'Not a Number', although this is more mnemonic than explanation. By the way, I know of no language other than R (perhaps Splus?) that has both. | What is the difference between NaN and NA?
I think of NA standing for 'Not Available', while NaN is 'Not a Number', although this is more mnemonic than explanation. By the way, I know of no language other than R (perhaps Splus?) that has both. Matlab, for example, has only NaN. | What is the difference between NaN and NA?
I think of NA standing for 'Not Available', while NaN is 'Not a Number', although this is more mnemonic than explanation. By the way, I know of no language other than R (perhaps Splus?) that has both. |
4,735 | What is the difference between NaN and NA? | NA means the error was already there when you imported the spreadsheet into R. NaN means you caused the error after importing the data. It's the third type of error that's really hard to catch. | What is the difference between NaN and NA? | NA means the error was already there when you imported the spreadsheet into R. NaN means you caused the error after importing the data. It's the third type of error that's really hard to catch. | What is the difference between NaN and NA?
NA means the error was already there when you imported the spreadsheet into R. NaN means you caused the error after importing the data. It's the third type of error that's really hard to catch. | What is the difference between NaN and NA?
NA means the error was already there when you imported the spreadsheet into R. NaN means you caused the error after importing the data. It's the third type of error that's really hard to catch. |
4,736 | What is the difference between NaN and NA? | NA = Not Available
NaN = Not a Number
I think once we expand the acronyms, it should be self explanatory. | What is the difference between NaN and NA? | NA = Not Available
NaN = Not a Number
I think once we expand the acronyms, it should be self explanatory. | What is the difference between NaN and NA?
NA = Not Available
NaN = Not a Number
I think once we expand the acronyms, it should be self explanatory. | What is the difference between NaN and NA?
NA = Not Available
NaN = Not a Number
I think once we expand the acronyms, it should be self explanatory. |
4,737 | Understanding Naive Bayes | I'm going to run through the whole Naive Bayes process from scratch, since it's not totally clear to me where you're getting hung up.
We want to find the probability that a new example belongs to each class: $P(class|feature_1, feature_2,..., feature_n$). We then compute that probability for each class, and pick the mo... | Understanding Naive Bayes | I'm going to run through the whole Naive Bayes process from scratch, since it's not totally clear to me where you're getting hung up.
We want to find the probability that a new example belongs to each | Understanding Naive Bayes
I'm going to run through the whole Naive Bayes process from scratch, since it's not totally clear to me where you're getting hung up.
We want to find the probability that a new example belongs to each class: $P(class|feature_1, feature_2,..., feature_n$). We then compute that probability for e... | Understanding Naive Bayes
I'm going to run through the whole Naive Bayes process from scratch, since it's not totally clear to me where you're getting hung up.
We want to find the probability that a new example belongs to each |
4,738 | Understanding Naive Bayes | Simplifying the notation with $D$ denoting the data, we want to find which of various $P(C_j\mid D)$ is the largest. Now, Bayes' formula gives
$$P(C_j\mid D) = \frac{P(D\mid C_j)P(C_j)}{P(D)}, ~ j = 1, 2, \ldots$$
where the denominator on the right is the same for all $j$. If we want to
find which of $P(C_1\mid D)$, ... | Understanding Naive Bayes | Simplifying the notation with $D$ denoting the data, we want to find which of various $P(C_j\mid D)$ is the largest. Now, Bayes' formula gives
$$P(C_j\mid D) = \frac{P(D\mid C_j)P(C_j)}{P(D)}, ~ j = | Understanding Naive Bayes
Simplifying the notation with $D$ denoting the data, we want to find which of various $P(C_j\mid D)$ is the largest. Now, Bayes' formula gives
$$P(C_j\mid D) = \frac{P(D\mid C_j)P(C_j)}{P(D)}, ~ j = 1, 2, \ldots$$
where the denominator on the right is the same for all $j$. If we want to
find... | Understanding Naive Bayes
Simplifying the notation with $D$ denoting the data, we want to find which of various $P(C_j\mid D)$ is the largest. Now, Bayes' formula gives
$$P(C_j\mid D) = \frac{P(D\mid C_j)P(C_j)}{P(D)}, ~ j = |
4,739 | Understanding Naive Bayes | The main assumption behind the naive bayes model is that each feature (x_i) is conditionally independent of all other features given the class. This assumption is what allows us to write the likelihood as a simple product (as you have shown).
This is also what helps the naive bayes model generalize well in practice. C... | Understanding Naive Bayes | The main assumption behind the naive bayes model is that each feature (x_i) is conditionally independent of all other features given the class. This assumption is what allows us to write the likelihoo | Understanding Naive Bayes
The main assumption behind the naive bayes model is that each feature (x_i) is conditionally independent of all other features given the class. This assumption is what allows us to write the likelihood as a simple product (as you have shown).
This is also what helps the naive bayes model gene... | Understanding Naive Bayes
The main assumption behind the naive bayes model is that each feature (x_i) is conditionally independent of all other features given the class. This assumption is what allows us to write the likelihoo |
4,740 | Gradient Boosting for Linear Regression - why does it not work? | What am I missing here?
I don't think you're really missing anything!
Another observation is that a sum of subsequent linear regression models can be represented as a single regression model as well (adding all intercepts and corresponding coefficients) so I cannot imagine how that could ever improve the model. The l... | Gradient Boosting for Linear Regression - why does it not work? | What am I missing here?
I don't think you're really missing anything!
Another observation is that a sum of subsequent linear regression models can be represented as a single regression model as well | Gradient Boosting for Linear Regression - why does it not work?
What am I missing here?
I don't think you're really missing anything!
Another observation is that a sum of subsequent linear regression models can be represented as a single regression model as well (adding all intercepts and corresponding coefficients) ... | Gradient Boosting for Linear Regression - why does it not work?
What am I missing here?
I don't think you're really missing anything!
Another observation is that a sum of subsequent linear regression models can be represented as a single regression model as well |
4,741 | Gradient Boosting for Linear Regression - why does it not work? | The least squares projection matrix is given by
$X(X^{T}X)^{-1}X^{T}$
We can use this to directly obtain our predicted values $\hat{y}$, e.g.
$\hat{y} = X(X^{T}X)^{-1}X^{T}y $
Let's say you fit a regression and subsequently you calculate your residuals
$e = y - \hat{y} = y - X(X^{T}X)^{-1}X^{T}y $
And then you use this... | Gradient Boosting for Linear Regression - why does it not work? | The least squares projection matrix is given by
$X(X^{T}X)^{-1}X^{T}$
We can use this to directly obtain our predicted values $\hat{y}$, e.g.
$\hat{y} = X(X^{T}X)^{-1}X^{T}y $
Let's say you fit a regr | Gradient Boosting for Linear Regression - why does it not work?
The least squares projection matrix is given by
$X(X^{T}X)^{-1}X^{T}$
We can use this to directly obtain our predicted values $\hat{y}$, e.g.
$\hat{y} = X(X^{T}X)^{-1}X^{T}y $
Let's say you fit a regression and subsequently you calculate your residuals
$e ... | Gradient Boosting for Linear Regression - why does it not work?
The least squares projection matrix is given by
$X(X^{T}X)^{-1}X^{T}$
We can use this to directly obtain our predicted values $\hat{y}$, e.g.
$\hat{y} = X(X^{T}X)^{-1}X^{T}y $
Let's say you fit a regr |
4,742 | Gradient Boosting for Linear Regression - why does it not work? | OP is absolutely right. However I came across an algorithm called RegBoost by Li et al. (2020) which attempts to adapt Linear Regression (LR) to be used as the weak learner in Gradient Boosting by combining it with a non-linearity. This is done by constructing a decision tree of LR models based on the sign (+ve or -ve)... | Gradient Boosting for Linear Regression - why does it not work? | OP is absolutely right. However I came across an algorithm called RegBoost by Li et al. (2020) which attempts to adapt Linear Regression (LR) to be used as the weak learner in Gradient Boosting by com | Gradient Boosting for Linear Regression - why does it not work?
OP is absolutely right. However I came across an algorithm called RegBoost by Li et al. (2020) which attempts to adapt Linear Regression (LR) to be used as the weak learner in Gradient Boosting by combining it with a non-linearity. This is done by construc... | Gradient Boosting for Linear Regression - why does it not work?
OP is absolutely right. However I came across an algorithm called RegBoost by Li et al. (2020) which attempts to adapt Linear Regression (LR) to be used as the weak learner in Gradient Boosting by com |
4,743 | Do we have a problem of "pity upvotes"? | You could use a multistate model or Markov chain (the msm package in R is one way to fit these). You could then look to see if the transition probability from -1 to 0 is greater than from 0 to 1, 1 to 2, etc. You can also look at the average time at -1 compared to the others to see if it is shorter. | Do we have a problem of "pity upvotes"? | You could use a multistate model or Markov chain (the msm package in R is one way to fit these). You could then look to see if the transition probability from -1 to 0 is greater than from 0 to 1, 1 t | Do we have a problem of "pity upvotes"?
You could use a multistate model or Markov chain (the msm package in R is one way to fit these). You could then look to see if the transition probability from -1 to 0 is greater than from 0 to 1, 1 to 2, etc. You can also look at the average time at -1 compared to the others to... | Do we have a problem of "pity upvotes"?
You could use a multistate model or Markov chain (the msm package in R is one way to fit these). You could then look to see if the transition probability from -1 to 0 is greater than from 0 to 1, 1 t |
4,744 | Do we have a problem of "pity upvotes"? | Conduct an experiment. Randomly downvote half of the new posts at a particular time every day. | Do we have a problem of "pity upvotes"? | Conduct an experiment. Randomly downvote half of the new posts at a particular time every day. | Do we have a problem of "pity upvotes"?
Conduct an experiment. Randomly downvote half of the new posts at a particular time every day. | Do we have a problem of "pity upvotes"?
Conduct an experiment. Randomly downvote half of the new posts at a particular time every day. |
4,745 | Do we have a problem of "pity upvotes"? | Summary of my answer. I like the Markov chain modeling but it misses the "temporal" aspect. On the other end, focusing on the temporal aspect (e.g. average time at $-1$) misses the "transition" aspect. I would go into the following general modelling (which with suitable assumption can lead to [markov process][1]). Also... | Do we have a problem of "pity upvotes"? | Summary of my answer. I like the Markov chain modeling but it misses the "temporal" aspect. On the other end, focusing on the temporal aspect (e.g. average time at $-1$) misses the "transition" aspect | Do we have a problem of "pity upvotes"?
Summary of my answer. I like the Markov chain modeling but it misses the "temporal" aspect. On the other end, focusing on the temporal aspect (e.g. average time at $-1$) misses the "transition" aspect. I would go into the following general modelling (which with suitable assumptio... | Do we have a problem of "pity upvotes"?
Summary of my answer. I like the Markov chain modeling but it misses the "temporal" aspect. On the other end, focusing on the temporal aspect (e.g. average time at $-1$) misses the "transition" aspect |
4,746 | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models | "Is this a statement about the feature as a whole or about specific values within the feature?"
"Global" variable importance is the mean decrease of accuracy over all out-of-bag cross validated predictions, when a given variable is permuted after training, but before prediction. "Global" is implicit. Local variable im... | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models | "Is this a statement about the feature as a whole or about specific values within the feature?"
"Global" variable importance is the mean decrease of accuracy over all out-of-bag cross validated predi | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models
"Is this a statement about the feature as a whole or about specific values within the feature?"
"Global" variable importance is the mean decrease of accuracy over all out-of-bag cross validated predictions, when a given variable ... | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models
"Is this a statement about the feature as a whole or about specific values within the feature?"
"Global" variable importance is the mean decrease of accuracy over all out-of-bag cross validated predi |
4,747 | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models | Here is the description of the mean decrease in accuracy (MDA) from the help manual of randomForest:
The first measure is computed from permuting OOB data: For each tree, the prediction error on the out-of-bag portion of the data is recorded (error rate for classification, MSE for regression). Then the same is done af... | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models | Here is the description of the mean decrease in accuracy (MDA) from the help manual of randomForest:
The first measure is computed from permuting OOB data: For each tree, the prediction error on the | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models
Here is the description of the mean decrease in accuracy (MDA) from the help manual of randomForest:
The first measure is computed from permuting OOB data: For each tree, the prediction error on the out-of-bag portion of the data... | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models
Here is the description of the mean decrease in accuracy (MDA) from the help manual of randomForest:
The first measure is computed from permuting OOB data: For each tree, the prediction error on the |
4,748 | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models | A recent blog post from a team at the University of San Francisco shows that default importance strategies in both R (randomForest) and Python (scikit) are unreliable in many data scenarios. Particularly, mean decrease in impurity importance metrics are biased when potential predictor variables vary in their scale of m... | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models | A recent blog post from a team at the University of San Francisco shows that default importance strategies in both R (randomForest) and Python (scikit) are unreliable in many data scenarios. Particula | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models
A recent blog post from a team at the University of San Francisco shows that default importance strategies in both R (randomForest) and Python (scikit) are unreliable in many data scenarios. Particularly, mean decrease in impurity... | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models
A recent blog post from a team at the University of San Francisco shows that default importance strategies in both R (randomForest) and Python (scikit) are unreliable in many data scenarios. Particula |
4,749 | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models | Relative Mean Decrease Accuracy?
"In either case, is the Mean Decrease in Accuracy the number or proportion of observations that are incorrectly classified by removing the feature (or values from the feature) in question from the model?"
train forest
measure out-of-bag CV accuracy → OOB_acc_base
permute variable i
... | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models | Relative Mean Decrease Accuracy?
"In either case, is the Mean Decrease in Accuracy the number or proportion of observations that are incorrectly classified by removing the feature (or values from the | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models
Relative Mean Decrease Accuracy?
"In either case, is the Mean Decrease in Accuracy the number or proportion of observations that are incorrectly classified by removing the feature (or values from the feature) in question from the... | How to interpret Mean Decrease in Accuracy and Mean Decrease GINI in Random Forest models
Relative Mean Decrease Accuracy?
"In either case, is the Mean Decrease in Accuracy the number or proportion of observations that are incorrectly classified by removing the feature (or values from the |
4,750 | Would PCA work for boolean (binary) data types? | I would like to suggest you a relatively recent technique for automatic structure extraction from categorical variable data (this includes binary). The method is called CorEx from Greg van Steeg from University of Southern California. The idea is to use the notion of Total Correlation based on the entropy measures. It ... | Would PCA work for boolean (binary) data types? | I would like to suggest you a relatively recent technique for automatic structure extraction from categorical variable data (this includes binary). The method is called CorEx from Greg van Steeg from | Would PCA work for boolean (binary) data types?
I would like to suggest you a relatively recent technique for automatic structure extraction from categorical variable data (this includes binary). The method is called CorEx from Greg van Steeg from University of Southern California. The idea is to use the notion of Tota... | Would PCA work for boolean (binary) data types?
I would like to suggest you a relatively recent technique for automatic structure extraction from categorical variable data (this includes binary). The method is called CorEx from Greg van Steeg from |
4,751 | Would PCA work for boolean (binary) data types? | You can also use Multiple Correspondence Analysis (MCA), which is an extension of principal component analysis when the variables to be analyzed are categorical instead of quantitative (which is the case here with your binary variables). See for instance Husson et al. (2010), or Abdi and Valentin (2007). An excellent R... | Would PCA work for boolean (binary) data types? | You can also use Multiple Correspondence Analysis (MCA), which is an extension of principal component analysis when the variables to be analyzed are categorical instead of quantitative (which is the c | Would PCA work for boolean (binary) data types?
You can also use Multiple Correspondence Analysis (MCA), which is an extension of principal component analysis when the variables to be analyzed are categorical instead of quantitative (which is the case here with your binary variables). See for instance Husson et al. (20... | Would PCA work for boolean (binary) data types?
You can also use Multiple Correspondence Analysis (MCA), which is an extension of principal component analysis when the variables to be analyzed are categorical instead of quantitative (which is the c |
4,752 | Would PCA work for boolean (binary) data types? | If you think of PCA as an exploratory technique to give you a way to visualise the relationships between variables (and in my opinion this is the only way to think about it) then yes, there is no reason why you can't put in binary variables. For example, here is a biplot of your data
It seems reasonably useful. For ex... | Would PCA work for boolean (binary) data types? | If you think of PCA as an exploratory technique to give you a way to visualise the relationships between variables (and in my opinion this is the only way to think about it) then yes, there is no reas | Would PCA work for boolean (binary) data types?
If you think of PCA as an exploratory technique to give you a way to visualise the relationships between variables (and in my opinion this is the only way to think about it) then yes, there is no reason why you can't put in binary variables. For example, here is a biplot ... | Would PCA work for boolean (binary) data types?
If you think of PCA as an exploratory technique to give you a way to visualise the relationships between variables (and in my opinion this is the only way to think about it) then yes, there is no reas |
4,753 | Would PCA work for boolean (binary) data types? | Although PCA is often used for binary data, it is argued that PCA assumptions are not appropriate for binary or count data (see e.g. Collins 2002 for an explanation) and generalizations exists: the strategy is similar in spirit to the development of generalized linear models to perform regression analysis for data belo... | Would PCA work for boolean (binary) data types? | Although PCA is often used for binary data, it is argued that PCA assumptions are not appropriate for binary or count data (see e.g. Collins 2002 for an explanation) and generalizations exists: the st | Would PCA work for boolean (binary) data types?
Although PCA is often used for binary data, it is argued that PCA assumptions are not appropriate for binary or count data (see e.g. Collins 2002 for an explanation) and generalizations exists: the strategy is similar in spirit to the development of generalized linear mod... | Would PCA work for boolean (binary) data types?
Although PCA is often used for binary data, it is argued that PCA assumptions are not appropriate for binary or count data (see e.g. Collins 2002 for an explanation) and generalizations exists: the st |
4,754 | What does the term saturating nonlinearities mean? | Intuition
A saturating activation function squeezes the input.
Definitions
$f$ is non-saturating iff $ (|\lim_{z\to-\infty} f(z)| = +\infty) \vee (|\lim_{z\to+\infty} f(z)| = +\infty) $
$f$ is saturating iff $f$ is not non-saturating.
These definitions are not specific to convolutional neural networks.
Examples
T... | What does the term saturating nonlinearities mean? | Intuition
A saturating activation function squeezes the input.
Definitions
$f$ is non-saturating iff $ (|\lim_{z\to-\infty} f(z)| = +\infty) \vee (|\lim_{z\to+\infty} f(z)| = +\infty) $
$f$ is satu | What does the term saturating nonlinearities mean?
Intuition
A saturating activation function squeezes the input.
Definitions
$f$ is non-saturating iff $ (|\lim_{z\to-\infty} f(z)| = +\infty) \vee (|\lim_{z\to+\infty} f(z)| = +\infty) $
$f$ is saturating iff $f$ is not non-saturating.
These definitions are not spe... | What does the term saturating nonlinearities mean?
Intuition
A saturating activation function squeezes the input.
Definitions
$f$ is non-saturating iff $ (|\lim_{z\to-\infty} f(z)| = +\infty) \vee (|\lim_{z\to+\infty} f(z)| = +\infty) $
$f$ is satu |
4,755 | What does the term saturating nonlinearities mean? | In the neural network context, the phenomenon of saturation refers to the state in which a neuron predominantly outputs values close to the asymptotic ends of the bounded activation function.
Measuring Saturation in Neural Networks (2015)
So, saturation refers to behaviour of a neuron in a neural network after a giv... | What does the term saturating nonlinearities mean? | In the neural network context, the phenomenon of saturation refers to the state in which a neuron predominantly outputs values close to the asymptotic ends of the bounded activation function.
Measur | What does the term saturating nonlinearities mean?
In the neural network context, the phenomenon of saturation refers to the state in which a neuron predominantly outputs values close to the asymptotic ends of the bounded activation function.
Measuring Saturation in Neural Networks (2015)
So, saturation refers to be... | What does the term saturating nonlinearities mean?
In the neural network context, the phenomenon of saturation refers to the state in which a neuron predominantly outputs values close to the asymptotic ends of the bounded activation function.
Measur |
4,756 | What does the term saturating nonlinearities mean? | The most common activation functions are LOG and TanH. These functions have a compact range, meaning that they compress the neural response into a bounded subset of the real numbers. The LOG compresses inputs to outputs between 0 and 1, the TAN H between -1 and 1. These functions display limiting behavior at the bounda... | What does the term saturating nonlinearities mean? | The most common activation functions are LOG and TanH. These functions have a compact range, meaning that they compress the neural response into a bounded subset of the real numbers. The LOG compresse | What does the term saturating nonlinearities mean?
The most common activation functions are LOG and TanH. These functions have a compact range, meaning that they compress the neural response into a bounded subset of the real numbers. The LOG compresses inputs to outputs between 0 and 1, the TAN H between -1 and 1. Thes... | What does the term saturating nonlinearities mean?
The most common activation functions are LOG and TanH. These functions have a compact range, meaning that they compress the neural response into a bounded subset of the real numbers. The LOG compresse |
4,757 | Correct spelling (capitalization, italicization, hyphenation) of "p-value"? | There do not appear to be "standards". For example:
The Nature style guide refers to "P value"
This APA style guide refers to "p value"
The Blood style guide says:
Capitalize and italicize the P that introduces a P value
Italicize the p that represents the Spearman rank correlation test
Wikipedia uses "p-value" (w... | Correct spelling (capitalization, italicization, hyphenation) of "p-value"? | There do not appear to be "standards". For example:
The Nature style guide refers to "P value"
This APA style guide refers to "p value"
The Blood style guide says:
Capitalize and italicize the P t | Correct spelling (capitalization, italicization, hyphenation) of "p-value"?
There do not appear to be "standards". For example:
The Nature style guide refers to "P value"
This APA style guide refers to "p value"
The Blood style guide says:
Capitalize and italicize the P that introduces a P value
Italicize the p tha... | Correct spelling (capitalization, italicization, hyphenation) of "p-value"?
There do not appear to be "standards". For example:
The Nature style guide refers to "P value"
This APA style guide refers to "p value"
The Blood style guide says:
Capitalize and italicize the P t |
4,758 | Correct spelling (capitalization, italicization, hyphenation) of "p-value"? | This seems to be a style issue with different journals and publishers adopting different conventions (or allowing a mixed muddle of styles depending on authors' preferences). My own preference, for what it's worth, is p-value, hyphenated with no italics and no capitalization. | Correct spelling (capitalization, italicization, hyphenation) of "p-value"? | This seems to be a style issue with different journals and publishers adopting different conventions (or allowing a mixed muddle of styles depending on authors' preferences). My own preference, for wh | Correct spelling (capitalization, italicization, hyphenation) of "p-value"?
This seems to be a style issue with different journals and publishers adopting different conventions (or allowing a mixed muddle of styles depending on authors' preferences). My own preference, for what it's worth, is p-value, hyphenated with n... | Correct spelling (capitalization, italicization, hyphenation) of "p-value"?
This seems to be a style issue with different journals and publishers adopting different conventions (or allowing a mixed muddle of styles depending on authors' preferences). My own preference, for wh |
4,759 | Correct spelling (capitalization, italicization, hyphenation) of "p-value"? | The ASA House Style seems to recommend italicizing the p with hyphen: p-value. A google scholar search shows varied spellings. | Correct spelling (capitalization, italicization, hyphenation) of "p-value"? | The ASA House Style seems to recommend italicizing the p with hyphen: p-value. A google scholar search shows varied spellings. | Correct spelling (capitalization, italicization, hyphenation) of "p-value"?
The ASA House Style seems to recommend italicizing the p with hyphen: p-value. A google scholar search shows varied spellings. | Correct spelling (capitalization, italicization, hyphenation) of "p-value"?
The ASA House Style seems to recommend italicizing the p with hyphen: p-value. A google scholar search shows varied spellings. |
4,760 | Correct spelling (capitalization, italicization, hyphenation) of "p-value"? | P value from theoretical point of view is some realization of random variable.
There is some standard (in probability) to use upper case letters for random variables and lower case for realizations.
In table headers we should use P (maybe italicize), in text together with its value p=0.0012 and in text describing for e... | Correct spelling (capitalization, italicization, hyphenation) of "p-value"? | P value from theoretical point of view is some realization of random variable.
There is some standard (in probability) to use upper case letters for random variables and lower case for realizations.
I | Correct spelling (capitalization, italicization, hyphenation) of "p-value"?
P value from theoretical point of view is some realization of random variable.
There is some standard (in probability) to use upper case letters for random variables and lower case for realizations.
In table headers we should use P (maybe itali... | Correct spelling (capitalization, italicization, hyphenation) of "p-value"?
P value from theoretical point of view is some realization of random variable.
There is some standard (in probability) to use upper case letters for random variables and lower case for realizations.
I |
4,761 | Correct spelling (capitalization, italicization, hyphenation) of "p-value"? | Omitting the hyphen can sometimes change the meaning of sentences or at least they can become ambiguous. This can occur especially in papers that describe statistical tests or introduce algorithms to evaluate p-values, but one may also describe methods that have nothing to do with statistics, and still calculate p valu... | Correct spelling (capitalization, italicization, hyphenation) of "p-value"? | Omitting the hyphen can sometimes change the meaning of sentences or at least they can become ambiguous. This can occur especially in papers that describe statistical tests or introduce algorithms to | Correct spelling (capitalization, italicization, hyphenation) of "p-value"?
Omitting the hyphen can sometimes change the meaning of sentences or at least they can become ambiguous. This can occur especially in papers that describe statistical tests or introduce algorithms to evaluate p-values, but one may also describe... | Correct spelling (capitalization, italicization, hyphenation) of "p-value"?
Omitting the hyphen can sometimes change the meaning of sentences or at least they can become ambiguous. This can occur especially in papers that describe statistical tests or introduce algorithms to |
4,762 | What are posterior predictive checks and what makes them useful? | Posterior predictive checks are, in simple words, "simulating replicated data under the
fitted model and then comparing these to the observed data" (Gelman and Hill, 2007, p. 158). So, you use posterior predictive to "look for systematic discrepancies between real and simulated data" (Gelman et al. 2004, p. 169).
The a... | What are posterior predictive checks and what makes them useful? | Posterior predictive checks are, in simple words, "simulating replicated data under the
fitted model and then comparing these to the observed data" (Gelman and Hill, 2007, p. 158). So, you use posteri | What are posterior predictive checks and what makes them useful?
Posterior predictive checks are, in simple words, "simulating replicated data under the
fitted model and then comparing these to the observed data" (Gelman and Hill, 2007, p. 158). So, you use posterior predictive to "look for systematic discrepancies bet... | What are posterior predictive checks and what makes them useful?
Posterior predictive checks are, in simple words, "simulating replicated data under the
fitted model and then comparing these to the observed data" (Gelman and Hill, 2007, p. 158). So, you use posteri |
4,763 | Should you ever standardise binary variables? | A binary variable with values 0, 1 can (usually) be scaled to (value - mean) / SD, which is presumably your z-score.
The most obvious constraint on that is that if you happen to get all zeros or all ones then plugging in SD blindly would mean that the z-score is undefined. There is a case for assigning zero too in so f... | Should you ever standardise binary variables? | A binary variable with values 0, 1 can (usually) be scaled to (value - mean) / SD, which is presumably your z-score.
The most obvious constraint on that is that if you happen to get all zeros or all o | Should you ever standardise binary variables?
A binary variable with values 0, 1 can (usually) be scaled to (value - mean) / SD, which is presumably your z-score.
The most obvious constraint on that is that if you happen to get all zeros or all ones then plugging in SD blindly would mean that the z-score is undefined. ... | Should you ever standardise binary variables?
A binary variable with values 0, 1 can (usually) be scaled to (value - mean) / SD, which is presumably your z-score.
The most obvious constraint on that is that if you happen to get all zeros or all o |
4,764 | Should you ever standardise binary variables? | Standardizing binary variables does not make any sense. The values are arbitrary; they don't mean anything in and of themselves. There may be a rationale for choosing some values like 0 & 1, with respect to numerical stability issues, but that's it. | Should you ever standardise binary variables? | Standardizing binary variables does not make any sense. The values are arbitrary; they don't mean anything in and of themselves. There may be a rationale for choosing some values like 0 & 1, with re | Should you ever standardise binary variables?
Standardizing binary variables does not make any sense. The values are arbitrary; they don't mean anything in and of themselves. There may be a rationale for choosing some values like 0 & 1, with respect to numerical stability issues, but that's it. | Should you ever standardise binary variables?
Standardizing binary variables does not make any sense. The values are arbitrary; they don't mean anything in and of themselves. There may be a rationale for choosing some values like 0 & 1, with re |
4,765 | Should you ever standardise binary variables? | One nice example where it can be useful to standardize in a slightly different way is given in section 4.2
of Gelman and Hill (http://www.stat.columbia.edu/~gelman/arm/). This is mostly when the interpretation of the coefficients is of interest, and perhaps when there are not many predictors.
There, they standardize a ... | Should you ever standardise binary variables? | One nice example where it can be useful to standardize in a slightly different way is given in section 4.2
of Gelman and Hill (http://www.stat.columbia.edu/~gelman/arm/). This is mostly when the inter | Should you ever standardise binary variables?
One nice example where it can be useful to standardize in a slightly different way is given in section 4.2
of Gelman and Hill (http://www.stat.columbia.edu/~gelman/arm/). This is mostly when the interpretation of the coefficients is of interest, and perhaps when there are n... | Should you ever standardise binary variables?
One nice example where it can be useful to standardize in a slightly different way is given in section 4.2
of Gelman and Hill (http://www.stat.columbia.edu/~gelman/arm/). This is mostly when the inter |
4,766 | Should you ever standardise binary variables? | What do you want to standardize, a binary random variable, or a proportion?
It makes no sense to standardize a binary random variable. A random variable is a function that assigns a real value to an event $Y:S\rightarrow \mathbb{R} $. In this case 0 for failure and 1 to success, i.e. $Y\in \lbrace 0,1\rbrace$.
In the ... | Should you ever standardise binary variables? | What do you want to standardize, a binary random variable, or a proportion?
It makes no sense to standardize a binary random variable. A random variable is a function that assigns a real value to an e | Should you ever standardise binary variables?
What do you want to standardize, a binary random variable, or a proportion?
It makes no sense to standardize a binary random variable. A random variable is a function that assigns a real value to an event $Y:S\rightarrow \mathbb{R} $. In this case 0 for failure and 1 to su... | Should you ever standardise binary variables?
What do you want to standardize, a binary random variable, or a proportion?
It makes no sense to standardize a binary random variable. A random variable is a function that assigns a real value to an e |
4,767 | Should you ever standardise binary variables? | In logistic regression binary variables may be standardise for combining them with continuos vars when you want to give to all of them a non informative prior such as N~(0,5) or Cauchy~(0,5).
The standardisation is adviced to be as follows:
Take the total count and give
1 = proportion of 1's
0 = 1 - proportion of 1's.
... | Should you ever standardise binary variables? | In logistic regression binary variables may be standardise for combining them with continuos vars when you want to give to all of them a non informative prior such as N~(0,5) or Cauchy~(0,5).
The stan | Should you ever standardise binary variables?
In logistic regression binary variables may be standardise for combining them with continuos vars when you want to give to all of them a non informative prior such as N~(0,5) or Cauchy~(0,5).
The standardisation is adviced to be as follows:
Take the total count and give
1 =... | Should you ever standardise binary variables?
In logistic regression binary variables may be standardise for combining them with continuos vars when you want to give to all of them a non informative prior such as N~(0,5) or Cauchy~(0,5).
The stan |
4,768 | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter? | One big difference is that regression "controls for" those characteristics in a linear fashion. Matching by propensity scores eliminates the linearity assumption, but, as some observations may not be matched, you may not be able to say anything about certain groups.
For example, if you are studying a worker training pr... | How are propensity scores different from adding covariates in a regression, and when are they prefer | One big difference is that regression "controls for" those characteristics in a linear fashion. Matching by propensity scores eliminates the linearity assumption, but, as some observations may not be | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter?
One big difference is that regression "controls for" those characteristics in a linear fashion. Matching by propensity scores eliminates the linearity assumption, but, as some observations may not be m... | How are propensity scores different from adding covariates in a regression, and when are they prefer
One big difference is that regression "controls for" those characteristics in a linear fashion. Matching by propensity scores eliminates the linearity assumption, but, as some observations may not be |
4,769 | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter? | The short answer is that propensity scores are not any better than the equivalent ANCOVA model, particularly with regard to causal interpretation.
Propensity scores are best understood as a data reduction method. They are an effective means to reduce many covariates into a single score that can be used to adjust an ef... | How are propensity scores different from adding covariates in a regression, and when are they prefer | The short answer is that propensity scores are not any better than the equivalent ANCOVA model, particularly with regard to causal interpretation.
Propensity scores are best understood as a data reduc | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter?
The short answer is that propensity scores are not any better than the equivalent ANCOVA model, particularly with regard to causal interpretation.
Propensity scores are best understood as a data reduct... | How are propensity scores different from adding covariates in a regression, and when are they prefer
The short answer is that propensity scores are not any better than the equivalent ANCOVA model, particularly with regard to causal interpretation.
Propensity scores are best understood as a data reduc |
4,770 | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter? | A likely obtuse reference, but if you by chance have access to it I would recommend reading this book chapter (Apel and Sweeten, 2010). It is aimed at social scientists and so perhaps not as mathematically rigorous as you seem to want, but it should go into enough depth to be more than a satisfactory answer to your que... | How are propensity scores different from adding covariates in a regression, and when are they prefer | A likely obtuse reference, but if you by chance have access to it I would recommend reading this book chapter (Apel and Sweeten, 2010). It is aimed at social scientists and so perhaps not as mathemati | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter?
A likely obtuse reference, but if you by chance have access to it I would recommend reading this book chapter (Apel and Sweeten, 2010). It is aimed at social scientists and so perhaps not as mathematic... | How are propensity scores different from adding covariates in a regression, and when are they prefer
A likely obtuse reference, but if you by chance have access to it I would recommend reading this book chapter (Apel and Sweeten, 2010). It is aimed at social scientists and so perhaps not as mathemati |
4,771 | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter? | I like to think of PS as a design portion of the study which completely separated from the analysis. That is, you might want to think in terms of design (PS) and analysis (regression etc...). Also, PS porvides a mean of supporting exchangeability for binary treatment; maybe others can comment on whether including the c... | How are propensity scores different from adding covariates in a regression, and when are they prefer | I like to think of PS as a design portion of the study which completely separated from the analysis. That is, you might want to think in terms of design (PS) and analysis (regression etc...). Also, PS | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter?
I like to think of PS as a design portion of the study which completely separated from the analysis. That is, you might want to think in terms of design (PS) and analysis (regression etc...). Also, PS ... | How are propensity scores different from adding covariates in a regression, and when are they prefer
I like to think of PS as a design portion of the study which completely separated from the analysis. That is, you might want to think in terms of design (PS) and analysis (regression etc...). Also, PS |
4,772 | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter? | Like the person who asked the question, I am relatively new to propensity score analysis. However, my scientific collaborator has deep knowledge and expertise in biostatistics and clinical trial analysis, so I posed this question to him. His answer provides additional insight beyond what was already posted:
When usin... | How are propensity scores different from adding covariates in a regression, and when are they prefer | Like the person who asked the question, I am relatively new to propensity score analysis. However, my scientific collaborator has deep knowledge and expertise in biostatistics and clinical trial anal | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter?
Like the person who asked the question, I am relatively new to propensity score analysis. However, my scientific collaborator has deep knowledge and expertise in biostatistics and clinical trial analy... | How are propensity scores different from adding covariates in a regression, and when are they prefer
Like the person who asked the question, I am relatively new to propensity score analysis. However, my scientific collaborator has deep knowledge and expertise in biostatistics and clinical trial anal |
4,773 | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter? | Stat Methods Med Res. 2016 Apr 19.
An evaluation of bias in propensity score-adjusted non-linear regression models.
Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the pr... | How are propensity scores different from adding covariates in a regression, and when are they prefer | Stat Methods Med Res. 2016 Apr 19.
An evaluation of bias in propensity score-adjusted non-linear regression models.
Propensity score methods are commonly used to adjust for observed confounding when | How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter?
Stat Methods Med Res. 2016 Apr 19.
An evaluation of bias in propensity score-adjusted non-linear regression models.
Propensity score methods are commonly used to adjust for observed confounding when e... | How are propensity scores different from adding covariates in a regression, and when are they prefer
Stat Methods Med Res. 2016 Apr 19.
An evaluation of bias in propensity score-adjusted non-linear regression models.
Propensity score methods are commonly used to adjust for observed confounding when |
4,774 | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7 | If $X$ and $Y$ are uncorrelated random variables with equal variance $\sigma^2$, then we have that
$$\begin{align}
\operatorname{var}(X-Y) &= \operatorname{var}(X) + \operatorname{var}(-Y)\\
&= \operatorname{var}(X) + \operatorname{var}(Y)\\
&=2\sigma^2,\\
\operatorname{cov}(X, X-Y) &= \operatorname{cov}(X,X) - \operat... | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7 | If $X$ and $Y$ are uncorrelated random variables with equal variance $\sigma^2$, then we have that
$$\begin{align}
\operatorname{var}(X-Y) &= \operatorname{var}(X) + \operatorname{var}(-Y)\\
&= \opera | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7
If $X$ and $Y$ are uncorrelated random variables with equal variance $\sigma^2$, then we have that
$$\begin{align}
\operatorname{var}(X-Y) &= \operatorname{var}(X) + \operatorname{var}(-Y)\\
&= \operatorname{var}(X) + \operatorname{v... | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7
If $X$ and $Y$ are uncorrelated random variables with equal variance $\sigma^2$, then we have that
$$\begin{align}
\operatorname{var}(X-Y) &= \operatorname{var}(X) + \operatorname{var}(-Y)\\
&= \opera |
4,775 | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7 | A geometrical-statistical explanation.
Imagine you make an "inside-out" scatterplot where the $n$ subjects are the axes and the $2$ variables $X$ and $Y$ are the points. This is called a subject space plot (as opposed to usual variable space plot). Because there is only 2 points to plot, all dimensions in such a space ... | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7 | A geometrical-statistical explanation.
Imagine you make an "inside-out" scatterplot where the $n$ subjects are the axes and the $2$ variables $X$ and $Y$ are the points. This is called a subject space | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7
A geometrical-statistical explanation.
Imagine you make an "inside-out" scatterplot where the $n$ subjects are the axes and the $2$ variables $X$ and $Y$ are the points. This is called a subject space plot (as opposed to usual variab... | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7
A geometrical-statistical explanation.
Imagine you make an "inside-out" scatterplot where the $n$ subjects are the axes and the $2$ variables $X$ and $Y$ are the points. This is called a subject space |
4,776 | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7 | I believe that there's a simple intuition based on symmetry here, too. Since X and Y have the same distributions and have a covariance of 0, the relationship of X ± Y with X should "explain" half of the variation in X ± Y; the other half should be explained by Y. So R2 should be 1/2, which means R is 1/√2 ≈ 0.707. | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7 | I believe that there's a simple intuition based on symmetry here, too. Since X and Y have the same distributions and have a covariance of 0, the relationship of X ± Y with X should "explain" half of t | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7
I believe that there's a simple intuition based on symmetry here, too. Since X and Y have the same distributions and have a covariance of 0, the relationship of X ± Y with X should "explain" half of the variation in X ± Y; the other ... | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7
I believe that there's a simple intuition based on symmetry here, too. Since X and Y have the same distributions and have a covariance of 0, the relationship of X ± Y with X should "explain" half of t |
4,777 | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7 | Here's a simple way to think about why there's a correlation here at all.
Imagine what goes on when you subtract two distributions. If the value of x is low then, on average, x - y will be a lower value than if the value of x is high. As x increases then x - y increase, on average, and thus, a positive correlation. | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7 | Here's a simple way to think about why there's a correlation here at all.
Imagine what goes on when you subtract two distributions. If the value of x is low then, on average, x - y will be a lower va | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7
Here's a simple way to think about why there's a correlation here at all.
Imagine what goes on when you subtract two distributions. If the value of x is low then, on average, x - y will be a lower value than if the value of x is hig... | Why does the correlation coefficient between X and X-Y random variables tend to be 0.7
Here's a simple way to think about why there's a correlation here at all.
Imagine what goes on when you subtract two distributions. If the value of x is low then, on average, x - y will be a lower va |
4,778 | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$ | A more conventional notation is
$$y(\mu, \sigma) = \int\Phi\left(\frac{x-\mu}{\sigma}\right)\phi(x) dx = \Phi\left(\frac{-\mu}{\sqrt{1+\sigma^2}}\right).$$
This can be found by differentiating the integral with respect to $\mu$ and $\sigma$, producing elementary integrals which can be expressed in closed form:
$$\frac{... | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$ | A more conventional notation is
$$y(\mu, \sigma) = \int\Phi\left(\frac{x-\mu}{\sigma}\right)\phi(x) dx = \Phi\left(\frac{-\mu}{\sqrt{1+\sigma^2}}\right).$$
This can be found by differentiating the int | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
A more conventional notation is
$$y(\mu, \sigma) = \int\Phi\left(\frac{x-\mu}{\sigma}\right)\phi(x) dx = \Phi\left(\frac{-\mu}{\sqrt{1+\sigma^2}}\right).$$
This can be found by differentiating the integral with respect to $\m... | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
A more conventional notation is
$$y(\mu, \sigma) = \int\Phi\left(\frac{x-\mu}{\sigma}\right)\phi(x) dx = \Phi\left(\frac{-\mu}{\sqrt{1+\sigma^2}}\right).$$
This can be found by differentiating the int |
4,779 | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$ | Let $X$ and $Y$ be independent normal random variables with $X \sim N(a,b^2)$ and $Y$ a standard normal random variable. Then, $$P\{X \leq Y \mid Y = w\} = P\{X \leq w\} = \Phi\left(\frac{w-a}{b}\right).$$ So, using the law of total probability, we get that
$$P\{X \leq Y\}
= \int_{-\infty}^\infty P\{X \leq Y \mid Y =... | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$ | Let $X$ and $Y$ be independent normal random variables with $X \sim N(a,b^2)$ and $Y$ a standard normal random variable. Then, $$P\{X \leq Y \mid Y = w\} = P\{X \leq w\} = \Phi\left(\frac{w-a}{b}\rig | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
Let $X$ and $Y$ be independent normal random variables with $X \sim N(a,b^2)$ and $Y$ a standard normal random variable. Then, $$P\{X \leq Y \mid Y = w\} = P\{X \leq w\} = \Phi\left(\frac{w-a}{b}\right).$$ So, using the law ... | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
Let $X$ and $Y$ be independent normal random variables with $X \sim N(a,b^2)$ and $Y$ a standard normal random variable. Then, $$P\{X \leq Y \mid Y = w\} = P\{X \leq w\} = \Phi\left(\frac{w-a}{b}\rig |
4,780 | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$ | Here is another solution: We define
\begin{align*}
I(\gamma) & =\int_{-\infty}^{\infty}\Phi(\xi x+\gamma)\mathcal{N}(x|0,\sigma^{2})dx,
\end{align*}
which we can evaluate $\gamma=-\xi\mu$ to obtain our desired expression.
We know at least one function value of $I(\gamma)$, e.g., $I(0)=0$
due to symmetry. We take the de... | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$ | Here is another solution: We define
\begin{align*}
I(\gamma) & =\int_{-\infty}^{\infty}\Phi(\xi x+\gamma)\mathcal{N}(x|0,\sigma^{2})dx,
\end{align*}
which we can evaluate $\gamma=-\xi\mu$ to obtain ou | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
Here is another solution: We define
\begin{align*}
I(\gamma) & =\int_{-\infty}^{\infty}\Phi(\xi x+\gamma)\mathcal{N}(x|0,\sigma^{2})dx,
\end{align*}
which we can evaluate $\gamma=-\xi\mu$ to obtain our desired expression.
We ... | How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
Here is another solution: We define
\begin{align*}
I(\gamma) & =\int_{-\infty}^{\infty}\Phi(\xi x+\gamma)\mathcal{N}(x|0,\sigma^{2})dx,
\end{align*}
which we can evaluate $\gamma=-\xi\mu$ to obtain ou |
4,781 | Most confusing statistical terms | "Significant" is the biggest one I run into, because it has both a common English-use meaning and that meaning will crop up in the discussion of research results. I even find myself mixing in "significant" to mean important in the same sentence where I've talked about statistical results.
That way lies madness. | Most confusing statistical terms | "Significant" is the biggest one I run into, because it has both a common English-use meaning and that meaning will crop up in the discussion of research results. I even find myself mixing in "signifi | Most confusing statistical terms
"Significant" is the biggest one I run into, because it has both a common English-use meaning and that meaning will crop up in the discussion of research results. I even find myself mixing in "significant" to mean important in the same sentence where I've talked about statistical result... | Most confusing statistical terms
"Significant" is the biggest one I run into, because it has both a common English-use meaning and that meaning will crop up in the discussion of research results. I even find myself mixing in "signifi |
4,782 | Most confusing statistical terms | I would suggest adding Linear to the list.
I asked a question
on math.SE about what I, as an engineer, think of as linear
minimum mean square error estimation of a random variable $Y$
given the value of a random variable $X$ (meaning estimating
$Y$ as $\hat{Y} = aX+b$ with $a$ and $b$ being chosen so as to
minimiz... | Most confusing statistical terms | I would suggest adding Linear to the list.
I asked a question
on math.SE about what I, as an engineer, think of as linear
minimum mean square error estimation of a random variable $Y$
given the v | Most confusing statistical terms
I would suggest adding Linear to the list.
I asked a question
on math.SE about what I, as an engineer, think of as linear
minimum mean square error estimation of a random variable $Y$
given the value of a random variable $X$ (meaning estimating
$Y$ as $\hat{Y} = aX+b$ with $a$ and ... | Most confusing statistical terms
I would suggest adding Linear to the list.
I asked a question
on math.SE about what I, as an engineer, think of as linear
minimum mean square error estimation of a random variable $Y$
given the v |
4,783 | Most confusing statistical terms | "Confidence"
It's very hard to dissuade non-statisticians that their confidence interval is not (directly) a statement about the credibility of different parameter values.
To have confidence, in the technical meaning of the term, we need to imagine some set of repeated experiments, each one computing an interval in s... | Most confusing statistical terms | "Confidence"
It's very hard to dissuade non-statisticians that their confidence interval is not (directly) a statement about the credibility of different parameter values.
To have confidence, in the | Most confusing statistical terms
"Confidence"
It's very hard to dissuade non-statisticians that their confidence interval is not (directly) a statement about the credibility of different parameter values.
To have confidence, in the technical meaning of the term, we need to imagine some set of repeated experiments, ea... | Most confusing statistical terms
"Confidence"
It's very hard to dissuade non-statisticians that their confidence interval is not (directly) a statement about the credibility of different parameter values.
To have confidence, in the |
4,784 | Most confusing statistical terms | probability
It seems to me that most of the problems associated with interpreting hypothesis tests and confidence intervals stem from the application of a Bayesian definition of "probability" when the procedure is based on a frequentist one. For example the p-value being the probability the null hypothesis is true, w... | Most confusing statistical terms | probability
It seems to me that most of the problems associated with interpreting hypothesis tests and confidence intervals stem from the application of a Bayesian definition of "probability" when th | Most confusing statistical terms
probability
It seems to me that most of the problems associated with interpreting hypothesis tests and confidence intervals stem from the application of a Bayesian definition of "probability" when the procedure is based on a frequentist one. For example the p-value being the probabili... | Most confusing statistical terms
probability
It seems to me that most of the problems associated with interpreting hypothesis tests and confidence intervals stem from the application of a Bayesian definition of "probability" when th |
4,785 | Most confusing statistical terms | "Likelihood" -- it is synonymous with "probability" in everyday speech, but in Statistics it has a special meaning: it is a function of the parameters of a statistical model and a particular data situation, whose value is the probability of the observed outcome assuming that the parameters are equal to the parameter va... | Most confusing statistical terms | "Likelihood" -- it is synonymous with "probability" in everyday speech, but in Statistics it has a special meaning: it is a function of the parameters of a statistical model and a particular data situ | Most confusing statistical terms
"Likelihood" -- it is synonymous with "probability" in everyday speech, but in Statistics it has a special meaning: it is a function of the parameters of a statistical model and a particular data situation, whose value is the probability of the observed outcome assuming that the paramet... | Most confusing statistical terms
"Likelihood" -- it is synonymous with "probability" in everyday speech, but in Statistics it has a special meaning: it is a function of the parameters of a statistical model and a particular data situ |
4,786 | Most confusing statistical terms | Error.
In statistics, an "error" is a deviation of an actual data value from the prediction of a model.
In real life, an error is a spllng mstake or other goof. | Most confusing statistical terms | Error.
In statistics, an "error" is a deviation of an actual data value from the prediction of a model.
In real life, an error is a spllng mstake or other goof. | Most confusing statistical terms
Error.
In statistics, an "error" is a deviation of an actual data value from the prediction of a model.
In real life, an error is a spllng mstake or other goof. | Most confusing statistical terms
Error.
In statistics, an "error" is a deviation of an actual data value from the prediction of a model.
In real life, an error is a spllng mstake or other goof. |
4,787 | Most confusing statistical terms | "Inference"
One of the hardest things for me to understand at first was the difference between a population and a sample. Statisticians write these fancy population level regression equations and then all of a sudden drop down into sample level work and the $\beta$s become $b$s. It took me a long time to realize that y... | Most confusing statistical terms | "Inference"
One of the hardest things for me to understand at first was the difference between a population and a sample. Statisticians write these fancy population level regression equations and then | Most confusing statistical terms
"Inference"
One of the hardest things for me to understand at first was the difference between a population and a sample. Statisticians write these fancy population level regression equations and then all of a sudden drop down into sample level work and the $\beta$s become $b$s. It took... | Most confusing statistical terms
"Inference"
One of the hardest things for me to understand at first was the difference between a population and a sample. Statisticians write these fancy population level regression equations and then |
4,788 | Most confusing statistical terms | To us (or at least me), "randomness" of a "sample" suggests that it is representative of the "population".
To others, "randomness" sometimes implies that a person/thing is unusual. | Most confusing statistical terms | To us (or at least me), "randomness" of a "sample" suggests that it is representative of the "population".
To others, "randomness" sometimes implies that a person/thing is unusual. | Most confusing statistical terms
To us (or at least me), "randomness" of a "sample" suggests that it is representative of the "population".
To others, "randomness" sometimes implies that a person/thing is unusual. | Most confusing statistical terms
To us (or at least me), "randomness" of a "sample" suggests that it is representative of the "population".
To others, "randomness" sometimes implies that a person/thing is unusual. |
4,789 | Most confusing statistical terms | I think one should distinguish between terms confusing the public and terms confusing statisticians. The above suggestions are mostly terms well understood by statisticians and (possibly) misunderstood by the public. I wish to add to the list some terms misunderstood by statisticians:
Bayesian: Originally referred to ... | Most confusing statistical terms | I think one should distinguish between terms confusing the public and terms confusing statisticians. The above suggestions are mostly terms well understood by statisticians and (possibly) misunderstoo | Most confusing statistical terms
I think one should distinguish between terms confusing the public and terms confusing statisticians. The above suggestions are mostly terms well understood by statisticians and (possibly) misunderstood by the public. I wish to add to the list some terms misunderstood by statisticians:
... | Most confusing statistical terms
I think one should distinguish between terms confusing the public and terms confusing statisticians. The above suggestions are mostly terms well understood by statisticians and (possibly) misunderstoo |
4,790 | Most confusing statistical terms | Ecological, commonly used to refer to biological systems, but also a statistical fallacy. From Wikipedia:
An ecological fallacy (or ecological inference fallacy) is an error in the interpretation of statistical data in an ecological study, whereby inferences about the nature of specific individuals are based solely up... | Most confusing statistical terms | Ecological, commonly used to refer to biological systems, but also a statistical fallacy. From Wikipedia:
An ecological fallacy (or ecological inference fallacy) is an error in the interpretation of | Most confusing statistical terms
Ecological, commonly used to refer to biological systems, but also a statistical fallacy. From Wikipedia:
An ecological fallacy (or ecological inference fallacy) is an error in the interpretation of statistical data in an ecological study, whereby inferences about the nature of specifi... | Most confusing statistical terms
Ecological, commonly used to refer to biological systems, but also a statistical fallacy. From Wikipedia:
An ecological fallacy (or ecological inference fallacy) is an error in the interpretation of |
4,791 | Most confusing statistical terms | Is a "survey" a type of math ("survey sampling") or a piece of paper ("questionnaire")?
I haven't conducted a survey on this, but I suspect that much of the public considers a "survey" to be the latter. I suspect further that they don't think about the former. | Most confusing statistical terms | Is a "survey" a type of math ("survey sampling") or a piece of paper ("questionnaire")?
I haven't conducted a survey on this, but I suspect that much of the public considers a "survey" to be the latte | Most confusing statistical terms
Is a "survey" a type of math ("survey sampling") or a piece of paper ("questionnaire")?
I haven't conducted a survey on this, but I suspect that much of the public considers a "survey" to be the latter. I suspect further that they don't think about the former. | Most confusing statistical terms
Is a "survey" a type of math ("survey sampling") or a piece of paper ("questionnaire")?
I haven't conducted a survey on this, but I suspect that much of the public considers a "survey" to be the latte |
4,792 | Most confusing statistical terms | "Loadings", "Coefficients" and "Weights"; when talking about Principal Component Analysis.
I usually find people being quite ad hoc when using them, employing them interchangeably without first explicitly defining what they mean and I have come across papers that refer to "loading vectors" and sometimes mean the PCs t... | Most confusing statistical terms | "Loadings", "Coefficients" and "Weights"; when talking about Principal Component Analysis.
I usually find people being quite ad hoc when using them, employing them interchangeably without first explic | Most confusing statistical terms
"Loadings", "Coefficients" and "Weights"; when talking about Principal Component Analysis.
I usually find people being quite ad hoc when using them, employing them interchangeably without first explicitly defining what they mean and I have come across papers that refer to "loading vect... | Most confusing statistical terms
"Loadings", "Coefficients" and "Weights"; when talking about Principal Component Analysis.
I usually find people being quite ad hoc when using them, employing them interchangeably without first explic |
4,793 | Most confusing statistical terms | Additive model. Still not really sure what this means. I think it refers to a model without interaction terms. But then I will come across an article where they're using it to refer to something else, i.e. a spline model. | Most confusing statistical terms | Additive model. Still not really sure what this means. I think it refers to a model without interaction terms. But then I will come across an article where they're using it to refer to something el | Most confusing statistical terms
Additive model. Still not really sure what this means. I think it refers to a model without interaction terms. But then I will come across an article where they're using it to refer to something else, i.e. a spline model. | Most confusing statistical terms
Additive model. Still not really sure what this means. I think it refers to a model without interaction terms. But then I will come across an article where they're using it to refer to something el |
4,794 | Most confusing statistical terms | Consistency
First, many other people read into this a notion of something like "does not have any (internal) contradictions", which is related, but surely not equivalent, to definitions used in statistics.
Second, even within statistics, it has more than one meaning, such as consistency of an estimator, consistency of ... | Most confusing statistical terms | Consistency
First, many other people read into this a notion of something like "does not have any (internal) contradictions", which is related, but surely not equivalent, to definitions used in statis | Most confusing statistical terms
Consistency
First, many other people read into this a notion of something like "does not have any (internal) contradictions", which is related, but surely not equivalent, to definitions used in statistics.
Second, even within statistics, it has more than one meaning, such as consistency... | Most confusing statistical terms
Consistency
First, many other people read into this a notion of something like "does not have any (internal) contradictions", which is related, but surely not equivalent, to definitions used in statis |
4,795 | Most confusing statistical terms | One of the terms that I find most confusing is the "confusion matrix".
Of course, The term used itself is confusing, not the concept.
I tried to track the history of the term and it is quite interesting too.
The confusion matrix was invented at 1904 by (http://en.wikipedia.org/wiki/Karl_Pearson). He used the term http:... | Most confusing statistical terms | One of the terms that I find most confusing is the "confusion matrix".
Of course, The term used itself is confusing, not the concept.
I tried to track the history of the term and it is quite interesti | Most confusing statistical terms
One of the terms that I find most confusing is the "confusion matrix".
Of course, The term used itself is confusing, not the concept.
I tried to track the history of the term and it is quite interesting too.
The confusion matrix was invented at 1904 by (http://en.wikipedia.org/wiki/Karl... | Most confusing statistical terms
One of the terms that I find most confusing is the "confusion matrix".
Of course, The term used itself is confusing, not the concept.
I tried to track the history of the term and it is quite interesti |
4,796 | Most confusing statistical terms | "Statistics"
To the general public, a substitute for, "now I'm about to lie to you and speak in a way you don't understand." | Most confusing statistical terms | "Statistics"
To the general public, a substitute for, "now I'm about to lie to you and speak in a way you don't understand." | Most confusing statistical terms
"Statistics"
To the general public, a substitute for, "now I'm about to lie to you and speak in a way you don't understand." | Most confusing statistical terms
"Statistics"
To the general public, a substitute for, "now I'm about to lie to you and speak in a way you don't understand." |
4,797 | How to assess the similarity of two histograms? | 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.
A recent paper that may be worth reading is:
Cao, Y. P... | How to assess the similarity of two histograms? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| How to assess the similarity of two histograms?
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.
A rece... | How to assess the similarity of two histograms?
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.
|
4,798 | How to assess the similarity of two histograms? | There are plenty of distance measures between two histograms. You can read a good categorization of these measures in:
K. Meshgi, and S. Ishii, “Expanding Histogram of Colors with Gridding
to Improve Tracking Accuracy,” in Proc. of MVA’15, Tokyo, Japan, May
2015.
The most popular distance functions are listed here fo... | How to assess the similarity of two histograms? | There are plenty of distance measures between two histograms. You can read a good categorization of these measures in:
K. Meshgi, and S. Ishii, “Expanding Histogram of Colors with Gridding
to Improve | How to assess the similarity of two histograms?
There are plenty of distance measures between two histograms. You can read a good categorization of these measures in:
K. Meshgi, and S. Ishii, “Expanding Histogram of Colors with Gridding
to Improve Tracking Accuracy,” in Proc. of MVA’15, Tokyo, Japan, May
2015.
The mo... | How to assess the similarity of two histograms?
There are plenty of distance measures between two histograms. You can read a good categorization of these measures in:
K. Meshgi, and S. Ishii, “Expanding Histogram of Colors with Gridding
to Improve |
4,799 | How to assess the similarity of two histograms? | The standard answer to this question is the chi-squared test. The KS test is for unbinned data, not binned data. (If you have the unbinned data, then by all means use a KS-style test, but if you only have the histogram, the KS test is not appropriate.) | How to assess the similarity of two histograms? | The standard answer to this question is the chi-squared test. The KS test is for unbinned data, not binned data. (If you have the unbinned data, then by all means use a KS-style test, but if you only | How to assess the similarity of two histograms?
The standard answer to this question is the chi-squared test. The KS test is for unbinned data, not binned data. (If you have the unbinned data, then by all means use a KS-style test, but if you only have the histogram, the KS test is not appropriate.) | How to assess the similarity of two histograms?
The standard answer to this question is the chi-squared test. The KS test is for unbinned data, not binned data. (If you have the unbinned data, then by all means use a KS-style test, but if you only |
4,800 | How to assess the similarity of two histograms? | You're looking for the Kolmogorov-Smirnov test. Don't forget to divide the bar heights by the sum of all observations of each histogram.
Note that the KS-test is also reporting a difference if e.g. the means of the distributions are shifted relative to one another. If translation of the histogram along the x-axis is no... | How to assess the similarity of two histograms? | You're looking for the Kolmogorov-Smirnov test. Don't forget to divide the bar heights by the sum of all observations of each histogram.
Note that the KS-test is also reporting a difference if e.g. th | How to assess the similarity of two histograms?
You're looking for the Kolmogorov-Smirnov test. Don't forget to divide the bar heights by the sum of all observations of each histogram.
Note that the KS-test is also reporting a difference if e.g. the means of the distributions are shifted relative to one another. If tra... | How to assess the similarity of two histograms?
You're looking for the Kolmogorov-Smirnov test. Don't forget to divide the bar heights by the sum of all observations of each histogram.
Note that the KS-test is also reporting a difference if e.g. th |
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