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 |
|---|---|---|---|---|---|---|
4,601 | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent? | The t-test with two groups assumes that each group is normally distributed with the same variance (although the means may differ under the alternative hypothesis). That is equivalent to a regression with a dummy variable as the regression allows the mean of each group to differ but not the variance. Hence the residuals... | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent? | The t-test with two groups assumes that each group is normally distributed with the same variance (although the means may differ under the alternative hypothesis). That is equivalent to a regression w | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?
The t-test with two groups assumes that each group is normally distributed with the same variance (although the means may differ under the alternative hypothesis). That is equivalent to a regression with a dummy variable... | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?
The t-test with two groups assumes that each group is normally distributed with the same variance (although the means may differ under the alternative hypothesis). That is equivalent to a regression w |
4,602 | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent? | The t-test simply a special case of the F-test where only two groups are being compared. The result of either will be exactly the same in terms of the p-value and there is a simple relationship between the F and t statistics as well. F = t^2. The two tests are algebraically equivalent and their assumptions are the s... | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent? | The t-test simply a special case of the F-test where only two groups are being compared. The result of either will be exactly the same in terms of the p-value and there is a simple relationship betwe | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?
The t-test simply a special case of the F-test where only two groups are being compared. The result of either will be exactly the same in terms of the p-value and there is a simple relationship between the F and t stati... | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?
The t-test simply a special case of the F-test where only two groups are being compared. The result of either will be exactly the same in terms of the p-value and there is a simple relationship betwe |
4,603 | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent? | I totally agree with Rob's answer, but let me put it another way (using wikipedia):
Assumptions ANOVA:
Independence of cases – this is an assumption of the model that simplifies the statistical analysis.
Normality – the distributions of the residuals are normal.
Equality (or "homogeneity") of variances, called homosce... | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent? | I totally agree with Rob's answer, but let me put it another way (using wikipedia):
Assumptions ANOVA:
Independence of cases – this is an assumption of the model that simplifies the statistical analy | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?
I totally agree with Rob's answer, but let me put it another way (using wikipedia):
Assumptions ANOVA:
Independence of cases – this is an assumption of the model that simplifies the statistical analysis.
Normality – the... | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?
I totally agree with Rob's answer, but let me put it another way (using wikipedia):
Assumptions ANOVA:
Independence of cases – this is an assumption of the model that simplifies the statistical analy |
4,604 | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent? | One obvious point that everyone's overlooked: With ANOVA you're testing the null that the mean is identical regardless of the values of your explanatory variables. With a T-Test you can also test the one-sided case, that the mean is specifically greater given one value of your explanatory variable than given the othe... | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent? | One obvious point that everyone's overlooked: With ANOVA you're testing the null that the mean is identical regardless of the values of your explanatory variables. With a T-Test you can also test th | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?
One obvious point that everyone's overlooked: With ANOVA you're testing the null that the mean is identical regardless of the values of your explanatory variables. With a T-Test you can also test the one-sided case, th... | If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?
One obvious point that everyone's overlooked: With ANOVA you're testing the null that the mean is identical regardless of the values of your explanatory variables. With a T-Test you can also test th |
4,605 | When is a biased estimator preferable to unbiased one? | Yes. Often it is the case that we are interested in minimizing the mean squared error, which can be decomposed into variance + bias squared. This is an extremely fundamental idea in machine learning, and statistics in general. Frequently we see that a small increase in bias can come with a large enough reduction in var... | When is a biased estimator preferable to unbiased one? | Yes. Often it is the case that we are interested in minimizing the mean squared error, which can be decomposed into variance + bias squared. This is an extremely fundamental idea in machine learning, | When is a biased estimator preferable to unbiased one?
Yes. Often it is the case that we are interested in minimizing the mean squared error, which can be decomposed into variance + bias squared. This is an extremely fundamental idea in machine learning, and statistics in general. Frequently we see that a small increas... | When is a biased estimator preferable to unbiased one?
Yes. Often it is the case that we are interested in minimizing the mean squared error, which can be decomposed into variance + bias squared. This is an extremely fundamental idea in machine learning, |
4,606 | When is a biased estimator preferable to unbiased one? | This paper [1] gives a simple example demostrating that a biased estimator can even achieve a lower variance than the Cramér–Rao bound (CRB).
Consider $i.i.d. X_1,...,X_n\sim N(0,\sigma^2)$, and let $k=\sigma^2$.
The maximum likelihood estimator for $k$ is $\hat{k}_{ML}=\frac{1}{n}\sum{X_i^2}$. It is unbiased with a va... | When is a biased estimator preferable to unbiased one? | This paper [1] gives a simple example demostrating that a biased estimator can even achieve a lower variance than the Cramér–Rao bound (CRB).
Consider $i.i.d. X_1,...,X_n\sim N(0,\sigma^2)$, and let $ | When is a biased estimator preferable to unbiased one?
This paper [1] gives a simple example demostrating that a biased estimator can even achieve a lower variance than the Cramér–Rao bound (CRB).
Consider $i.i.d. X_1,...,X_n\sim N(0,\sigma^2)$, and let $k=\sigma^2$.
The maximum likelihood estimator for $k$ is $\hat{k}... | When is a biased estimator preferable to unbiased one?
This paper [1] gives a simple example demostrating that a biased estimator can even achieve a lower variance than the Cramér–Rao bound (CRB).
Consider $i.i.d. X_1,...,X_n\sim N(0,\sigma^2)$, and let $ |
4,607 | When is a biased estimator preferable to unbiased one? | The other examples in this thread are fantastic, but I wanted to provide an extremely simple example that illustrates that a biased estimator can sometimes have drastically smaller variance.
Let $X_1, X_2, \ldots X_n \stackrel{\text{iid}}{\sim} \text{Unif}(0, \theta)$.
First we consider the Method of Moments estimator... | When is a biased estimator preferable to unbiased one? | The other examples in this thread are fantastic, but I wanted to provide an extremely simple example that illustrates that a biased estimator can sometimes have drastically smaller variance.
Let $X_1 | When is a biased estimator preferable to unbiased one?
The other examples in this thread are fantastic, but I wanted to provide an extremely simple example that illustrates that a biased estimator can sometimes have drastically smaller variance.
Let $X_1, X_2, \ldots X_n \stackrel{\text{iid}}{\sim} \text{Unif}(0, \the... | When is a biased estimator preferable to unbiased one?
The other examples in this thread are fantastic, but I wanted to provide an extremely simple example that illustrates that a biased estimator can sometimes have drastically smaller variance.
Let $X_1 |
4,608 | When is a biased estimator preferable to unbiased one? | Two reasons come to mind, aside from the MSE explanation above (the commonly accepted answer to the question):
Managing risk
Efficient testing
Risk, roughly, is the sense of how much something can explode when certain conditions aren't met. Take superefficient estimators: $T(X) = \bar{X}_n$ if $\bar{X}_n$ lies beyond... | When is a biased estimator preferable to unbiased one? | Two reasons come to mind, aside from the MSE explanation above (the commonly accepted answer to the question):
Managing risk
Efficient testing
Risk, roughly, is the sense of how much something can e | When is a biased estimator preferable to unbiased one?
Two reasons come to mind, aside from the MSE explanation above (the commonly accepted answer to the question):
Managing risk
Efficient testing
Risk, roughly, is the sense of how much something can explode when certain conditions aren't met. Take superefficient es... | When is a biased estimator preferable to unbiased one?
Two reasons come to mind, aside from the MSE explanation above (the commonly accepted answer to the question):
Managing risk
Efficient testing
Risk, roughly, is the sense of how much something can e |
4,609 | When is a biased estimator preferable to unbiased one? | The maximum-likelihood estimator $\frac 1 n \sum_{i=1}^n (X_i - \overline X)^2$ of the population variance for a normally distributed population has a lower mean squared error than does the commonplace unbiased estimator, in which the denominator is $n-1.$ But that's a somewhat weak example.
I wrote a paper addressing ... | When is a biased estimator preferable to unbiased one? | The maximum-likelihood estimator $\frac 1 n \sum_{i=1}^n (X_i - \overline X)^2$ of the population variance for a normally distributed population has a lower mean squared error than does the commonplac | When is a biased estimator preferable to unbiased one?
The maximum-likelihood estimator $\frac 1 n \sum_{i=1}^n (X_i - \overline X)^2$ of the population variance for a normally distributed population has a lower mean squared error than does the commonplace unbiased estimator, in which the denominator is $n-1.$ But that... | When is a biased estimator preferable to unbiased one?
The maximum-likelihood estimator $\frac 1 n \sum_{i=1}^n (X_i - \overline X)^2$ of the population variance for a normally distributed population has a lower mean squared error than does the commonplac |
4,610 | Is there any difference between lm and glm for the gaussian family of glm? | While for the specific form of model mentioned in the body of the question (i.e. lm(y ~ x1 + x2) vs glm(y ~ x1 + x2, family=gaussian)), regression and GLMs are the same model, the title question asks something slightly more general:
Is there any difference between lm and glm for the gaussian family of glm?
To which t... | Is there any difference between lm and glm for the gaussian family of glm? | While for the specific form of model mentioned in the body of the question (i.e. lm(y ~ x1 + x2) vs glm(y ~ x1 + x2, family=gaussian)), regression and GLMs are the same model, the title question asks | Is there any difference between lm and glm for the gaussian family of glm?
While for the specific form of model mentioned in the body of the question (i.e. lm(y ~ x1 + x2) vs glm(y ~ x1 + x2, family=gaussian)), regression and GLMs are the same model, the title question asks something slightly more general:
Is there an... | Is there any difference between lm and glm for the gaussian family of glm?
While for the specific form of model mentioned in the body of the question (i.e. lm(y ~ x1 + x2) vs glm(y ~ x1 + x2, family=gaussian)), regression and GLMs are the same model, the title question asks |
4,611 | Is there any difference between lm and glm for the gaussian family of glm? | From @Repmat's answer, the model summary are the same, but the C.I.'s of the regression coefficients from confint are slightly different between lm and glm.
> confint(reg1, level=0.95)
2.5 % 97.5 %
(Intercept) 2.474742 11.526174
x1 1.971466 2.014002
x2 2.958422 3.023291
> confint(r... | Is there any difference between lm and glm for the gaussian family of glm? | From @Repmat's answer, the model summary are the same, but the C.I.'s of the regression coefficients from confint are slightly different between lm and glm.
> confint(reg1, level=0.95)
| Is there any difference between lm and glm for the gaussian family of glm?
From @Repmat's answer, the model summary are the same, but the C.I.'s of the regression coefficients from confint are slightly different between lm and glm.
> confint(reg1, level=0.95)
2.5 % 97.5 %
(Intercept) 2.474742 11.52617... | Is there any difference between lm and glm for the gaussian family of glm?
From @Repmat's answer, the model summary are the same, but the C.I.'s of the regression coefficients from confint are slightly different between lm and glm.
> confint(reg1, level=0.95)
|
4,612 | Is there any difference between lm and glm for the gaussian family of glm? | Short answer, they are exactly the same:
# Simulate data:
set.seed(42)
n <- 1000
x1 <- rnorm(n, mean = 150, sd = 3)
x2 <- rnorm(n, mean = 100, sd = 2)
u <- rnorm(n)
y <- 5 + 2*x1 + 3*x2 + u
# Estimate with OLS:
reg1 <- lm(y ~ x1 + x2)
# Estimate with GLS
reg2 <- glm(y ~ x1 + x2, family=gaussian)
# Compare:
require... | Is there any difference between lm and glm for the gaussian family of glm? | Short answer, they are exactly the same:
# Simulate data:
set.seed(42)
n <- 1000
x1 <- rnorm(n, mean = 150, sd = 3)
x2 <- rnorm(n, mean = 100, sd = 2)
u <- rnorm(n)
y <- 5 + 2*x1 + 3*x2 + u
# Esti | Is there any difference between lm and glm for the gaussian family of glm?
Short answer, they are exactly the same:
# Simulate data:
set.seed(42)
n <- 1000
x1 <- rnorm(n, mean = 150, sd = 3)
x2 <- rnorm(n, mean = 100, sd = 2)
u <- rnorm(n)
y <- 5 + 2*x1 + 3*x2 + u
# Estimate with OLS:
reg1 <- lm(y ~ x1 + x2)
# Esti... | Is there any difference between lm and glm for the gaussian family of glm?
Short answer, they are exactly the same:
# Simulate data:
set.seed(42)
n <- 1000
x1 <- rnorm(n, mean = 150, sd = 3)
x2 <- rnorm(n, mean = 100, sd = 2)
u <- rnorm(n)
y <- 5 + 2*x1 + 3*x2 + u
# Esti |
4,613 | When will L1 regularization work better than L2 and vice versa? | How to decide which regularization (L1 or L2) to use?
What is your goal? Both can improve model generalization by penalizing coefficients, since features with opposite relationship to the outcome can "offset" each other (a large positive value is counterbalanced by a large negative value). This can arise when there ar... | When will L1 regularization work better than L2 and vice versa? | How to decide which regularization (L1 or L2) to use?
What is your goal? Both can improve model generalization by penalizing coefficients, since features with opposite relationship to the outcome can | When will L1 regularization work better than L2 and vice versa?
How to decide which regularization (L1 or L2) to use?
What is your goal? Both can improve model generalization by penalizing coefficients, since features with opposite relationship to the outcome can "offset" each other (a large positive value is counterb... | When will L1 regularization work better than L2 and vice versa?
How to decide which regularization (L1 or L2) to use?
What is your goal? Both can improve model generalization by penalizing coefficients, since features with opposite relationship to the outcome can |
4,614 | When will L1 regularization work better than L2 and vice versa? | Generally speaking if you want optimum prediction use L2. If you want parsimony at some sacrifice of predictive discrimination use L1. But note that the parsimony can be illusory, e.g., repeating the lasso process using the bootstrap will often reveal significant instability in the list of features "selected" especia... | When will L1 regularization work better than L2 and vice versa? | Generally speaking if you want optimum prediction use L2. If you want parsimony at some sacrifice of predictive discrimination use L1. But note that the parsimony can be illusory, e.g., repeating th | When will L1 regularization work better than L2 and vice versa?
Generally speaking if you want optimum prediction use L2. If you want parsimony at some sacrifice of predictive discrimination use L1. But note that the parsimony can be illusory, e.g., repeating the lasso process using the bootstrap will often reveal si... | When will L1 regularization work better than L2 and vice versa?
Generally speaking if you want optimum prediction use L2. If you want parsimony at some sacrifice of predictive discrimination use L1. But note that the parsimony can be illusory, e.g., repeating th |
4,615 | Online vs offline learning? | Online learning means that you are doing it as the data comes in. Offline means that you have a static dataset.
So, for online learning, you (typically) have more data, but you have time constraints. Another wrinkle that can affect online learning is that your concepts might change through time.
Let's say you want to b... | Online vs offline learning? | Online learning means that you are doing it as the data comes in. Offline means that you have a static dataset.
So, for online learning, you (typically) have more data, but you have time constraints. | Online vs offline learning?
Online learning means that you are doing it as the data comes in. Offline means that you have a static dataset.
So, for online learning, you (typically) have more data, but you have time constraints. Another wrinkle that can affect online learning is that your concepts might change through t... | Online vs offline learning?
Online learning means that you are doing it as the data comes in. Offline means that you have a static dataset.
So, for online learning, you (typically) have more data, but you have time constraints. |
4,616 | Online vs offline learning? | The term "online" is overloaded, and therefore causes confusion in the domain of machine learning.
The opposite of "online" is batch learning. In batch learning, the learning algorithm updates its parameters after consuming the whole batch, whereas in online learning, the algorithm updates its parameters after learnin... | Online vs offline learning? | The term "online" is overloaded, and therefore causes confusion in the domain of machine learning.
The opposite of "online" is batch learning. In batch learning, the learning algorithm updates its pa | Online vs offline learning?
The term "online" is overloaded, and therefore causes confusion in the domain of machine learning.
The opposite of "online" is batch learning. In batch learning, the learning algorithm updates its parameters after consuming the whole batch, whereas in online learning, the algorithm updates ... | Online vs offline learning?
The term "online" is overloaded, and therefore causes confusion in the domain of machine learning.
The opposite of "online" is batch learning. In batch learning, the learning algorithm updates its pa |
4,617 | Online vs offline learning? | Online learning (also called incremental learning): we consider a single presentation of the examples. In this case, each example is used sequentially in a manner as prescribed by the learning algorithm, and then thrown away. The weight changes made at a given stage depend specifically only on the (current) example bei... | Online vs offline learning? | Online learning (also called incremental learning): we consider a single presentation of the examples. In this case, each example is used sequentially in a manner as prescribed by the learning algorit | Online vs offline learning?
Online learning (also called incremental learning): we consider a single presentation of the examples. In this case, each example is used sequentially in a manner as prescribed by the learning algorithm, and then thrown away. The weight changes made at a given stage depend specifically only ... | Online vs offline learning?
Online learning (also called incremental learning): we consider a single presentation of the examples. In this case, each example is used sequentially in a manner as prescribed by the learning algorit |
4,618 | How large should the batch size be for stochastic gradient descent? | The "sample size" you're talking about is referred to as batch size, $B$. The batch size parameter is just one of the hyper-parameters you'll be tuning when you train a neural network with mini-batch Stochastic Gradient Descent (SGD) and is data dependent. The most basic method of hyper-parameter search is to do a grid... | How large should the batch size be for stochastic gradient descent? | The "sample size" you're talking about is referred to as batch size, $B$. The batch size parameter is just one of the hyper-parameters you'll be tuning when you train a neural network with mini-batch | How large should the batch size be for stochastic gradient descent?
The "sample size" you're talking about is referred to as batch size, $B$. The batch size parameter is just one of the hyper-parameters you'll be tuning when you train a neural network with mini-batch Stochastic Gradient Descent (SGD) and is data depend... | How large should the batch size be for stochastic gradient descent?
The "sample size" you're talking about is referred to as batch size, $B$. The batch size parameter is just one of the hyper-parameters you'll be tuning when you train a neural network with mini-batch |
4,619 | Clustering a long list of strings (words) into similarity groups | Seconding @micans recommendation for Affinity Propagation.
From the paper: L Frey, Brendan J., and Delbert Dueck. "Clustering by passing messages between data points." science 315.5814 (2007): 972-976..
It's super easy to use via many packages.
It works on anything you can define the pairwise similarity on. Which you c... | Clustering a long list of strings (words) into similarity groups | Seconding @micans recommendation for Affinity Propagation.
From the paper: L Frey, Brendan J., and Delbert Dueck. "Clustering by passing messages between data points." science 315.5814 (2007): 972-976 | Clustering a long list of strings (words) into similarity groups
Seconding @micans recommendation for Affinity Propagation.
From the paper: L Frey, Brendan J., and Delbert Dueck. "Clustering by passing messages between data points." science 315.5814 (2007): 972-976..
It's super easy to use via many packages.
It works o... | Clustering a long list of strings (words) into similarity groups
Seconding @micans recommendation for Affinity Propagation.
From the paper: L Frey, Brendan J., and Delbert Dueck. "Clustering by passing messages between data points." science 315.5814 (2007): 972-976 |
4,620 | Clustering a long list of strings (words) into similarity groups | Use graph clustering algorithms, such as Louvain clustering, Restricted Neighbourhood Search Clustering (RNSC), Affinity Propgation Clustering (APC), or the Markov Cluster algorithm (MCL). | Clustering a long list of strings (words) into similarity groups | Use graph clustering algorithms, such as Louvain clustering, Restricted Neighbourhood Search Clustering (RNSC), Affinity Propgation Clustering (APC), or the Markov Cluster algorithm (MCL). | Clustering a long list of strings (words) into similarity groups
Use graph clustering algorithms, such as Louvain clustering, Restricted Neighbourhood Search Clustering (RNSC), Affinity Propgation Clustering (APC), or the Markov Cluster algorithm (MCL). | Clustering a long list of strings (words) into similarity groups
Use graph clustering algorithms, such as Louvain clustering, Restricted Neighbourhood Search Clustering (RNSC), Affinity Propgation Clustering (APC), or the Markov Cluster algorithm (MCL). |
4,621 | Clustering a long list of strings (words) into similarity groups | You could try the vector space model with the n-grams of the words as the vector space entries. I think you would have to use a measure like cosine similarity in this case instead of edit distance. | Clustering a long list of strings (words) into similarity groups | You could try the vector space model with the n-grams of the words as the vector space entries. I think you would have to use a measure like cosine similarity in this case instead of edit distance. | Clustering a long list of strings (words) into similarity groups
You could try the vector space model with the n-grams of the words as the vector space entries. I think you would have to use a measure like cosine similarity in this case instead of edit distance. | Clustering a long list of strings (words) into similarity groups
You could try the vector space model with the n-grams of the words as the vector space entries. I think you would have to use a measure like cosine similarity in this case instead of edit distance. |
4,622 | Probability distribution for different probabilities | This is the sum of 16 (presumably independent) Binomial trials. The assumption of independence allows us to multiply probabilities. Whence, after two trials with probabilities $p_1$ and $p_2$ of success the chance of success on both trials is $p_1 p_2$, the chance of no successes is $(1-p_1)(1-p_2)$, and the chance o... | Probability distribution for different probabilities | This is the sum of 16 (presumably independent) Binomial trials. The assumption of independence allows us to multiply probabilities. Whence, after two trials with probabilities $p_1$ and $p_2$ of suc | Probability distribution for different probabilities
This is the sum of 16 (presumably independent) Binomial trials. The assumption of independence allows us to multiply probabilities. Whence, after two trials with probabilities $p_1$ and $p_2$ of success the chance of success on both trials is $p_1 p_2$, the chance ... | Probability distribution for different probabilities
This is the sum of 16 (presumably independent) Binomial trials. The assumption of independence allows us to multiply probabilities. Whence, after two trials with probabilities $p_1$ and $p_2$ of suc |
4,623 | Probability distribution for different probabilities | One alternative to @whuber's normal approximation is to use "mixing" probabilities, or a hierarchical model. This would apply when the $p_i$ are similar in some way, and you can model this by a probability distribution $p_i\sim Dist(\theta)$ with a density function of $g(p|\theta)$ indexed by some parameter $\theta$. ... | Probability distribution for different probabilities | One alternative to @whuber's normal approximation is to use "mixing" probabilities, or a hierarchical model. This would apply when the $p_i$ are similar in some way, and you can model this by a proba | Probability distribution for different probabilities
One alternative to @whuber's normal approximation is to use "mixing" probabilities, or a hierarchical model. This would apply when the $p_i$ are similar in some way, and you can model this by a probability distribution $p_i\sim Dist(\theta)$ with a density function ... | Probability distribution for different probabilities
One alternative to @whuber's normal approximation is to use "mixing" probabilities, or a hierarchical model. This would apply when the $p_i$ are similar in some way, and you can model this by a proba |
4,624 | Probability distribution for different probabilities | Let $X_i$ ~ $Bernoulli(p_i)$ with probability generating function (pgf):
$$\text{pgf} = E[t^{X_i}] = 1 - p_i (1-t)$$
Let $S = \sum_{i=1}^n X_i$ denote the sum of $n$ such independent random variables. Then, the pgf for the sum $S$ of $n=16$ such variables is:
$$\begin{align*}\displaystyle \text{pgfS} &= E[t^S]
\\&= ... | Probability distribution for different probabilities | Let $X_i$ ~ $Bernoulli(p_i)$ with probability generating function (pgf):
$$\text{pgf} = E[t^{X_i}] = 1 - p_i (1-t)$$
Let $S = \sum_{i=1}^n X_i$ denote the sum of $n$ such independent random variables. | Probability distribution for different probabilities
Let $X_i$ ~ $Bernoulli(p_i)$ with probability generating function (pgf):
$$\text{pgf} = E[t^{X_i}] = 1 - p_i (1-t)$$
Let $S = \sum_{i=1}^n X_i$ denote the sum of $n$ such independent random variables. Then, the pgf for the sum $S$ of $n=16$ such variables is:
$$\begi... | Probability distribution for different probabilities
Let $X_i$ ~ $Bernoulli(p_i)$ with probability generating function (pgf):
$$\text{pgf} = E[t^{X_i}] = 1 - p_i (1-t)$$
Let $S = \sum_{i=1}^n X_i$ denote the sum of $n$ such independent random variables. |
4,625 | Probability distribution for different probabilities | The (in general intractable) pmf is
$$
\Pr(S=k) = \sum_{\substack{A\subset\{1,\dots,n\}\\ |A|=k}} \left( \prod_{i\in A} p_i \right)\left(\prod_{j\in \{1,\dots,n\}\setminus A} (1-p_j) \right) \, .
$$
R code:
p <- seq(1, 16) / 17
cat(p, "\n")
n <- length(p)
k <- 9
S <- seq(1, n)
A <- combn(S, k)
pr <- 0
for (i in 1:cho... | Probability distribution for different probabilities | The (in general intractable) pmf is
$$
\Pr(S=k) = \sum_{\substack{A\subset\{1,\dots,n\}\\ |A|=k}} \left( \prod_{i\in A} p_i \right)\left(\prod_{j\in \{1,\dots,n\}\setminus A} (1-p_j) \right) \, .
$$ | Probability distribution for different probabilities
The (in general intractable) pmf is
$$
\Pr(S=k) = \sum_{\substack{A\subset\{1,\dots,n\}\\ |A|=k}} \left( \prod_{i\in A} p_i \right)\left(\prod_{j\in \{1,\dots,n\}\setminus A} (1-p_j) \right) \, .
$$
R code:
p <- seq(1, 16) / 17
cat(p, "\n")
n <- length(p)
k <- 9
S ... | Probability distribution for different probabilities
The (in general intractable) pmf is
$$
\Pr(S=k) = \sum_{\substack{A\subset\{1,\dots,n\}\\ |A|=k}} \left( \prod_{i\in A} p_i \right)\left(\prod_{j\in \{1,\dots,n\}\setminus A} (1-p_j) \right) \, .
$$ |
4,626 | Probability distribution for different probabilities | @wolfies comment, and my attempt at a response to it revealed an important problem with my other answer, which I will discuss later.
Specific Case (n=16)
There is a fairly efficient way to code up the full distribution by using the "trick" of using base 2 (binary) numbers in the calculation. It only requires 4 lines o... | Probability distribution for different probabilities | @wolfies comment, and my attempt at a response to it revealed an important problem with my other answer, which I will discuss later.
Specific Case (n=16)
There is a fairly efficient way to code up the | Probability distribution for different probabilities
@wolfies comment, and my attempt at a response to it revealed an important problem with my other answer, which I will discuss later.
Specific Case (n=16)
There is a fairly efficient way to code up the full distribution by using the "trick" of using base 2 (binary) nu... | Probability distribution for different probabilities
@wolfies comment, and my attempt at a response to it revealed an important problem with my other answer, which I will discuss later.
Specific Case (n=16)
There is a fairly efficient way to code up the |
4,627 | How do we decide when a small sample is statistically significant or not? | I will describe how a statistician interprets count data. With a tiny bit of practice you can do it, too.
The basic analysis
When cases arise randomly and independently, the times of their occurrences are reasonably accurately modeled with a Poisson process. This implies that the number of cases appearing in any pred... | How do we decide when a small sample is statistically significant or not? | I will describe how a statistician interprets count data. With a tiny bit of practice you can do it, too.
The basic analysis
When cases arise randomly and independently, the times of their occurrence | How do we decide when a small sample is statistically significant or not?
I will describe how a statistician interprets count data. With a tiny bit of practice you can do it, too.
The basic analysis
When cases arise randomly and independently, the times of their occurrences are reasonably accurately modeled with a Poi... | How do we decide when a small sample is statistically significant or not?
I will describe how a statistician interprets count data. With a tiny bit of practice you can do it, too.
The basic analysis
When cases arise randomly and independently, the times of their occurrence |
4,628 | How do we decide when a small sample is statistically significant or not? | Quoting Wikipedia:
In statistical hypothesis testing, a result has statistical
significance when it is very unlikely to have occurred given the null
hypothesis.
Result of a statistical test can be significant, or not. Size of the sample is not a test. Significant in what sense? Prevalence of COVID-19 is a characteris... | How do we decide when a small sample is statistically significant or not? | Quoting Wikipedia:
In statistical hypothesis testing, a result has statistical
significance when it is very unlikely to have occurred given the null
hypothesis.
Result of a statistical test can be s | How do we decide when a small sample is statistically significant or not?
Quoting Wikipedia:
In statistical hypothesis testing, a result has statistical
significance when it is very unlikely to have occurred given the null
hypothesis.
Result of a statistical test can be significant, or not. Size of the sample is not ... | How do we decide when a small sample is statistically significant or not?
Quoting Wikipedia:
In statistical hypothesis testing, a result has statistical
significance when it is very unlikely to have occurred given the null
hypothesis.
Result of a statistical test can be s |
4,629 | How do we decide when a small sample is statistically significant or not? | @Avroham. I think the word "significant" is so ambiguous, you shouldn't use it in your question. It has a very definite technial meaning in statistics, but has many other meanings more generally. I think the phrase "statistically convincing" would be better. It is even more ambiguous in one sense, but it doesn't have a... | How do we decide when a small sample is statistically significant or not? | @Avroham. I think the word "significant" is so ambiguous, you shouldn't use it in your question. It has a very definite technial meaning in statistics, but has many other meanings more generally. I th | How do we decide when a small sample is statistically significant or not?
@Avroham. I think the word "significant" is so ambiguous, you shouldn't use it in your question. It has a very definite technial meaning in statistics, but has many other meanings more generally. I think the phrase "statistically convincing" woul... | How do we decide when a small sample is statistically significant or not?
@Avroham. I think the word "significant" is so ambiguous, you shouldn't use it in your question. It has a very definite technial meaning in statistics, but has many other meanings more generally. I th |
4,630 | How do we decide when a small sample is statistically significant or not? | I think what you're asking is if there is some predetermined minimal sample size that needs to be taken in order to have statistical significance. In the case of looking at the World vs the Vatican in terms of cases/million its obvious with a ratio of 7.8 billion to 807 makes any comparison insignificant. ie, neither i... | How do we decide when a small sample is statistically significant or not? | I think what you're asking is if there is some predetermined minimal sample size that needs to be taken in order to have statistical significance. In the case of looking at the World vs the Vatican in | How do we decide when a small sample is statistically significant or not?
I think what you're asking is if there is some predetermined minimal sample size that needs to be taken in order to have statistical significance. In the case of looking at the World vs the Vatican in terms of cases/million its obvious with a rat... | How do we decide when a small sample is statistically significant or not?
I think what you're asking is if there is some predetermined minimal sample size that needs to be taken in order to have statistical significance. In the case of looking at the World vs the Vatican in |
4,631 | Intuitive explanations of differences between Gradient Boosting Trees (GBM) & Adaboost | I found this introduction which provides some intuitive explanations:
In Gradient Boosting, ‘shortcomings’ (of existing weak learners) are identified by gradients.
In AdaBoost, ‘shortcomings’ are identified by high-weight data points.
By means of an exponential loss function, AdaBoost gives more weights to those sa... | Intuitive explanations of differences between Gradient Boosting Trees (GBM) & Adaboost | I found this introduction which provides some intuitive explanations:
In Gradient Boosting, ‘shortcomings’ (of existing weak learners) are identified by gradients.
In AdaBoost, ‘shortcomings’ are id | Intuitive explanations of differences between Gradient Boosting Trees (GBM) & Adaboost
I found this introduction which provides some intuitive explanations:
In Gradient Boosting, ‘shortcomings’ (of existing weak learners) are identified by gradients.
In AdaBoost, ‘shortcomings’ are identified by high-weight data poin... | Intuitive explanations of differences between Gradient Boosting Trees (GBM) & Adaboost
I found this introduction which provides some intuitive explanations:
In Gradient Boosting, ‘shortcomings’ (of existing weak learners) are identified by gradients.
In AdaBoost, ‘shortcomings’ are id |
4,632 | Intuitive explanations of differences between Gradient Boosting Trees (GBM) & Adaboost | An intuitive explanation of AdaBoost algorithn
Let me build upon @Randel's excellent answer with an illustration of the following point
In AdaBoost, ‘shortcomings’ are identified by high-weight data points
AdaBoost recap
Let $G_m(x) \ m = 1,2,...,M$ be the sequence of weak classifiers, our objective is to build th... | Intuitive explanations of differences between Gradient Boosting Trees (GBM) & Adaboost | An intuitive explanation of AdaBoost algorithn
Let me build upon @Randel's excellent answer with an illustration of the following point
In AdaBoost, ‘shortcomings’ are identified by high-weight dat | Intuitive explanations of differences between Gradient Boosting Trees (GBM) & Adaboost
An intuitive explanation of AdaBoost algorithn
Let me build upon @Randel's excellent answer with an illustration of the following point
In AdaBoost, ‘shortcomings’ are identified by high-weight data points
AdaBoost recap
Let $G_... | Intuitive explanations of differences between Gradient Boosting Trees (GBM) & Adaboost
An intuitive explanation of AdaBoost algorithn
Let me build upon @Randel's excellent answer with an illustration of the following point
In AdaBoost, ‘shortcomings’ are identified by high-weight dat |
4,633 | How does linear regression use the normal distribution? | Linear regression by itself does not need the normal (gaussian) assumption, the estimators can be calculated (by linear least squares) without any need of such assumption, and makes perfect sense without it.
But then, as statisticians we want to understand some of the properties of this method, answers to questions suc... | How does linear regression use the normal distribution? | Linear regression by itself does not need the normal (gaussian) assumption, the estimators can be calculated (by linear least squares) without any need of such assumption, and makes perfect sense with | How does linear regression use the normal distribution?
Linear regression by itself does not need the normal (gaussian) assumption, the estimators can be calculated (by linear least squares) without any need of such assumption, and makes perfect sense without it.
But then, as statisticians we want to understand some of... | How does linear regression use the normal distribution?
Linear regression by itself does not need the normal (gaussian) assumption, the estimators can be calculated (by linear least squares) without any need of such assumption, and makes perfect sense with |
4,634 | How does linear regression use the normal distribution? | But why is each predicted value assumed to have come from a normal distribution?
There is no deep reason for it, and you are free to change the distributional assumptions, moving to GLMs, or to robust regression. The LM (normal distribution) is popular because its easy to calculate, quite stable and residuals are in p... | How does linear regression use the normal distribution? | But why is each predicted value assumed to have come from a normal distribution?
There is no deep reason for it, and you are free to change the distributional assumptions, moving to GLMs, or to robus | How does linear regression use the normal distribution?
But why is each predicted value assumed to have come from a normal distribution?
There is no deep reason for it, and you are free to change the distributional assumptions, moving to GLMs, or to robust regression. The LM (normal distribution) is popular because it... | How does linear regression use the normal distribution?
But why is each predicted value assumed to have come from a normal distribution?
There is no deep reason for it, and you are free to change the distributional assumptions, moving to GLMs, or to robus |
4,635 | How does linear regression use the normal distribution? | This discussionWhat if residuals are normally distributed, but y is not? has well addressed this question.
In short, for a regression problem, we only assume that the response is normal conditioned on the value of x. It is not necessary that the independent or response variables are independent. | How does linear regression use the normal distribution? | This discussionWhat if residuals are normally distributed, but y is not? has well addressed this question.
In short, for a regression problem, we only assume that the response is normal conditioned on | How does linear regression use the normal distribution?
This discussionWhat if residuals are normally distributed, but y is not? has well addressed this question.
In short, for a regression problem, we only assume that the response is normal conditioned on the value of x. It is not necessary that the independent or res... | How does linear regression use the normal distribution?
This discussionWhat if residuals are normally distributed, but y is not? has well addressed this question.
In short, for a regression problem, we only assume that the response is normal conditioned on |
4,636 | How does linear regression use the normal distribution? | Let me stick to the case of a one variable regression. The details are the same, but the notation is more cumbersome in the case of a multivariate regression. Given any data set $(x_i,y_i)$ one can find the 'least squares line' $ y = \beta x +c$ , that is find $\beta$ so that $\sum_i (y_i - \sum_i \beta x_i - c)^2$ is... | How does linear regression use the normal distribution? | Let me stick to the case of a one variable regression. The details are the same, but the notation is more cumbersome in the case of a multivariate regression. Given any data set $(x_i,y_i)$ one can f | How does linear regression use the normal distribution?
Let me stick to the case of a one variable regression. The details are the same, but the notation is more cumbersome in the case of a multivariate regression. Given any data set $(x_i,y_i)$ one can find the 'least squares line' $ y = \beta x +c$ , that is find $\... | How does linear regression use the normal distribution?
Let me stick to the case of a one variable regression. The details are the same, but the notation is more cumbersome in the case of a multivariate regression. Given any data set $(x_i,y_i)$ one can f |
4,637 | Using deep learning for time series prediction | There has been some work on adapting deep learning methods for sequential data. A lot of this work has focused on developing "modules" which can be stacked in a way analogous to stacking restricted boltzmann machines (RBMs) or autoencoders to form a deep neural network. I'll highlight a few below:
Conditional RBMs: Pr... | Using deep learning for time series prediction | There has been some work on adapting deep learning methods for sequential data. A lot of this work has focused on developing "modules" which can be stacked in a way analogous to stacking restricted bo | Using deep learning for time series prediction
There has been some work on adapting deep learning methods for sequential data. A lot of this work has focused on developing "modules" which can be stacked in a way analogous to stacking restricted boltzmann machines (RBMs) or autoencoders to form a deep neural network. I'... | Using deep learning for time series prediction
There has been some work on adapting deep learning methods for sequential data. A lot of this work has focused on developing "modules" which can be stacked in a way analogous to stacking restricted bo |
4,638 | Using deep learning for time series prediction | Yes, deep learning can be applied for time series predictions. In fact, it has been done many times already, for example:
http://cs229.stanford.edu/proj2012/BussetiOsbandWong-DeepLearningForTimeSeriesModeling.pdf
http://link.springer.com/article/10.1007/s00134-013-2964-2#page-1
This is not really any "special case", ... | Using deep learning for time series prediction | Yes, deep learning can be applied for time series predictions. In fact, it has been done many times already, for example:
http://cs229.stanford.edu/proj2012/BussetiOsbandWong-DeepLearningForTimeSerie | Using deep learning for time series prediction
Yes, deep learning can be applied for time series predictions. In fact, it has been done many times already, for example:
http://cs229.stanford.edu/proj2012/BussetiOsbandWong-DeepLearningForTimeSeriesModeling.pdf
http://link.springer.com/article/10.1007/s00134-013-2964-2#... | Using deep learning for time series prediction
Yes, deep learning can be applied for time series predictions. In fact, it has been done many times already, for example:
http://cs229.stanford.edu/proj2012/BussetiOsbandWong-DeepLearningForTimeSerie |
4,639 | Using deep learning for time series prediction | Recurrent Neural Networks are considered a type of Deep Learning (DL). I think they are the most popular DL tool for (1d) sequence-to-sequence learning. They are currently the basis of Neural Machine Translation (NMT) approaches (pioneered 2014 at LISA (UdeM), Google, and probably a couple others I'm not remembering)... | Using deep learning for time series prediction | Recurrent Neural Networks are considered a type of Deep Learning (DL). I think they are the most popular DL tool for (1d) sequence-to-sequence learning. They are currently the basis of Neural Machin | Using deep learning for time series prediction
Recurrent Neural Networks are considered a type of Deep Learning (DL). I think they are the most popular DL tool for (1d) sequence-to-sequence learning. They are currently the basis of Neural Machine Translation (NMT) approaches (pioneered 2014 at LISA (UdeM), Google, an... | Using deep learning for time series prediction
Recurrent Neural Networks are considered a type of Deep Learning (DL). I think they are the most popular DL tool for (1d) sequence-to-sequence learning. They are currently the basis of Neural Machin |
4,640 | Using deep learning for time series prediction | Alex Graves' Generating sequences with Recurrent Neural Networks uses recurrent networks and Long short term memory Cells to predict text and do handwriting synthesis.
Andrej Karpathy has written a blog about generating character level sequences from scratch. He uses RNNs in his tutorial.
For more examples, you should ... | Using deep learning for time series prediction | Alex Graves' Generating sequences with Recurrent Neural Networks uses recurrent networks and Long short term memory Cells to predict text and do handwriting synthesis.
Andrej Karpathy has written a bl | Using deep learning for time series prediction
Alex Graves' Generating sequences with Recurrent Neural Networks uses recurrent networks and Long short term memory Cells to predict text and do handwriting synthesis.
Andrej Karpathy has written a blog about generating character level sequences from scratch. He uses RNNs ... | Using deep learning for time series prediction
Alex Graves' Generating sequences with Recurrent Neural Networks uses recurrent networks and Long short term memory Cells to predict text and do handwriting synthesis.
Andrej Karpathy has written a bl |
4,641 | Using deep learning for time series prediction | Maybe this will help:
I. Sutskever, O. Vinyals, and Q. V. V Le, “Sequence to sequence learning with neural networks,” in Advances in Neural Information Processing Systems, 2014, pp. 3104–3112.
If you have definition for your exact time window on the data like sentences in this paper or paragraphs then you will be fin... | Using deep learning for time series prediction | Maybe this will help:
I. Sutskever, O. Vinyals, and Q. V. V Le, “Sequence to sequence learning with neural networks,” in Advances in Neural Information Processing Systems, 2014, pp. 3104–3112.
If yo | Using deep learning for time series prediction
Maybe this will help:
I. Sutskever, O. Vinyals, and Q. V. V Le, “Sequence to sequence learning with neural networks,” in Advances in Neural Information Processing Systems, 2014, pp. 3104–3112.
If you have definition for your exact time window on the data like sentences i... | Using deep learning for time series prediction
Maybe this will help:
I. Sutskever, O. Vinyals, and Q. V. V Le, “Sequence to sequence learning with neural networks,” in Advances in Neural Information Processing Systems, 2014, pp. 3104–3112.
If yo |
4,642 | Understanding LSTM units vs. cells | The terminology is unfortunately inconsistent. num_units in TensorFlow is the number of hidden states, i.e. the dimension of $h_t$ in the equations you gave.
Also, from https://github.com/tensorflow/tensorflow/blob/master/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.nn.rnn_cell.RNNCell.md :
The def... | Understanding LSTM units vs. cells | The terminology is unfortunately inconsistent. num_units in TensorFlow is the number of hidden states, i.e. the dimension of $h_t$ in the equations you gave.
Also, from https://github.com/tensorflow/t | Understanding LSTM units vs. cells
The terminology is unfortunately inconsistent. num_units in TensorFlow is the number of hidden states, i.e. the dimension of $h_t$ in the equations you gave.
Also, from https://github.com/tensorflow/tensorflow/blob/master/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/t... | Understanding LSTM units vs. cells
The terminology is unfortunately inconsistent. num_units in TensorFlow is the number of hidden states, i.e. the dimension of $h_t$ in the equations you gave.
Also, from https://github.com/tensorflow/t |
4,643 | Understanding LSTM units vs. cells | Most LSTM/RNN diagrams just show the hidden cells but never the units of those cells. Hence, the confusion.
Each hidden layer has hidden cells, as many as the number of time steps.
And further, each hidden cell is made up of multiple hidden units, like in the diagram below. Therefore, the dimensionality of a hidden la... | Understanding LSTM units vs. cells | Most LSTM/RNN diagrams just show the hidden cells but never the units of those cells. Hence, the confusion.
Each hidden layer has hidden cells, as many as the number of time steps.
And further, each | Understanding LSTM units vs. cells
Most LSTM/RNN diagrams just show the hidden cells but never the units of those cells. Hence, the confusion.
Each hidden layer has hidden cells, as many as the number of time steps.
And further, each hidden cell is made up of multiple hidden units, like in the diagram below. Therefore... | Understanding LSTM units vs. cells
Most LSTM/RNN diagrams just show the hidden cells but never the units of those cells. Hence, the confusion.
Each hidden layer has hidden cells, as many as the number of time steps.
And further, each |
4,644 | Understanding LSTM units vs. cells | Although the issue is almost the same as I answered in this answer, I'd like to illustrate this issue, which also confused me a bit today in the seq2seq model (thanks to @Franck Dernoncourt's answer), in the graph. In this simple encoder diagram:
Each $h_i$ above is the same cell in different time-step (cell eithe... | Understanding LSTM units vs. cells | Although the issue is almost the same as I answered in this answer, I'd like to illustrate this issue, which also confused me a bit today in the seq2seq model (thanks to @Franck Dernoncourt's answer), | Understanding LSTM units vs. cells
Although the issue is almost the same as I answered in this answer, I'd like to illustrate this issue, which also confused me a bit today in the seq2seq model (thanks to @Franck Dernoncourt's answer), in the graph. In this simple encoder diagram:
Each $h_i$ above is the same cell... | Understanding LSTM units vs. cells
Although the issue is almost the same as I answered in this answer, I'd like to illustrate this issue, which also confused me a bit today in the seq2seq model (thanks to @Franck Dernoncourt's answer), |
4,645 | Understanding LSTM units vs. cells | In keras.layers.LSTM(units, activation='tanh', ....), the units refers to the dimensionality or length of the hidden state or the length of the activation vector passed on the next LSTM cell/unit - the next LSTM cell/unit is the "green picture above with the gates etc from http://colah.github.io/posts/2015-08-Understan... | Understanding LSTM units vs. cells | In keras.layers.LSTM(units, activation='tanh', ....), the units refers to the dimensionality or length of the hidden state or the length of the activation vector passed on the next LSTM cell/unit - th | Understanding LSTM units vs. cells
In keras.layers.LSTM(units, activation='tanh', ....), the units refers to the dimensionality or length of the hidden state or the length of the activation vector passed on the next LSTM cell/unit - the next LSTM cell/unit is the "green picture above with the gates etc from http://cola... | Understanding LSTM units vs. cells
In keras.layers.LSTM(units, activation='tanh', ....), the units refers to the dimensionality or length of the hidden state or the length of the activation vector passed on the next LSTM cell/unit - th |
4,646 | Understanding LSTM units vs. cells | In my opinion, cell means a node such as hidden cell which is also called hidden node, for multilayer LSTM model,the number of cell can be computed by time_steps*num_layers, and the num_units is equal to time_steps | Understanding LSTM units vs. cells | In my opinion, cell means a node such as hidden cell which is also called hidden node, for multilayer LSTM model,the number of cell can be computed by time_steps*num_layers, and the num_units is equal | Understanding LSTM units vs. cells
In my opinion, cell means a node such as hidden cell which is also called hidden node, for multilayer LSTM model,the number of cell can be computed by time_steps*num_layers, and the num_units is equal to time_steps | Understanding LSTM units vs. cells
In my opinion, cell means a node such as hidden cell which is also called hidden node, for multilayer LSTM model,the number of cell can be computed by time_steps*num_layers, and the num_units is equal |
4,647 | Understanding LSTM units vs. cells | Quoting from TF's tutorial on RNNs:
In addition to the built-in RNN layers, the RNN API also provides cell-level APIs. Unlike RNN layers, which processes whole batches of input sequences, the RNN cell only processes a single timestep. | Understanding LSTM units vs. cells | Quoting from TF's tutorial on RNNs:
In addition to the built-in RNN layers, the RNN API also provides cell-level APIs. Unlike RNN layers, which processes whole batches of input sequences, the RNN cel | Understanding LSTM units vs. cells
Quoting from TF's tutorial on RNNs:
In addition to the built-in RNN layers, the RNN API also provides cell-level APIs. Unlike RNN layers, which processes whole batches of input sequences, the RNN cell only processes a single timestep. | Understanding LSTM units vs. cells
Quoting from TF's tutorial on RNNs:
In addition to the built-in RNN layers, the RNN API also provides cell-level APIs. Unlike RNN layers, which processes whole batches of input sequences, the RNN cel |
4,648 | Best PCA algorithm for huge number of features (>10K)? | I've implemented the Randomized SVD as given in "Halko, N., Martinsson, P. G., Shkolnisky, Y., & Tygert, M. (2010). An algorithm for the principal component analysis of large data sets. Arxiv preprint arXiv:1007.5510, 0526. Retrieved April 1, 2011, from http://arxiv.org/abs/1007.5510.". If you want to get truncated SVD... | Best PCA algorithm for huge number of features (>10K)? | I've implemented the Randomized SVD as given in "Halko, N., Martinsson, P. G., Shkolnisky, Y., & Tygert, M. (2010). An algorithm for the principal component analysis of large data sets. Arxiv preprint | Best PCA algorithm for huge number of features (>10K)?
I've implemented the Randomized SVD as given in "Halko, N., Martinsson, P. G., Shkolnisky, Y., & Tygert, M. (2010). An algorithm for the principal component analysis of large data sets. Arxiv preprint arXiv:1007.5510, 0526. Retrieved April 1, 2011, from http://arxi... | Best PCA algorithm for huge number of features (>10K)?
I've implemented the Randomized SVD as given in "Halko, N., Martinsson, P. G., Shkolnisky, Y., & Tygert, M. (2010). An algorithm for the principal component analysis of large data sets. Arxiv preprint |
4,649 | Best PCA algorithm for huge number of features (>10K)? | you could trying using a couple of options.
1- Penalized Matrix Decomposition. You apply some penalty constraints on the u's and v's to get some sparsity. Quick algorithm that has been used on genomics data
See Whitten Tibshirani. They also have an R-pkg. " A penalized matrix decomposition, with applications to sparse ... | Best PCA algorithm for huge number of features (>10K)? | you could trying using a couple of options.
1- Penalized Matrix Decomposition. You apply some penalty constraints on the u's and v's to get some sparsity. Quick algorithm that has been used on genomic | Best PCA algorithm for huge number of features (>10K)?
you could trying using a couple of options.
1- Penalized Matrix Decomposition. You apply some penalty constraints on the u's and v's to get some sparsity. Quick algorithm that has been used on genomics data
See Whitten Tibshirani. They also have an R-pkg. " A penal... | Best PCA algorithm for huge number of features (>10K)?
you could trying using a couple of options.
1- Penalized Matrix Decomposition. You apply some penalty constraints on the u's and v's to get some sparsity. Quick algorithm that has been used on genomic |
4,650 | Best PCA algorithm for huge number of features (>10K)? | It sounds like maybe you want to use the Lanczos Algorithm. Failing that, you might want to consult Golub & Van Loan. I once coded a SVD algorithm (in SML, of all languages) from their text, and it worked reasonably well. | Best PCA algorithm for huge number of features (>10K)? | It sounds like maybe you want to use the Lanczos Algorithm. Failing that, you might want to consult Golub & Van Loan. I once coded a SVD algorithm (in SML, of all languages) from their text, and it wo | Best PCA algorithm for huge number of features (>10K)?
It sounds like maybe you want to use the Lanczos Algorithm. Failing that, you might want to consult Golub & Van Loan. I once coded a SVD algorithm (in SML, of all languages) from their text, and it worked reasonably well. | Best PCA algorithm for huge number of features (>10K)?
It sounds like maybe you want to use the Lanczos Algorithm. Failing that, you might want to consult Golub & Van Loan. I once coded a SVD algorithm (in SML, of all languages) from their text, and it wo |
4,651 | Best PCA algorithm for huge number of features (>10K)? | I'd suggest trying kernel PCA which has a time/space complexity dependent on the number of examples (N) rather than number of features (P), which I think would be more suitable in your setting (P>>N)). Kernel PCA basically works with NxN kernel matrix (matrix of similarities between the data points), rather than the Px... | Best PCA algorithm for huge number of features (>10K)? | I'd suggest trying kernel PCA which has a time/space complexity dependent on the number of examples (N) rather than number of features (P), which I think would be more suitable in your setting (P>>N)) | Best PCA algorithm for huge number of features (>10K)?
I'd suggest trying kernel PCA which has a time/space complexity dependent on the number of examples (N) rather than number of features (P), which I think would be more suitable in your setting (P>>N)). Kernel PCA basically works with NxN kernel matrix (matrix of si... | Best PCA algorithm for huge number of features (>10K)?
I'd suggest trying kernel PCA which has a time/space complexity dependent on the number of examples (N) rather than number of features (P), which I think would be more suitable in your setting (P>>N)) |
4,652 | Best PCA algorithm for huge number of features (>10K)? | I seem to recall that it is possible to perform PCA by computing the eigen-decomposition of X^TX rather than XX^T and then transform to get the PCs. However I can't remember the details off-hand, but it is in Jolliffe's (excellent) book and I'll look it up when I am next at work. I'd transliterate the linear algebra ... | Best PCA algorithm for huge number of features (>10K)? | I seem to recall that it is possible to perform PCA by computing the eigen-decomposition of X^TX rather than XX^T and then transform to get the PCs. However I can't remember the details off-hand, but | Best PCA algorithm for huge number of features (>10K)?
I seem to recall that it is possible to perform PCA by computing the eigen-decomposition of X^TX rather than XX^T and then transform to get the PCs. However I can't remember the details off-hand, but it is in Jolliffe's (excellent) book and I'll look it up when I ... | Best PCA algorithm for huge number of features (>10K)?
I seem to recall that it is possible to perform PCA by computing the eigen-decomposition of X^TX rather than XX^T and then transform to get the PCs. However I can't remember the details off-hand, but |
4,653 | Best PCA algorithm for huge number of features (>10K)? | See Sam Roweis' paper, EM Algorithms for PCA and SPCA. | Best PCA algorithm for huge number of features (>10K)? | See Sam Roweis' paper, EM Algorithms for PCA and SPCA. | Best PCA algorithm for huge number of features (>10K)?
See Sam Roweis' paper, EM Algorithms for PCA and SPCA. | Best PCA algorithm for huge number of features (>10K)?
See Sam Roweis' paper, EM Algorithms for PCA and SPCA. |
4,654 | Best PCA algorithm for huge number of features (>10K)? | 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.
There is also the bootstrap method by Fisher et al, de... | Best PCA algorithm for huge number of features (>10K)? | 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.
| Best PCA algorithm for huge number of features (>10K)?
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.
... | Best PCA algorithm for huge number of features (>10K)?
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.
|
4,655 | Multivariate linear regression vs neural network? | Neural networks can in principle model nonlinearities automatically (see the universal approximation theorem), which you would need to explicitly model using transformations (splines etc.) in linear regression.
The caveat: the temptation to overfit can be (even) stronger in neural networks than in regression, since add... | Multivariate linear regression vs neural network? | Neural networks can in principle model nonlinearities automatically (see the universal approximation theorem), which you would need to explicitly model using transformations (splines etc.) in linear r | Multivariate linear regression vs neural network?
Neural networks can in principle model nonlinearities automatically (see the universal approximation theorem), which you would need to explicitly model using transformations (splines etc.) in linear regression.
The caveat: the temptation to overfit can be (even) stronge... | Multivariate linear regression vs neural network?
Neural networks can in principle model nonlinearities automatically (see the universal approximation theorem), which you would need to explicitly model using transformations (splines etc.) in linear r |
4,656 | Multivariate linear regression vs neural network? | You mention linear regression. This is related to logistic regression, which has a similar fast optimization algorithm. If you have bounds on the target values, such as with a classification problem, you can view logistic regression as a generalization of linear regression.
Neural networks are strictly more general tha... | Multivariate linear regression vs neural network? | You mention linear regression. This is related to logistic regression, which has a similar fast optimization algorithm. If you have bounds on the target values, such as with a classification problem, | Multivariate linear regression vs neural network?
You mention linear regression. This is related to logistic regression, which has a similar fast optimization algorithm. If you have bounds on the target values, such as with a classification problem, you can view logistic regression as a generalization of linear regress... | Multivariate linear regression vs neural network?
You mention linear regression. This is related to logistic regression, which has a similar fast optimization algorithm. If you have bounds on the target values, such as with a classification problem, |
4,657 | Multivariate linear regression vs neural network? | Linear Regression aims to separate the data that is linearly separable, yes you may use additional third> degree polynomials but in that way you indicated again some assumptions about the data you have since you define the objective function's structure. In Neural Net. generally you have input layer that creates the li... | Multivariate linear regression vs neural network? | Linear Regression aims to separate the data that is linearly separable, yes you may use additional third> degree polynomials but in that way you indicated again some assumptions about the data you hav | Multivariate linear regression vs neural network?
Linear Regression aims to separate the data that is linearly separable, yes you may use additional third> degree polynomials but in that way you indicated again some assumptions about the data you have since you define the objective function's structure. In Neural Net. ... | Multivariate linear regression vs neural network?
Linear Regression aims to separate the data that is linearly separable, yes you may use additional third> degree polynomials but in that way you indicated again some assumptions about the data you hav |
4,658 | Empirical justification for the one standard error rule when using cross-validation | For an empirical justification, have a look at page 12 on these Tibshirani data-mining course notes, which shows the CV error as a function of lambda for a particular modeling problem. The suggestion seems to be that, below a certain value, all lambdas give about the same CV error. This makes sense because, unlike ridg... | Empirical justification for the one standard error rule when using cross-validation | For an empirical justification, have a look at page 12 on these Tibshirani data-mining course notes, which shows the CV error as a function of lambda for a particular modeling problem. The suggestion | Empirical justification for the one standard error rule when using cross-validation
For an empirical justification, have a look at page 12 on these Tibshirani data-mining course notes, which shows the CV error as a function of lambda for a particular modeling problem. The suggestion seems to be that, below a certain va... | Empirical justification for the one standard error rule when using cross-validation
For an empirical justification, have a look at page 12 on these Tibshirani data-mining course notes, which shows the CV error as a function of lambda for a particular modeling problem. The suggestion |
4,659 | Empirical justification for the one standard error rule when using cross-validation | The following is not an empirical study, which is why I originally wanted to post it as a comment, not an answer - but it really turns out to be too long for a comment.
Cawley & Talbot (J of Machine Learning Research, 2010) draw attention to the difference between overfitting during the model selection phase and overfi... | Empirical justification for the one standard error rule when using cross-validation | The following is not an empirical study, which is why I originally wanted to post it as a comment, not an answer - but it really turns out to be too long for a comment.
Cawley & Talbot (J of Machine L | Empirical justification for the one standard error rule when using cross-validation
The following is not an empirical study, which is why I originally wanted to post it as a comment, not an answer - but it really turns out to be too long for a comment.
Cawley & Talbot (J of Machine Learning Research, 2010) draw attenti... | Empirical justification for the one standard error rule when using cross-validation
The following is not an empirical study, which is why I originally wanted to post it as a comment, not an answer - but it really turns out to be too long for a comment.
Cawley & Talbot (J of Machine L |
4,660 | Empirical justification for the one standard error rule when using cross-validation | The number of variables selected by the Lasso estimator is decided by a penalty value $\lambda$. The larger is $\lambda$, the smaller is the set of selected variables.
Let $\hat S(\lambda)$ be the set of selected variables using as penalty $\lambda$.
Let $\lambda^ \star$ be the penalty selected using the minimum o... | Empirical justification for the one standard error rule when using cross-validation | The number of variables selected by the Lasso estimator is decided by a penalty value $\lambda$. The larger is $\lambda$, the smaller is the set of selected variables.
Let $\hat S(\lambda)$ be the | Empirical justification for the one standard error rule when using cross-validation
The number of variables selected by the Lasso estimator is decided by a penalty value $\lambda$. The larger is $\lambda$, the smaller is the set of selected variables.
Let $\hat S(\lambda)$ be the set of selected variables using as p... | Empirical justification for the one standard error rule when using cross-validation
The number of variables selected by the Lasso estimator is decided by a penalty value $\lambda$. The larger is $\lambda$, the smaller is the set of selected variables.
Let $\hat S(\lambda)$ be the |
4,661 | What do "endogeneity" and "exogeneity" mean substantively? | JohnRos's answer is very good. In plain English, endogeneity means you got the causation wrong. That the model you wrote down and estimated does not properly capture the way causation works in the real world. When you write:
\begin{equation}
Y_i=\beta_0+\beta_1X_i+\epsilon_i
\end{equation}
you can think of this equa... | What do "endogeneity" and "exogeneity" mean substantively? | JohnRos's answer is very good. In plain English, endogeneity means you got the causation wrong. That the model you wrote down and estimated does not properly capture the way causation works in the r | What do "endogeneity" and "exogeneity" mean substantively?
JohnRos's answer is very good. In plain English, endogeneity means you got the causation wrong. That the model you wrote down and estimated does not properly capture the way causation works in the real world. When you write:
\begin{equation}
Y_i=\beta_0+\bet... | What do "endogeneity" and "exogeneity" mean substantively?
JohnRos's answer is very good. In plain English, endogeneity means you got the causation wrong. That the model you wrote down and estimated does not properly capture the way causation works in the r |
4,662 | What do "endogeneity" and "exogeneity" mean substantively? | Let me use an example:
Say you want to quantify the (causal) effect of education on income. You take education years and income data and regress one against the other. Did you recover what you wanted? Probably not! This is because the income is also caused by things other than education, but which are correlated to edu... | What do "endogeneity" and "exogeneity" mean substantively? | Let me use an example:
Say you want to quantify the (causal) effect of education on income. You take education years and income data and regress one against the other. Did you recover what you wanted? | What do "endogeneity" and "exogeneity" mean substantively?
Let me use an example:
Say you want to quantify the (causal) effect of education on income. You take education years and income data and regress one against the other. Did you recover what you wanted? Probably not! This is because the income is also caused by t... | What do "endogeneity" and "exogeneity" mean substantively?
Let me use an example:
Say you want to quantify the (causal) effect of education on income. You take education years and income data and regress one against the other. Did you recover what you wanted? |
4,663 | What do "endogeneity" and "exogeneity" mean substantively? | User25901 is looking for a straight-forward, simple, real-world explanation of what the terms exogenous and endogenous mean. To respond with arcane examples or mathematical definitions is to not really answer the question that was asked.
How do I, 'get a gut understanding of these two terms?'
Here's what I came up wit... | What do "endogeneity" and "exogeneity" mean substantively? | User25901 is looking for a straight-forward, simple, real-world explanation of what the terms exogenous and endogenous mean. To respond with arcane examples or mathematical definitions is to not real | What do "endogeneity" and "exogeneity" mean substantively?
User25901 is looking for a straight-forward, simple, real-world explanation of what the terms exogenous and endogenous mean. To respond with arcane examples or mathematical definitions is to not really answer the question that was asked.
How do I, 'get a gut u... | What do "endogeneity" and "exogeneity" mean substantively?
User25901 is looking for a straight-forward, simple, real-world explanation of what the terms exogenous and endogenous mean. To respond with arcane examples or mathematical definitions is to not real |
4,664 | What do "endogeneity" and "exogeneity" mean substantively? | The OLS regression, by construction, gives $X'\epsilon=0$. Actually that is not correct. It gives $X'\hat\epsilon=0$ by construction. Your estimated residuals are uncorrelated with your regressors, but your estimated residuals are "wrong" in a sense.
If the true data-generating-process operates by $Y=\alpha +\beta... | What do "endogeneity" and "exogeneity" mean substantively? | The OLS regression, by construction, gives $X'\epsilon=0$. Actually that is not correct. It gives $X'\hat\epsilon=0$ by construction. Your estimated residuals are uncorrelated with your regressors, | What do "endogeneity" and "exogeneity" mean substantively?
The OLS regression, by construction, gives $X'\epsilon=0$. Actually that is not correct. It gives $X'\hat\epsilon=0$ by construction. Your estimated residuals are uncorrelated with your regressors, but your estimated residuals are "wrong" in a sense.
If th... | What do "endogeneity" and "exogeneity" mean substantively?
The OLS regression, by construction, gives $X'\epsilon=0$. Actually that is not correct. It gives $X'\hat\epsilon=0$ by construction. Your estimated residuals are uncorrelated with your regressors, |
4,665 | What do "endogeneity" and "exogeneity" mean substantively? | Think of a system as $x,y$. When we're trying to explain it by a model $y=f(x)+\varepsilon$, is the error $\varepsilon$ a part of the system or not?
When the error is not part of the system, we call it exogenous, i.e. it's added to $f(x)$ after $x$ had its input into the system.
When the error is a part of the system, ... | What do "endogeneity" and "exogeneity" mean substantively? | Think of a system as $x,y$. When we're trying to explain it by a model $y=f(x)+\varepsilon$, is the error $\varepsilon$ a part of the system or not?
When the error is not part of the system, we call i | What do "endogeneity" and "exogeneity" mean substantively?
Think of a system as $x,y$. When we're trying to explain it by a model $y=f(x)+\varepsilon$, is the error $\varepsilon$ a part of the system or not?
When the error is not part of the system, we call it exogenous, i.e. it's added to $f(x)$ after $x$ had its inpu... | What do "endogeneity" and "exogeneity" mean substantively?
Think of a system as $x,y$. When we're trying to explain it by a model $y=f(x)+\varepsilon$, is the error $\varepsilon$ a part of the system or not?
When the error is not part of the system, we call i |
4,666 | What do "endogeneity" and "exogeneity" mean substantively? | In regression we want to capture the quantitative impact of an independent variable (which we assume is exogenous and not being itself dependent on something else) on an identified dependent variable. We want to know what net effect an exogenous variable has on a dependent variable- meaning the independent variable sho... | What do "endogeneity" and "exogeneity" mean substantively? | In regression we want to capture the quantitative impact of an independent variable (which we assume is exogenous and not being itself dependent on something else) on an identified dependent variable. | What do "endogeneity" and "exogeneity" mean substantively?
In regression we want to capture the quantitative impact of an independent variable (which we assume is exogenous and not being itself dependent on something else) on an identified dependent variable. We want to know what net effect an exogenous variable has on... | What do "endogeneity" and "exogeneity" mean substantively?
In regression we want to capture the quantitative impact of an independent variable (which we assume is exogenous and not being itself dependent on something else) on an identified dependent variable. |
4,667 | Debunking wrong CLT statement | This is quite a ubiquitous misunderstanding of the central limit theorem, which I have also encountered in my statistical teaching. Over the years I have encountered this problem so often that I have developed a Socratic method to deal with it. I identify a student that has accepted this idea and then engage the stud... | Debunking wrong CLT statement | This is quite a ubiquitous misunderstanding of the central limit theorem, which I have also encountered in my statistical teaching. Over the years I have encountered this problem so often that I have | Debunking wrong CLT statement
This is quite a ubiquitous misunderstanding of the central limit theorem, which I have also encountered in my statistical teaching. Over the years I have encountered this problem so often that I have developed a Socratic method to deal with it. I identify a student that has accepted this... | Debunking wrong CLT statement
This is quite a ubiquitous misunderstanding of the central limit theorem, which I have also encountered in my statistical teaching. Over the years I have encountered this problem so often that I have |
4,668 | Debunking wrong CLT statement | As whuber notes, you can always point your collaborators to a binary discrete distribution. But they might consider that "cheating" and retreat to the weaker claim that the proposed statement only applied to continuous distributions.
So use the uniform distribution on the unit interval $[0,1]$. It has a mean of $\mu=0.... | Debunking wrong CLT statement | As whuber notes, you can always point your collaborators to a binary discrete distribution. But they might consider that "cheating" and retreat to the weaker claim that the proposed statement only app | Debunking wrong CLT statement
As whuber notes, you can always point your collaborators to a binary discrete distribution. But they might consider that "cheating" and retreat to the weaker claim that the proposed statement only applied to continuous distributions.
So use the uniform distribution on the unit interval $[0... | Debunking wrong CLT statement
As whuber notes, you can always point your collaborators to a binary discrete distribution. But they might consider that "cheating" and retreat to the weaker claim that the proposed statement only app |
4,669 | Debunking wrong CLT statement | The central limit theorem states that the mean of the data will become normally distributed as the sample size increases, it says nothing about the data itself. Another way to put it is the distribution of the parameter (the mean) is normal, but that is entirely separate from the distribution of the underlying data.
M... | Debunking wrong CLT statement | The central limit theorem states that the mean of the data will become normally distributed as the sample size increases, it says nothing about the data itself. Another way to put it is the distribut | Debunking wrong CLT statement
The central limit theorem states that the mean of the data will become normally distributed as the sample size increases, it says nothing about the data itself. Another way to put it is the distribution of the parameter (the mean) is normal, but that is entirely separate from the distribu... | Debunking wrong CLT statement
The central limit theorem states that the mean of the data will become normally distributed as the sample size increases, it says nothing about the data itself. Another way to put it is the distribut |
4,670 | Debunking wrong CLT statement | CLT is about convergence of a sum of random variables. If we have an iid sample $X_1,...,X_n$, where $EX_i=\mu$ and $Var(X_i)<\infty$ then
$$
\frac{1}{\sqrt{n}}\left(X_1+...+X_n-n\mu\right) \to N(0, Var(X_i))
$$
This statement is solely about closeness of a distribution of suitably normalized sum $(X_1+...+X_n)$ to th... | Debunking wrong CLT statement | CLT is about convergence of a sum of random variables. If we have an iid sample $X_1,...,X_n$, where $EX_i=\mu$ and $Var(X_i)<\infty$ then
$$
\frac{1}{\sqrt{n}}\left(X_1+...+X_n-n\mu\right) \to N(0, | Debunking wrong CLT statement
CLT is about convergence of a sum of random variables. If we have an iid sample $X_1,...,X_n$, where $EX_i=\mu$ and $Var(X_i)<\infty$ then
$$
\frac{1}{\sqrt{n}}\left(X_1+...+X_n-n\mu\right) \to N(0, Var(X_i))
$$
This statement is solely about closeness of a distribution of suitably normal... | Debunking wrong CLT statement
CLT is about convergence of a sum of random variables. If we have an iid sample $X_1,...,X_n$, where $EX_i=\mu$ and $Var(X_i)<\infty$ then
$$
\frac{1}{\sqrt{n}}\left(X_1+...+X_n-n\mu\right) \to N(0, |
4,671 | Debunking wrong CLT statement | This is how I like to visualize the CLT. I'm not 100% sure the argument is correct though, please check.
Start with a population of values whose distribution is nowhere near normal. E.g., a uniform distribution:
X <- runif(n= 50000)
hist(X)
Now, take $n$ samples from this population, calculate the mean of each sample... | Debunking wrong CLT statement | This is how I like to visualize the CLT. I'm not 100% sure the argument is correct though, please check.
Start with a population of values whose distribution is nowhere near normal. E.g., a uniform di | Debunking wrong CLT statement
This is how I like to visualize the CLT. I'm not 100% sure the argument is correct though, please check.
Start with a population of values whose distribution is nowhere near normal. E.g., a uniform distribution:
X <- runif(n= 50000)
hist(X)
Now, take $n$ samples from this population, cal... | Debunking wrong CLT statement
This is how I like to visualize the CLT. I'm not 100% sure the argument is correct though, please check.
Start with a population of values whose distribution is nowhere near normal. E.g., a uniform di |
4,672 | Debunking wrong CLT statement | The point of confusion here is what is actually converging to a normal distribution. I think the easiest way to overcome this is to explain examples of the extremes of a sampling distribution, one with one measurement per sample (just as if taking measurements straight from the population as you describe) and one where... | Debunking wrong CLT statement | The point of confusion here is what is actually converging to a normal distribution. I think the easiest way to overcome this is to explain examples of the extremes of a sampling distribution, one wit | Debunking wrong CLT statement
The point of confusion here is what is actually converging to a normal distribution. I think the easiest way to overcome this is to explain examples of the extremes of a sampling distribution, one with one measurement per sample (just as if taking measurements straight from the population ... | Debunking wrong CLT statement
The point of confusion here is what is actually converging to a normal distribution. I think the easiest way to overcome this is to explain examples of the extremes of a sampling distribution, one wit |
4,673 | R - QQPlot: how to see whether data are normally distributed | "The test showed that it is likely that the population is normally distributed."
No; it didn't show that.
Hypothesis tests don't tell you how likely the null is. In fact you can bet this null is false.
The Q-Q plot doesn't give a strong indication of non-normality (the plot is fairly straight); there's perhaps a sligh... | R - QQPlot: how to see whether data are normally distributed | "The test showed that it is likely that the population is normally distributed."
No; it didn't show that.
Hypothesis tests don't tell you how likely the null is. In fact you can bet this null is fals | R - QQPlot: how to see whether data are normally distributed
"The test showed that it is likely that the population is normally distributed."
No; it didn't show that.
Hypothesis tests don't tell you how likely the null is. In fact you can bet this null is false.
The Q-Q plot doesn't give a strong indication of non-nor... | R - QQPlot: how to see whether data are normally distributed
"The test showed that it is likely that the population is normally distributed."
No; it didn't show that.
Hypothesis tests don't tell you how likely the null is. In fact you can bet this null is fals |
4,674 | R - QQPlot: how to see whether data are normally distributed | If the data is normally distributed, the points in the QQ-normal plot lie on a straight diagonal line. You can add this line to you QQ plot with the command qqline(x), where x is the vector of values.
Examples of normal and non-normal distribution:
Normal distribution
set.seed(42)
x <- rnorm(100)
The QQ-normal plot wi... | R - QQPlot: how to see whether data are normally distributed | If the data is normally distributed, the points in the QQ-normal plot lie on a straight diagonal line. You can add this line to you QQ plot with the command qqline(x), where x is the vector of values. | R - QQPlot: how to see whether data are normally distributed
If the data is normally distributed, the points in the QQ-normal plot lie on a straight diagonal line. You can add this line to you QQ plot with the command qqline(x), where x is the vector of values.
Examples of normal and non-normal distribution:
Normal dis... | R - QQPlot: how to see whether data are normally distributed
If the data is normally distributed, the points in the QQ-normal plot lie on a straight diagonal line. You can add this line to you QQ plot with the command qqline(x), where x is the vector of values. |
4,675 | R - QQPlot: how to see whether data are normally distributed | Some tools for checking the validity of the assumption of normality in R
library(moments)
library(nortest)
library(e1071)
set.seed(777)
x <- rnorm(250,10,1)
# skewness and kurtosis, they should be around (0,3)
skewness(x)
kurtosis(x)
# Shapiro-Wilks test
shapiro.test(x)
# Kolmogorov-Smirnov test
ks.test(x,"pnorm",m... | R - QQPlot: how to see whether data are normally distributed | Some tools for checking the validity of the assumption of normality in R
library(moments)
library(nortest)
library(e1071)
set.seed(777)
x <- rnorm(250,10,1)
# skewness and kurtosis, they should be a | R - QQPlot: how to see whether data are normally distributed
Some tools for checking the validity of the assumption of normality in R
library(moments)
library(nortest)
library(e1071)
set.seed(777)
x <- rnorm(250,10,1)
# skewness and kurtosis, they should be around (0,3)
skewness(x)
kurtosis(x)
# Shapiro-Wilks test
s... | R - QQPlot: how to see whether data are normally distributed
Some tools for checking the validity of the assumption of normality in R
library(moments)
library(nortest)
library(e1071)
set.seed(777)
x <- rnorm(250,10,1)
# skewness and kurtosis, they should be a |
4,676 | R - QQPlot: how to see whether data are normally distributed | While it's a good idea to check visually whether your intuition matches the result of some test, you cannot expect this to be easy every time. If the people trying to detect the Higgs Boson would only trust their results if they could visually assess them, they would need a very sharp eye.
Especially with big datasets ... | R - QQPlot: how to see whether data are normally distributed | While it's a good idea to check visually whether your intuition matches the result of some test, you cannot expect this to be easy every time. If the people trying to detect the Higgs Boson would only | R - QQPlot: how to see whether data are normally distributed
While it's a good idea to check visually whether your intuition matches the result of some test, you cannot expect this to be easy every time. If the people trying to detect the Higgs Boson would only trust their results if they could visually assess them, th... | R - QQPlot: how to see whether data are normally distributed
While it's a good idea to check visually whether your intuition matches the result of some test, you cannot expect this to be easy every time. If the people trying to detect the Higgs Boson would only |
4,677 | R - QQPlot: how to see whether data are normally distributed | I like the version out of the 'R' library car because it provides not only the central tendency but the confidence intervals. It gives visual guidance to help confirm whether the behavior of the data is consistent with the hypothetical distribution.
library(car)
qqPlot(lm(prestige ~ income + education + type, data=Dun... | R - QQPlot: how to see whether data are normally distributed | I like the version out of the 'R' library car because it provides not only the central tendency but the confidence intervals. It gives visual guidance to help confirm whether the behavior of the data | R - QQPlot: how to see whether data are normally distributed
I like the version out of the 'R' library car because it provides not only the central tendency but the confidence intervals. It gives visual guidance to help confirm whether the behavior of the data is consistent with the hypothetical distribution.
library(c... | R - QQPlot: how to see whether data are normally distributed
I like the version out of the 'R' library car because it provides not only the central tendency but the confidence intervals. It gives visual guidance to help confirm whether the behavior of the data |
4,678 | How to tell the probability of failure if there were no failures? | The probability that a product will fail is surely a function of time and use. We don't have any data on use, and with only one year there are no failures (congratulations!). Thus, this aspect (called the survival function), cannot be estimated from your data.
You can think of failures within one year as draws from... | How to tell the probability of failure if there were no failures? | The probability that a product will fail is surely a function of time and use. We don't have any data on use, and with only one year there are no failures (congratulations!). Thus, this aspect (call | How to tell the probability of failure if there were no failures?
The probability that a product will fail is surely a function of time and use. We don't have any data on use, and with only one year there are no failures (congratulations!). Thus, this aspect (called the survival function), cannot be estimated from yo... | How to tell the probability of failure if there were no failures?
The probability that a product will fail is surely a function of time and use. We don't have any data on use, and with only one year there are no failures (congratulations!). Thus, this aspect (call |
4,679 | How to tell the probability of failure if there were no failures? | You can take a bayesian approach. denote the probability of failure by $\Theta$ and think of it as a random variable. A priori, before you see the results of the experiments, you might believe that $\Theta \sim U(0,1)$. If you trust the engineers to make this product reliable, maybe you can take $\Theta \sim U(0,0.1)$ ... | How to tell the probability of failure if there were no failures? | You can take a bayesian approach. denote the probability of failure by $\Theta$ and think of it as a random variable. A priori, before you see the results of the experiments, you might believe that $\ | How to tell the probability of failure if there were no failures?
You can take a bayesian approach. denote the probability of failure by $\Theta$ and think of it as a random variable. A priori, before you see the results of the experiments, you might believe that $\Theta \sim U(0,1)$. If you trust the engineers to make... | How to tell the probability of failure if there were no failures?
You can take a bayesian approach. denote the probability of failure by $\Theta$ and think of it as a random variable. A priori, before you see the results of the experiments, you might believe that $\ |
4,680 | How to tell the probability of failure if there were no failures? | Rather than computing a probability, why not predict how many products might fail?
Modeling the Observations
There are $n=100000$ products in the field and another $m=10000$ under consideration. Assume their failures are all independent and constant with probability $p$.
We may model this situation by means of a Binom... | How to tell the probability of failure if there were no failures? | Rather than computing a probability, why not predict how many products might fail?
Modeling the Observations
There are $n=100000$ products in the field and another $m=10000$ under consideration. Assu | How to tell the probability of failure if there were no failures?
Rather than computing a probability, why not predict how many products might fail?
Modeling the Observations
There are $n=100000$ products in the field and another $m=10000$ under consideration. Assume their failures are all independent and constant wit... | How to tell the probability of failure if there were no failures?
Rather than computing a probability, why not predict how many products might fail?
Modeling the Observations
There are $n=100000$ products in the field and another $m=10000$ under consideration. Assu |
4,681 | How to tell the probability of failure if there were no failures? | The following is a Bayesian answer to "Out of 10,000 new products, how many are expected to fail if all the former 100,000 produced didn't fail?", but you should consider the sensitivity to different priors.
Suppose that $X_1,\dots,X_n$ are conditionally independent and identically distributed, given $\Theta=\theta$, ... | How to tell the probability of failure if there were no failures? | The following is a Bayesian answer to "Out of 10,000 new products, how many are expected to fail if all the former 100,000 produced didn't fail?", but you should consider the sensitivity to different | How to tell the probability of failure if there were no failures?
The following is a Bayesian answer to "Out of 10,000 new products, how many are expected to fail if all the former 100,000 produced didn't fail?", but you should consider the sensitivity to different priors.
Suppose that $X_1,\dots,X_n$ are conditionall... | How to tell the probability of failure if there were no failures?
The following is a Bayesian answer to "Out of 10,000 new products, how many are expected to fail if all the former 100,000 produced didn't fail?", but you should consider the sensitivity to different |
4,682 | How to tell the probability of failure if there were no failures? | Using Laplace's sunrise problem approach, we get the probability that a product would fail within a year $$p=\frac{1}{100000+1}$$. Next, the probability that of $n$ new products none fails within a year is $$(1-p)^n$$
Hence, the probability that at least one product of $n$ will fail in next year is $$1-\left(1-\frac{1}... | How to tell the probability of failure if there were no failures? | Using Laplace's sunrise problem approach, we get the probability that a product would fail within a year $$p=\frac{1}{100000+1}$$. Next, the probability that of $n$ new products none fails within a ye | How to tell the probability of failure if there were no failures?
Using Laplace's sunrise problem approach, we get the probability that a product would fail within a year $$p=\frac{1}{100000+1}$$. Next, the probability that of $n$ new products none fails within a year is $$(1-p)^n$$
Hence, the probability that at least... | How to tell the probability of failure if there were no failures?
Using Laplace's sunrise problem approach, we get the probability that a product would fail within a year $$p=\frac{1}{100000+1}$$. Next, the probability that of $n$ new products none fails within a ye |
4,683 | How to tell the probability of failure if there were no failures? | Several good answers were provided for this question, but recently I had a chance to review few resources on this topic and so I decided to share the results.
There are multiple possible estimators for zero-failures data. Let's denote $k=0$ as number of failures and $n$ as sample size. Maximum likelihood estimator for ... | How to tell the probability of failure if there were no failures? | Several good answers were provided for this question, but recently I had a chance to review few resources on this topic and so I decided to share the results.
There are multiple possible estimators fo | How to tell the probability of failure if there were no failures?
Several good answers were provided for this question, but recently I had a chance to review few resources on this topic and so I decided to share the results.
There are multiple possible estimators for zero-failures data. Let's denote $k=0$ as number of ... | How to tell the probability of failure if there were no failures?
Several good answers were provided for this question, but recently I had a chance to review few resources on this topic and so I decided to share the results.
There are multiple possible estimators fo |
4,684 | How to tell the probability of failure if there were no failures? | You really need to go back to the designers of your products.
It is a fundamental engineering problem not an observational statistical one.
They will have an idea of the failure probability of each component and from that the net failure probabilty of the total assembled product.
They can give you the expected number o... | How to tell the probability of failure if there were no failures? | You really need to go back to the designers of your products.
It is a fundamental engineering problem not an observational statistical one.
They will have an idea of the failure probability of each co | How to tell the probability of failure if there were no failures?
You really need to go back to the designers of your products.
It is a fundamental engineering problem not an observational statistical one.
They will have an idea of the failure probability of each component and from that the net failure probabilty of th... | How to tell the probability of failure if there were no failures?
You really need to go back to the designers of your products.
It is a fundamental engineering problem not an observational statistical one.
They will have an idea of the failure probability of each co |
4,685 | How to tell the probability of failure if there were no failures? | This is similar to a problem I faced when we introduced a new manufacturing process to eliminate a failure in production.
The new system produced no failures so people were asking the same question: how do we predict the failure rate? In your case, because you have stipulated a period over which the failure can occur ... | How to tell the probability of failure if there were no failures? | This is similar to a problem I faced when we introduced a new manufacturing process to eliminate a failure in production.
The new system produced no failures so people were asking the same question: | How to tell the probability of failure if there were no failures?
This is similar to a problem I faced when we introduced a new manufacturing process to eliminate a failure in production.
The new system produced no failures so people were asking the same question: how do we predict the failure rate? In your case, beca... | How to tell the probability of failure if there were no failures?
This is similar to a problem I faced when we introduced a new manufacturing process to eliminate a failure in production.
The new system produced no failures so people were asking the same question: |
4,686 | How to tell the probability of failure if there were no failures? | Median unbiased estimates can be used to estimate sample proportions and (non-singular) 95% CIs in Bernoulli samples with no variability. In a sample with no positive cases, you can estimate the upper bound of a 95% confidence interval with the following formula:
$$ p_{1-\alpha/2} : P(Y=0)/2 + P(Y>y) > 0.975$$
that is ... | How to tell the probability of failure if there were no failures? | Median unbiased estimates can be used to estimate sample proportions and (non-singular) 95% CIs in Bernoulli samples with no variability. In a sample with no positive cases, you can estimate the upper | How to tell the probability of failure if there were no failures?
Median unbiased estimates can be used to estimate sample proportions and (non-singular) 95% CIs in Bernoulli samples with no variability. In a sample with no positive cases, you can estimate the upper bound of a 95% confidence interval with the following... | How to tell the probability of failure if there were no failures?
Median unbiased estimates can be used to estimate sample proportions and (non-singular) 95% CIs in Bernoulli samples with no variability. In a sample with no positive cases, you can estimate the upper |
4,687 | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite? | The variance of a weighted sum $\sum_i a_i X_i$ of random variables must be nonnegative
for all choices of real numbers $a_i$.
Since the variance can be expressed as
$$\operatorname{var}\left(\sum_i a_i X_i\right) = \sum_i \sum_j a_ia_j \operatorname{cov}(X_i,X_j) = \sum_i \sum_j a_ia_j \Sigma_{i,j},$$
we have that the... | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to | The variance of a weighted sum $\sum_i a_i X_i$ of random variables must be nonnegative
for all choices of real numbers $a_i$.
Since the variance can be expressed as
$$\operatorname{var}\left(\sum_i a | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite?
The variance of a weighted sum $\sum_i a_i X_i$ of random variables must be nonnegative
for all choices of real numbers $a_i$.
Since the variance can be expressed as
$$\operatorname{var}\left(\... | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to
The variance of a weighted sum $\sum_i a_i X_i$ of random variables must be nonnegative
for all choices of real numbers $a_i$.
Since the variance can be expressed as
$$\operatorname{var}\left(\sum_i a |
4,688 | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite? | The answer is quite simple.
The correlation matrix is defined thus:
Let $X = [x_1, x_2, ..., x_n]$ be the $m\times n$ data matrix: $m$ observations, $n$ variables.
Define $X_b= [\frac{(x_1-\mu_1 e)}{s_1}, \frac{(x_2-\mu_2 e)}{s_2}, \frac{(x_3-\mu_3 e)}{s_3}, ...]$ as the matrix of normalized data, with $\mu_1$ being me... | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to | The answer is quite simple.
The correlation matrix is defined thus:
Let $X = [x_1, x_2, ..., x_n]$ be the $m\times n$ data matrix: $m$ observations, $n$ variables.
Define $X_b= [\frac{(x_1-\mu_1 e)}{s | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite?
The answer is quite simple.
The correlation matrix is defined thus:
Let $X = [x_1, x_2, ..., x_n]$ be the $m\times n$ data matrix: $m$ observations, $n$ variables.
Define $X_b= [\frac{(x_1-\mu_... | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to
The answer is quite simple.
The correlation matrix is defined thus:
Let $X = [x_1, x_2, ..., x_n]$ be the $m\times n$ data matrix: $m$ observations, $n$ variables.
Define $X_b= [\frac{(x_1-\mu_1 e)}{s |
4,689 | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite? | (Possible looseness in reasoning would be mine. I'm not a mathematician: this is a depiction, not proof, and is from my numeric experimenting, not from books.)
A positive semidefinite (psd) matrix, also called Gramian matrix, is a
matrix with no negative eigenvalues. Matrix with negative eigenvalues is not positive se... | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to | (Possible looseness in reasoning would be mine. I'm not a mathematician: this is a depiction, not proof, and is from my numeric experimenting, not from books.)
A positive semidefinite (psd) matrix, a | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite?
(Possible looseness in reasoning would be mine. I'm not a mathematician: this is a depiction, not proof, and is from my numeric experimenting, not from books.)
A positive semidefinite (psd) ma... | Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to
(Possible looseness in reasoning would be mine. I'm not a mathematician: this is a depiction, not proof, and is from my numeric experimenting, not from books.)
A positive semidefinite (psd) matrix, a |
4,690 | Why do my p-values differ between logistic regression output, chi-squared test, and the confidence interval for the OR? | With generalized linear models, there are three different types of statistical tests that can be run. These are: Wald tests, likelihood ratio tests, and score tests. The excellent UCLA statistics help site has a discussion of them here. The following figure (copied from their site) helps to illustrate them:
The ... | Why do my p-values differ between logistic regression output, chi-squared test, and the confidence i | With generalized linear models, there are three different types of statistical tests that can be run. These are: Wald tests, likelihood ratio tests, and score tests. The excellent UCLA statistics he | Why do my p-values differ between logistic regression output, chi-squared test, and the confidence interval for the OR?
With generalized linear models, there are three different types of statistical tests that can be run. These are: Wald tests, likelihood ratio tests, and score tests. The excellent UCLA statistics he... | Why do my p-values differ between logistic regression output, chi-squared test, and the confidence i
With generalized linear models, there are three different types of statistical tests that can be run. These are: Wald tests, likelihood ratio tests, and score tests. The excellent UCLA statistics he |
4,691 | Fast linear regression robust to outliers | If your data contains a single outlier, then it can be found reliably using the approach you suggest (without the iterations though). A formal approach to this
is
Cook, R. Dennis (1979). Influential Observations in Linear Regression. Journal of the American Statistical Association (American Statistical Association) 74... | Fast linear regression robust to outliers | If your data contains a single outlier, then it can be found reliably using the approach you suggest (without the iterations though). A formal approach to this
is
Cook, R. Dennis (1979). Influential | Fast linear regression robust to outliers
If your data contains a single outlier, then it can be found reliably using the approach you suggest (without the iterations though). A formal approach to this
is
Cook, R. Dennis (1979). Influential Observations in Linear Regression. Journal of the American Statistical Associa... | Fast linear regression robust to outliers
If your data contains a single outlier, then it can be found reliably using the approach you suggest (without the iterations though). A formal approach to this
is
Cook, R. Dennis (1979). Influential |
4,692 | Fast linear regression robust to outliers | For simple regression (single x), there's something to be said for the Theil-Sen line in terms of robustness to y-outliers and to influential points as well as generally good efficiency (at the normal) compared to LS for the slope. The breakdown point for the slope is nearly 30%; as long as the intercept (there are a v... | Fast linear regression robust to outliers | For simple regression (single x), there's something to be said for the Theil-Sen line in terms of robustness to y-outliers and to influential points as well as generally good efficiency (at the normal | Fast linear regression robust to outliers
For simple regression (single x), there's something to be said for the Theil-Sen line in terms of robustness to y-outliers and to influential points as well as generally good efficiency (at the normal) compared to LS for the slope. The breakdown point for the slope is nearly 30... | Fast linear regression robust to outliers
For simple regression (single x), there's something to be said for the Theil-Sen line in terms of robustness to y-outliers and to influential points as well as generally good efficiency (at the normal |
4,693 | Fast linear regression robust to outliers | Have you looked at RANSAC (Wikipedia)?
This should be good at computing a reasonable linear model even when there are a lot of outliers and noise, as it is built on the assumption that only part of the data will actually belong to the mechanism. | Fast linear regression robust to outliers | Have you looked at RANSAC (Wikipedia)?
This should be good at computing a reasonable linear model even when there are a lot of outliers and noise, as it is built on the assumption that only part of th | Fast linear regression robust to outliers
Have you looked at RANSAC (Wikipedia)?
This should be good at computing a reasonable linear model even when there are a lot of outliers and noise, as it is built on the assumption that only part of the data will actually belong to the mechanism. | Fast linear regression robust to outliers
Have you looked at RANSAC (Wikipedia)?
This should be good at computing a reasonable linear model even when there are a lot of outliers and noise, as it is built on the assumption that only part of th |
4,694 | Fast linear regression robust to outliers | I found the $l_1$ penalized error regression best.
You can also use it iteratively and reweight samples, which are not very consistent with the solution.
The basic idea is to augment your model with errors:
$$y=Ax+e$$ where $e$ is the unknown error vector.
Now you perform the regression on
$$\parallel y-Ax-e \parallel_... | Fast linear regression robust to outliers | I found the $l_1$ penalized error regression best.
You can also use it iteratively and reweight samples, which are not very consistent with the solution.
The basic idea is to augment your model with e | Fast linear regression robust to outliers
I found the $l_1$ penalized error regression best.
You can also use it iteratively and reweight samples, which are not very consistent with the solution.
The basic idea is to augment your model with errors:
$$y=Ax+e$$ where $e$ is the unknown error vector.
Now you perform the r... | Fast linear regression robust to outliers
I found the $l_1$ penalized error regression best.
You can also use it iteratively and reweight samples, which are not very consistent with the solution.
The basic idea is to augment your model with e |
4,695 | How to read Cook's distance plots? | Some texts tell you that points for which Cook's distance is higher than 1 are to be considered as influential. Other texts give you a threshold of $4/N$ or $4/(N - k - 1)$, where $N$ is the number of observations and $k$ the number of explanatory variables. In your case the latter formula should yield a threshold arou... | How to read Cook's distance plots? | Some texts tell you that points for which Cook's distance is higher than 1 are to be considered as influential. Other texts give you a threshold of $4/N$ or $4/(N - k - 1)$, where $N$ is the number of | How to read Cook's distance plots?
Some texts tell you that points for which Cook's distance is higher than 1 are to be considered as influential. Other texts give you a threshold of $4/N$ or $4/(N - k - 1)$, where $N$ is the number of observations and $k$ the number of explanatory variables. In your case the latter fo... | How to read Cook's distance plots?
Some texts tell you that points for which Cook's distance is higher than 1 are to be considered as influential. Other texts give you a threshold of $4/N$ or $4/(N - k - 1)$, where $N$ is the number of |
4,696 | How to read Cook's distance plots? | +1 to both @lejohn and @whuber. I wanted to expand a little on @whuber's comment. Cook's distance can be contrasted with dfbeta. Cook's distance refers to how far, on average, predicted y-values will move if the observation in question is dropped from the data set. dfbeta refers to how much a parameter estimate cha... | How to read Cook's distance plots? | +1 to both @lejohn and @whuber. I wanted to expand a little on @whuber's comment. Cook's distance can be contrasted with dfbeta. Cook's distance refers to how far, on average, predicted y-values wi | How to read Cook's distance plots?
+1 to both @lejohn and @whuber. I wanted to expand a little on @whuber's comment. Cook's distance can be contrasted with dfbeta. Cook's distance refers to how far, on average, predicted y-values will move if the observation in question is dropped from the data set. dfbeta refers t... | How to read Cook's distance plots?
+1 to both @lejohn and @whuber. I wanted to expand a little on @whuber's comment. Cook's distance can be contrasted with dfbeta. Cook's distance refers to how far, on average, predicted y-values wi |
4,697 | Logistic regression: anova chi-square test vs. significance of coefficients (anova() vs summary() in R) | In addition to @gung's answer, I'll try to provide an example of what the anova function actually tests. I hope this enables you to decide what tests are appropriate for the hypotheses you are interested in testing.
Let's assume that you have an outcome $y$ and 3 predictor variables: $x_{1}$, $x_{2}$, and $x_{3}$. Now,... | Logistic regression: anova chi-square test vs. significance of coefficients (anova() vs summary() in | In addition to @gung's answer, I'll try to provide an example of what the anova function actually tests. I hope this enables you to decide what tests are appropriate for the hypotheses you are interes | Logistic regression: anova chi-square test vs. significance of coefficients (anova() vs summary() in R)
In addition to @gung's answer, I'll try to provide an example of what the anova function actually tests. I hope this enables you to decide what tests are appropriate for the hypotheses you are interested in testing.
... | Logistic regression: anova chi-square test vs. significance of coefficients (anova() vs summary() in
In addition to @gung's answer, I'll try to provide an example of what the anova function actually tests. I hope this enables you to decide what tests are appropriate for the hypotheses you are interes |
4,698 | Suppression effect in regression: definition and visual explanation/depiction | There exist a number of frequenly mentioned regressional effects which conceptually are different but share much in common when seen purely statistically (see e.g. this paper "Equivalence of the Mediation, Confounding and Suppression
Effect" by David MacKinnon et al., or Wikipedia articles):
Mediator: IV which conveys... | Suppression effect in regression: definition and visual explanation/depiction | There exist a number of frequenly mentioned regressional effects which conceptually are different but share much in common when seen purely statistically (see e.g. this paper "Equivalence of the Media | Suppression effect in regression: definition and visual explanation/depiction
There exist a number of frequenly mentioned regressional effects which conceptually are different but share much in common when seen purely statistically (see e.g. this paper "Equivalence of the Mediation, Confounding and Suppression
Effect" ... | Suppression effect in regression: definition and visual explanation/depiction
There exist a number of frequenly mentioned regressional effects which conceptually are different but share much in common when seen purely statistically (see e.g. this paper "Equivalence of the Media |
4,699 | Suppression effect in regression: definition and visual explanation/depiction | Here is another geometric view of suppression, but rather than being in the observation space as @ttnphns's example is, this one is in the variable space, the space where everyday scatterplots live.
Consider a regression $\hat{y}_i=x_i+z_i$, that is, the intercept is 0 and both predictors have a partial slope of 1. Now... | Suppression effect in regression: definition and visual explanation/depiction | Here is another geometric view of suppression, but rather than being in the observation space as @ttnphns's example is, this one is in the variable space, the space where everyday scatterplots live.
C | Suppression effect in regression: definition and visual explanation/depiction
Here is another geometric view of suppression, but rather than being in the observation space as @ttnphns's example is, this one is in the variable space, the space where everyday scatterplots live.
Consider a regression $\hat{y}_i=x_i+z_i$, ... | Suppression effect in regression: definition and visual explanation/depiction
Here is another geometric view of suppression, but rather than being in the observation space as @ttnphns's example is, this one is in the variable space, the space where everyday scatterplots live.
C |
4,700 | Suppression effect in regression: definition and visual explanation/depiction | Here is how I think about the suppressor effect. But please let me know if I am wrong.
Here is an example of a binary outcome (classification, logistic regression). We can see that there is no significant difference in X1, there is no difference in X2, but put X1 and X2 together (i.e. correct x1 for x2 or vice versa) ... | Suppression effect in regression: definition and visual explanation/depiction | Here is how I think about the suppressor effect. But please let me know if I am wrong.
Here is an example of a binary outcome (classification, logistic regression). We can see that there is no signif | Suppression effect in regression: definition and visual explanation/depiction
Here is how I think about the suppressor effect. But please let me know if I am wrong.
Here is an example of a binary outcome (classification, logistic regression). We can see that there is no significant difference in X1, there is no differ... | Suppression effect in regression: definition and visual explanation/depiction
Here is how I think about the suppressor effect. But please let me know if I am wrong.
Here is an example of a binary outcome (classification, logistic regression). We can see that there is no signif |
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