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 |
|---|---|---|---|---|---|---|
12,601 | When are Bayesian methods preferable to Frequentist? | The Bayesian approach to hypothesis testing is a lot more intuitive. Suppose you wish to calculate a two-sample T-test. You can use the T-statistic to do this and then find the p-value. One can argue this is not a very intuitive method, it is very ad hoc, and very specific to the problem. The Bayesian approach is to si... | When are Bayesian methods preferable to Frequentist? | The Bayesian approach to hypothesis testing is a lot more intuitive. Suppose you wish to calculate a two-sample T-test. You can use the T-statistic to do this and then find the p-value. One can argue | When are Bayesian methods preferable to Frequentist?
The Bayesian approach to hypothesis testing is a lot more intuitive. Suppose you wish to calculate a two-sample T-test. You can use the T-statistic to do this and then find the p-value. One can argue this is not a very intuitive method, it is very ad hoc, and very sp... | When are Bayesian methods preferable to Frequentist?
The Bayesian approach to hypothesis testing is a lot more intuitive. Suppose you wish to calculate a two-sample T-test. You can use the T-statistic to do this and then find the p-value. One can argue |
12,602 | When are Bayesian methods preferable to Frequentist? | Imagine you estimate a probability that AC Milan beats Real Madrid and they have played 3 games in their current line-up. All 3 games were won by Real Madrid. Then a frequentist says that Milan can never beat Real Madrid, which makes no sense. A Bayesian might take a prior from the previous seasons, which would result ... | When are Bayesian methods preferable to Frequentist? | Imagine you estimate a probability that AC Milan beats Real Madrid and they have played 3 games in their current line-up. All 3 games were won by Real Madrid. Then a frequentist says that Milan can ne | When are Bayesian methods preferable to Frequentist?
Imagine you estimate a probability that AC Milan beats Real Madrid and they have played 3 games in their current line-up. All 3 games were won by Real Madrid. Then a frequentist says that Milan can never beat Real Madrid, which makes no sense. A Bayesian might take a... | When are Bayesian methods preferable to Frequentist?
Imagine you estimate a probability that AC Milan beats Real Madrid and they have played 3 games in their current line-up. All 3 games were won by Real Madrid. Then a frequentist says that Milan can ne |
12,603 | Euclidean distance score and similarity | The inverse is to change from distance to similarity.
The 1 in the denominator is to make it so that the maximum value is 1 (if the distance is 0).
The square root - I am not sure. If distance is usually larger than 1, the root will make large distances less important; if distance is less than 1, it will make large dis... | Euclidean distance score and similarity | The inverse is to change from distance to similarity.
The 1 in the denominator is to make it so that the maximum value is 1 (if the distance is 0).
The square root - I am not sure. If distance is usua | Euclidean distance score and similarity
The inverse is to change from distance to similarity.
The 1 in the denominator is to make it so that the maximum value is 1 (if the distance is 0).
The square root - I am not sure. If distance is usually larger than 1, the root will make large distances less important; if distanc... | Euclidean distance score and similarity
The inverse is to change from distance to similarity.
The 1 in the denominator is to make it so that the maximum value is 1 (if the distance is 0).
The square root - I am not sure. If distance is usua |
12,604 | Euclidean distance score and similarity | To measure the distance and similarity (in the semantic sense) the first thing to check is if you are moving in a Euclidean space or not. An empirical way to verify this is to estimate the distance of a pair of values for which you know the meaning. | Euclidean distance score and similarity | To measure the distance and similarity (in the semantic sense) the first thing to check is if you are moving in a Euclidean space or not. An empirical way to verify this is to estimate the distance of | Euclidean distance score and similarity
To measure the distance and similarity (in the semantic sense) the first thing to check is if you are moving in a Euclidean space or not. An empirical way to verify this is to estimate the distance of a pair of values for which you know the meaning. | Euclidean distance score and similarity
To measure the distance and similarity (in the semantic sense) the first thing to check is if you are moving in a Euclidean space or not. An empirical way to verify this is to estimate the distance of |
12,605 | Euclidean distance score and similarity | As you mentioned you know the calculation of Euclidence distance so I am explaining the second formula.
Euclidean formula calculates the distance, which will be smaller for people or items who are more similar. Like if they are the same then the distance is 0 and totally different then higher than 0.
However, we need a... | Euclidean distance score and similarity | As you mentioned you know the calculation of Euclidence distance so I am explaining the second formula.
Euclidean formula calculates the distance, which will be smaller for people or items who are mor | Euclidean distance score and similarity
As you mentioned you know the calculation of Euclidence distance so I am explaining the second formula.
Euclidean formula calculates the distance, which will be smaller for people or items who are more similar. Like if they are the same then the distance is 0 and totally differen... | Euclidean distance score and similarity
As you mentioned you know the calculation of Euclidence distance so I am explaining the second formula.
Euclidean formula calculates the distance, which will be smaller for people or items who are mor |
12,606 | Euclidean distance score and similarity | Euclidean is basically calculate the dissimilarity of two vectors, because it'll return 0 if two vectors are similar. While Cosine Similarity gives 1 in return to similarity. Somewhat the writer on that book wants a similarity-based measure, but he wants to use Euclidean. So, in order to get a similarity-based distance... | Euclidean distance score and similarity | Euclidean is basically calculate the dissimilarity of two vectors, because it'll return 0 if two vectors are similar. While Cosine Similarity gives 1 in return to similarity. Somewhat the writer on th | Euclidean distance score and similarity
Euclidean is basically calculate the dissimilarity of two vectors, because it'll return 0 if two vectors are similar. While Cosine Similarity gives 1 in return to similarity. Somewhat the writer on that book wants a similarity-based measure, but he wants to use Euclidean. So, in ... | Euclidean distance score and similarity
Euclidean is basically calculate the dissimilarity of two vectors, because it'll return 0 if two vectors are similar. While Cosine Similarity gives 1 in return to similarity. Somewhat the writer on th |
12,607 | Plotting confidence intervals for the predicted probabilities from a logistic regression | The code you used estimates a logistic regression model using the glm function. You didn't include data, so I'll just make some up.
set.seed(1234)
mydat <- data.frame(
won=as.factor(sample(c(0, 1), 250, replace=TRUE)),
bid=runif(250, min=0, max=1000)
)
mod1 <- glm(won~bid, data=mydat, family=binomial(link="log... | Plotting confidence intervals for the predicted probabilities from a logistic regression | The code you used estimates a logistic regression model using the glm function. You didn't include data, so I'll just make some up.
set.seed(1234)
mydat <- data.frame(
won=as.factor(sample(c(0, 1) | Plotting confidence intervals for the predicted probabilities from a logistic regression
The code you used estimates a logistic regression model using the glm function. You didn't include data, so I'll just make some up.
set.seed(1234)
mydat <- data.frame(
won=as.factor(sample(c(0, 1), 250, replace=TRUE)),
bid... | Plotting confidence intervals for the predicted probabilities from a logistic regression
The code you used estimates a logistic regression model using the glm function. You didn't include data, so I'll just make some up.
set.seed(1234)
mydat <- data.frame(
won=as.factor(sample(c(0, 1) |
12,608 | Plotting confidence intervals for the predicted probabilities from a logistic regression | Here's a modification of @smillig's solution. I use tidyverse tools here, and also use the linkinv function that is a part of the GLM model object mod1. That way, you don't have to manually invert the logistic function, and this approach will work regardless of what specific GLM you fit.
library(tidyverse)
library(mag... | Plotting confidence intervals for the predicted probabilities from a logistic regression | Here's a modification of @smillig's solution. I use tidyverse tools here, and also use the linkinv function that is a part of the GLM model object mod1. That way, you don't have to manually invert the | Plotting confidence intervals for the predicted probabilities from a logistic regression
Here's a modification of @smillig's solution. I use tidyverse tools here, and also use the linkinv function that is a part of the GLM model object mod1. That way, you don't have to manually invert the logistic function, and this ap... | Plotting confidence intervals for the predicted probabilities from a logistic regression
Here's a modification of @smillig's solution. I use tidyverse tools here, and also use the linkinv function that is a part of the GLM model object mod1. That way, you don't have to manually invert the |
12,609 | What is a tight lower bound on the coupon collector time? | I'm providing this as a second answer since the analysis is completely elementary and provides exactly the desired result.
Proposition For $c > 0$ and $n \geq 1$,
$$
\mathbb{P}(T < n \log n - c n ) < e^{-c} \>.
$$
The idea behind the proof is simple:
Represent the time until all coupons are collected as $T = \sum_{i... | What is a tight lower bound on the coupon collector time? | I'm providing this as a second answer since the analysis is completely elementary and provides exactly the desired result.
Proposition For $c > 0$ and $n \geq 1$,
$$
\mathbb{P}(T < n \log n - c n ) < | What is a tight lower bound on the coupon collector time?
I'm providing this as a second answer since the analysis is completely elementary and provides exactly the desired result.
Proposition For $c > 0$ and $n \geq 1$,
$$
\mathbb{P}(T < n \log n - c n ) < e^{-c} \>.
$$
The idea behind the proof is simple:
Represen... | What is a tight lower bound on the coupon collector time?
I'm providing this as a second answer since the analysis is completely elementary and provides exactly the desired result.
Proposition For $c > 0$ and $n \geq 1$,
$$
\mathbb{P}(T < n \log n - c n ) < |
12,610 | What is a tight lower bound on the coupon collector time? | Although @cardinal has already given an answer that gives precisely the bound I was looking for, I have found a similar Chernoff-style argument that can give a stronger bound:
Proposition:
$$
Pr (T \leq n \log n - c n) \leq \exp(- \frac{3c^2}{\pi^2} ) \> .
$$
(this is stronger for $c > \frac{\pi^2}{3}$ )
Proof:
As i... | What is a tight lower bound on the coupon collector time? | Although @cardinal has already given an answer that gives precisely the bound I was looking for, I have found a similar Chernoff-style argument that can give a stronger bound:
Proposition:
$$
Pr (T \ | What is a tight lower bound on the coupon collector time?
Although @cardinal has already given an answer that gives precisely the bound I was looking for, I have found a similar Chernoff-style argument that can give a stronger bound:
Proposition:
$$
Pr (T \leq n \log n - c n) \leq \exp(- \frac{3c^2}{\pi^2} ) \> .
$$... | What is a tight lower bound on the coupon collector time?
Although @cardinal has already given an answer that gives precisely the bound I was looking for, I have found a similar Chernoff-style argument that can give a stronger bound:
Proposition:
$$
Pr (T \ |
12,611 | What is a tight lower bound on the coupon collector time? | Important Note: I've decided to remove the proof I gave originally in this answer. It was longer, more computational, used bigger hammers, and proved a weaker result as compared to the other proof I've given. All around, an inferior approach (in my view). If you're really interested, I suppose you can look at the edits... | What is a tight lower bound on the coupon collector time? | Important Note: I've decided to remove the proof I gave originally in this answer. It was longer, more computational, used bigger hammers, and proved a weaker result as compared to the other proof I'v | What is a tight lower bound on the coupon collector time?
Important Note: I've decided to remove the proof I gave originally in this answer. It was longer, more computational, used bigger hammers, and proved a weaker result as compared to the other proof I've given. All around, an inferior approach (in my view). If you... | What is a tight lower bound on the coupon collector time?
Important Note: I've decided to remove the proof I gave originally in this answer. It was longer, more computational, used bigger hammers, and proved a weaker result as compared to the other proof I'v |
12,612 | What is a tight lower bound on the coupon collector time? | Benjamin Doerr gives (in the chapter "
Analyzing Randomized Search Heuristics: Tools from Probability Theory" in the book "Theory of Randomized Search Heuristics", see the link for an online PDF) a somewhat simple proof of
Proposition Let $T$ be the stopping time of the coupon collection process. Then $\Pr[T\le (1-\eps... | What is a tight lower bound on the coupon collector time? | Benjamin Doerr gives (in the chapter "
Analyzing Randomized Search Heuristics: Tools from Probability Theory" in the book "Theory of Randomized Search Heuristics", see the link for an online PDF) a so | What is a tight lower bound on the coupon collector time?
Benjamin Doerr gives (in the chapter "
Analyzing Randomized Search Heuristics: Tools from Probability Theory" in the book "Theory of Randomized Search Heuristics", see the link for an online PDF) a somewhat simple proof of
Proposition Let $T$ be the stopping tim... | What is a tight lower bound on the coupon collector time?
Benjamin Doerr gives (in the chapter "
Analyzing Randomized Search Heuristics: Tools from Probability Theory" in the book "Theory of Randomized Search Heuristics", see the link for an online PDF) a so |
12,613 | Expected number of tosses till first head comes up | This can be answered using the geometric distribution as follows:
The number of failures k - 1 before the first success (heads) with a probability of success p ("heads") is given by:
$$p(X=k)=(1−p)^{k−1}p$$
with k being the total number of tosses including the first 'heads' that terminates the experiment.
And the expec... | Expected number of tosses till first head comes up | This can be answered using the geometric distribution as follows:
The number of failures k - 1 before the first success (heads) with a probability of success p ("heads") is given by:
$$p(X=k)=(1−p)^{k | Expected number of tosses till first head comes up
This can be answered using the geometric distribution as follows:
The number of failures k - 1 before the first success (heads) with a probability of success p ("heads") is given by:
$$p(X=k)=(1−p)^{k−1}p$$
with k being the total number of tosses including the first 'h... | Expected number of tosses till first head comes up
This can be answered using the geometric distribution as follows:
The number of failures k - 1 before the first success (heads) with a probability of success p ("heads") is given by:
$$p(X=k)=(1−p)^{k |
12,614 | Expected number of tosses till first head comes up | Model the game by drawing a ticket out of a box. There are two kinds of tickets. On one is written "Stop, you tossed heads"; on the other is written "Continue, you tossed tails." The expected number of additional tosses in the first case is $0$ while the expected number of additional tosses in the second case is $x$... | Expected number of tosses till first head comes up | Model the game by drawing a ticket out of a box. There are two kinds of tickets. On one is written "Stop, you tossed heads"; on the other is written "Continue, you tossed tails." The expected numbe | Expected number of tosses till first head comes up
Model the game by drawing a ticket out of a box. There are two kinds of tickets. On one is written "Stop, you tossed heads"; on the other is written "Continue, you tossed tails." The expected number of additional tosses in the first case is $0$ while the expected nu... | Expected number of tosses till first head comes up
Model the game by drawing a ticket out of a box. There are two kinds of tickets. On one is written "Stop, you tossed heads"; on the other is written "Continue, you tossed tails." The expected numbe |
12,615 | Expected number of tosses till first head comes up | Let X be the number of coin flips required until a head is obtained.
So, we need to calculate E(X) (i.e. expected value of X).
We can condition E(X) on whatever our first flip is.
Let E(X|H) denote the number of remaining coin flips given I got a head on the first flip.
Similarly, let E(X|T) denote the number of remain... | Expected number of tosses till first head comes up | Let X be the number of coin flips required until a head is obtained.
So, we need to calculate E(X) (i.e. expected value of X).
We can condition E(X) on whatever our first flip is.
Let E(X|H) denote th | Expected number of tosses till first head comes up
Let X be the number of coin flips required until a head is obtained.
So, we need to calculate E(X) (i.e. expected value of X).
We can condition E(X) on whatever our first flip is.
Let E(X|H) denote the number of remaining coin flips given I got a head on the first flip... | Expected number of tosses till first head comes up
Let X be the number of coin flips required until a head is obtained.
So, we need to calculate E(X) (i.e. expected value of X).
We can condition E(X) on whatever our first flip is.
Let E(X|H) denote th |
12,616 | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$ | Stylistic conventions, mainly, but with some underlying rationale.
$\mathbb{P}()$ and $\Pr()$ can be seen as two ways to "free up" the letter $\text{P}$ for other use—it is used to denote other things than "probability", for example in research with complicated and extensive notation where one starts to exhaust availab... | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$ | Stylistic conventions, mainly, but with some underlying rationale.
$\mathbb{P}()$ and $\Pr()$ can be seen as two ways to "free up" the letter $\text{P}$ for other use—it is used to denote other things | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$
Stylistic conventions, mainly, but with some underlying rationale.
$\mathbb{P}()$ and $\Pr()$ can be seen as two ways to "free up" the letter $\text{P}$ for other use—it is used to denote other things than "probability", for example in re... | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$
Stylistic conventions, mainly, but with some underlying rationale.
$\mathbb{P}()$ and $\Pr()$ can be seen as two ways to "free up" the letter $\text{P}$ for other use—it is used to denote other things |
12,617 | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$ | I've seen all three used in different undergrad classes and as far as I know, they're stylistic differences and all represent probability as you're thinking of it.
One other notation I've seen is in Sheldon Ross's "Introduction to Probability Theory", where $\mathbf{P}$ represents a probability matrix. He also uses $\... | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$ | I've seen all three used in different undergrad classes and as far as I know, they're stylistic differences and all represent probability as you're thinking of it.
One other notation I've seen is in S | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$
I've seen all three used in different undergrad classes and as far as I know, they're stylistic differences and all represent probability as you're thinking of it.
One other notation I've seen is in Sheldon Ross's "Introduction to Probabi... | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$
I've seen all three used in different undergrad classes and as far as I know, they're stylistic differences and all represent probability as you're thinking of it.
One other notation I've seen is in S |
12,618 | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$ | This makes me think of Meyn and Tweedie's book. They use $P$ to denote the transition kernel for a Markov chain, and $\mathsf{P}$ for the law of the entire chain on $\mathsf{X}^{\infty}$. This answer is specific to Markov chains, but the distinction is obviously important.
The difference between $P$ and $\mathbb{P}$ (a... | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$ | This makes me think of Meyn and Tweedie's book. They use $P$ to denote the transition kernel for a Markov chain, and $\mathsf{P}$ for the law of the entire chain on $\mathsf{X}^{\infty}$. This answer | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$
This makes me think of Meyn and Tweedie's book. They use $P$ to denote the transition kernel for a Markov chain, and $\mathsf{P}$ for the law of the entire chain on $\mathsf{X}^{\infty}$. This answer is specific to Markov chains, but the ... | Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$
This makes me think of Meyn and Tweedie's book. They use $P$ to denote the transition kernel for a Markov chain, and $\mathsf{P}$ for the law of the entire chain on $\mathsf{X}^{\infty}$. This answer |
12,619 | How does logistic regression use the binomial distribution? | Suppose you observe several nests at different mean daily temperatures $t$. How does the probability $\pi(t)$ of nest success depend on the temperature $t$? (If nests are independent, the number of nests with success at temperature $t$ is then binomially distributed with $n$ equal to the number of nests observed and su... | How does logistic regression use the binomial distribution? | Suppose you observe several nests at different mean daily temperatures $t$. How does the probability $\pi(t)$ of nest success depend on the temperature $t$? (If nests are independent, the number of ne | How does logistic regression use the binomial distribution?
Suppose you observe several nests at different mean daily temperatures $t$. How does the probability $\pi(t)$ of nest success depend on the temperature $t$? (If nests are independent, the number of nests with success at temperature $t$ is then binomially distr... | How does logistic regression use the binomial distribution?
Suppose you observe several nests at different mean daily temperatures $t$. How does the probability $\pi(t)$ of nest success depend on the temperature $t$? (If nests are independent, the number of ne |
12,620 | How does logistic regression use the binomial distribution? | Without equations? Yikes. Let's see:
The logistic regression model is literally a model for the $p$ parameter of a binomial distribution; with a continuous predictor, each point can have its own distribution. (In the cases where the observations are 0-1, we deal with the Bernoulli special case; this is a common situati... | How does logistic regression use the binomial distribution? | Without equations? Yikes. Let's see:
The logistic regression model is literally a model for the $p$ parameter of a binomial distribution; with a continuous predictor, each point can have its own distr | How does logistic regression use the binomial distribution?
Without equations? Yikes. Let's see:
The logistic regression model is literally a model for the $p$ parameter of a binomial distribution; with a continuous predictor, each point can have its own distribution. (In the cases where the observations are 0-1, we de... | How does logistic regression use the binomial distribution?
Without equations? Yikes. Let's see:
The logistic regression model is literally a model for the $p$ parameter of a binomial distribution; with a continuous predictor, each point can have its own distr |
12,621 | How does logistic regression use the binomial distribution? | Your model assumes the success of a nest can be viewed as a gamble: God flips a loaded coin with sides labeled "success" and "failure." The outcome of the flip for one nest is independent of the outcome of the flip for any other nest.
The birds do have something going for them, though: the coin might heavily favor suc... | How does logistic regression use the binomial distribution? | Your model assumes the success of a nest can be viewed as a gamble: God flips a loaded coin with sides labeled "success" and "failure." The outcome of the flip for one nest is independent of the outc | How does logistic regression use the binomial distribution?
Your model assumes the success of a nest can be viewed as a gamble: God flips a loaded coin with sides labeled "success" and "failure." The outcome of the flip for one nest is independent of the outcome of the flip for any other nest.
The birds do have someth... | How does logistic regression use the binomial distribution?
Your model assumes the success of a nest can be viewed as a gamble: God flips a loaded coin with sides labeled "success" and "failure." The outcome of the flip for one nest is independent of the outc |
12,622 | What happens when you apply SVD to a collaborative filtering problem? What is the difference between the two? | $\DeclareMathOperator*{\argmin}{arg\,min}$
Ok, when you say SVD, presumably you're talking about truncated SVD (where you only keep the $k$ biggest singular values). There are two different ways to look at the truncated SVD of a matrix. One is the standard definition:
First you do the SVD: $\underset{n\times m}{X} = \... | What happens when you apply SVD to a collaborative filtering problem? What is the difference between | $\DeclareMathOperator*{\argmin}{arg\,min}$
Ok, when you say SVD, presumably you're talking about truncated SVD (where you only keep the $k$ biggest singular values). There are two different ways to lo | What happens when you apply SVD to a collaborative filtering problem? What is the difference between the two?
$\DeclareMathOperator*{\argmin}{arg\,min}$
Ok, when you say SVD, presumably you're talking about truncated SVD (where you only keep the $k$ biggest singular values). There are two different ways to look at the ... | What happens when you apply SVD to a collaborative filtering problem? What is the difference between
$\DeclareMathOperator*{\argmin}{arg\,min}$
Ok, when you say SVD, presumably you're talking about truncated SVD (where you only keep the $k$ biggest singular values). There are two different ways to lo |
12,623 | What happens when you apply SVD to a collaborative filtering problem? What is the difference between the two? | 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.
It seems like there are a lot of approaches on how to ... | What happens when you apply SVD to a collaborative filtering problem? What is the difference between | 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.
| What happens when you apply SVD to a collaborative filtering problem? What is the difference between the two?
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.
... | What happens when you apply SVD to a collaborative filtering problem? What is the difference between
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.
|
12,624 | What happens when you apply SVD to a collaborative filtering problem? What is the difference between the two? | I need more reputation to comment on Stumpy Joe Pete's answer therefore I post this as an answer.
Stumpy thanks for the answer although I think it needs a bit of clarification. Particularly I mean this sentence:
Basically you're looking for a k-rank matrix that minimizes the element-wise mean squared error across the ... | What happens when you apply SVD to a collaborative filtering problem? What is the difference between | I need more reputation to comment on Stumpy Joe Pete's answer therefore I post this as an answer.
Stumpy thanks for the answer although I think it needs a bit of clarification. Particularly I mean thi | What happens when you apply SVD to a collaborative filtering problem? What is the difference between the two?
I need more reputation to comment on Stumpy Joe Pete's answer therefore I post this as an answer.
Stumpy thanks for the answer although I think it needs a bit of clarification. Particularly I mean this sentence... | What happens when you apply SVD to a collaborative filtering problem? What is the difference between
I need more reputation to comment on Stumpy Joe Pete's answer therefore I post this as an answer.
Stumpy thanks for the answer although I think it needs a bit of clarification. Particularly I mean thi |
12,625 | Computing standard error in weighted mean estimation | I ran into the same issue recently. The following is what I found:
Unlike a simple random sample with equal weights, there is no widely accepted definition of standard error of the weighted mean. These days, it would be straight-forward to do a bootstrap and obtain the empirical distribution of the mean, and based on ... | Computing standard error in weighted mean estimation | I ran into the same issue recently. The following is what I found:
Unlike a simple random sample with equal weights, there is no widely accepted definition of standard error of the weighted mean. The | Computing standard error in weighted mean estimation
I ran into the same issue recently. The following is what I found:
Unlike a simple random sample with equal weights, there is no widely accepted definition of standard error of the weighted mean. These days, it would be straight-forward to do a bootstrap and obtain ... | Computing standard error in weighted mean estimation
I ran into the same issue recently. The following is what I found:
Unlike a simple random sample with equal weights, there is no widely accepted definition of standard error of the weighted mean. The |
12,626 | Computing standard error in weighted mean estimation | The variance of your estimate given the $w_i$ is
$$
\frac{\sum w_i^2 Var(X)}{(\sum w_i)^2} = Var(X) \frac{\sum w_i^2 }{(\sum w_i)^2}.
$$
Because your estimate is unbiased for any $w_i$, the variance of its conditional mean is zero. Hence, the variance of your estimate is
$$
Var(X) \mathbb{E}\left(\frac{\sum w_i^2 }{... | Computing standard error in weighted mean estimation | The variance of your estimate given the $w_i$ is
$$
\frac{\sum w_i^2 Var(X)}{(\sum w_i)^2} = Var(X) \frac{\sum w_i^2 }{(\sum w_i)^2}.
$$
Because your estimate is unbiased for any $w_i$, the variance | Computing standard error in weighted mean estimation
The variance of your estimate given the $w_i$ is
$$
\frac{\sum w_i^2 Var(X)}{(\sum w_i)^2} = Var(X) \frac{\sum w_i^2 }{(\sum w_i)^2}.
$$
Because your estimate is unbiased for any $w_i$, the variance of its conditional mean is zero. Hence, the variance of your estim... | Computing standard error in weighted mean estimation
The variance of your estimate given the $w_i$ is
$$
\frac{\sum w_i^2 Var(X)}{(\sum w_i)^2} = Var(X) \frac{\sum w_i^2 }{(\sum w_i)^2}.
$$
Because your estimate is unbiased for any $w_i$, the variance |
12,627 | Computing standard error in weighted mean estimation | @Ming K 's equation is not working for me. @Hugh mentioned Hmisc::wtd.var(x, w), but this is for variance, if you are wondering about weighted standard error, this would be useful. But read assumption and equation here, following
$$
\sigma _{x}^{-} = \sigma \sqrt{\sum_{i=1}^{n}\omega _{i}^{'2}}
$$
For your convenient,... | Computing standard error in weighted mean estimation | @Ming K 's equation is not working for me. @Hugh mentioned Hmisc::wtd.var(x, w), but this is for variance, if you are wondering about weighted standard error, this would be useful. But read assumptio | Computing standard error in weighted mean estimation
@Ming K 's equation is not working for me. @Hugh mentioned Hmisc::wtd.var(x, w), but this is for variance, if you are wondering about weighted standard error, this would be useful. But read assumption and equation here, following
$$
\sigma _{x}^{-} = \sigma \sqrt{\s... | Computing standard error in weighted mean estimation
@Ming K 's equation is not working for me. @Hugh mentioned Hmisc::wtd.var(x, w), but this is for variance, if you are wondering about weighted standard error, this would be useful. But read assumptio |
12,628 | When is a repeated measures ANOVA preferred over a mixed-effects model? | I'm not totally sure what actual model "repeated measures ANOVA" describes, but I think one general issue is whether to put random effects of any kind in a model rather than e.g. just adjust variance estimates to cover the induced dependencies (as in the Panel Corrected Standard Errors vs multilevel models debate in ti... | When is a repeated measures ANOVA preferred over a mixed-effects model? | I'm not totally sure what actual model "repeated measures ANOVA" describes, but I think one general issue is whether to put random effects of any kind in a model rather than e.g. just adjust variance | When is a repeated measures ANOVA preferred over a mixed-effects model?
I'm not totally sure what actual model "repeated measures ANOVA" describes, but I think one general issue is whether to put random effects of any kind in a model rather than e.g. just adjust variance estimates to cover the induced dependencies (as ... | When is a repeated measures ANOVA preferred over a mixed-effects model?
I'm not totally sure what actual model "repeated measures ANOVA" describes, but I think one general issue is whether to put random effects of any kind in a model rather than e.g. just adjust variance |
12,629 | When is a repeated measures ANOVA preferred over a mixed-effects model? | If your participants see the exact same pictures in each condition (which is obviously not the case in your original example because each category will presumably contain different pictures), an ANOVA on the cell means probably tells you exactly what you want to know. One reason to prefer it is that it's somewhat easie... | When is a repeated measures ANOVA preferred over a mixed-effects model? | If your participants see the exact same pictures in each condition (which is obviously not the case in your original example because each category will presumably contain different pictures), an ANOVA | When is a repeated measures ANOVA preferred over a mixed-effects model?
If your participants see the exact same pictures in each condition (which is obviously not the case in your original example because each category will presumably contain different pictures), an ANOVA on the cell means probably tells you exactly wh... | When is a repeated measures ANOVA preferred over a mixed-effects model?
If your participants see the exact same pictures in each condition (which is obviously not the case in your original example because each category will presumably contain different pictures), an ANOVA |
12,630 | When is a repeated measures ANOVA preferred over a mixed-effects model? | Never. A repeated measures ANOVA is one type, probably the simplest, of mixed effects model. I would recommend not even learning repeated measures except to know how to fit one as a mixed effects, but to learn mixed effects methods. It takes more effort as they can't be understood as recipes but are much more powerful ... | When is a repeated measures ANOVA preferred over a mixed-effects model? | Never. A repeated measures ANOVA is one type, probably the simplest, of mixed effects model. I would recommend not even learning repeated measures except to know how to fit one as a mixed effects, but | When is a repeated measures ANOVA preferred over a mixed-effects model?
Never. A repeated measures ANOVA is one type, probably the simplest, of mixed effects model. I would recommend not even learning repeated measures except to know how to fit one as a mixed effects, but to learn mixed effects methods. It takes more e... | When is a repeated measures ANOVA preferred over a mixed-effects model?
Never. A repeated measures ANOVA is one type, probably the simplest, of mixed effects model. I would recommend not even learning repeated measures except to know how to fit one as a mixed effects, but |
12,631 | Combining machine learning models | It actually boils down to one of the "3B" techniques: bagging, boosting or blending.
In bagging, you train a lot of classifiers on different subsets of object and combine answers by average for regression and voting for classification (there are some other options for more complex situations, but I'll skip it). Vote pr... | Combining machine learning models | It actually boils down to one of the "3B" techniques: bagging, boosting or blending.
In bagging, you train a lot of classifiers on different subsets of object and combine answers by average for regres | Combining machine learning models
It actually boils down to one of the "3B" techniques: bagging, boosting or blending.
In bagging, you train a lot of classifiers on different subsets of object and combine answers by average for regression and voting for classification (there are some other options for more complex situ... | Combining machine learning models
It actually boils down to one of the "3B" techniques: bagging, boosting or blending.
In bagging, you train a lot of classifiers on different subsets of object and combine answers by average for regres |
12,632 | Combining machine learning models | The expression "combining models" is vague, but my guess is that you are asking about ensemble learning methods. The best reference to learn about them is perhaps Rich Caruana's papers:
http://www.cs.cornell.edu/~caruana/ctp/ct.papers/caruana.icml04.icdm06long.pdf
There is no actual code in this paper, but the algorit... | Combining machine learning models | The expression "combining models" is vague, but my guess is that you are asking about ensemble learning methods. The best reference to learn about them is perhaps Rich Caruana's papers:
http://www.cs | Combining machine learning models
The expression "combining models" is vague, but my guess is that you are asking about ensemble learning methods. The best reference to learn about them is perhaps Rich Caruana's papers:
http://www.cs.cornell.edu/~caruana/ctp/ct.papers/caruana.icml04.icdm06long.pdf
There is no actual c... | Combining machine learning models
The expression "combining models" is vague, but my guess is that you are asking about ensemble learning methods. The best reference to learn about them is perhaps Rich Caruana's papers:
http://www.cs |
12,633 | Combining machine learning models | After looking around for a bit with the help of the above answers, I realized what my problem was. I had been trying to use the predictions of other models in the same model as was used to predict them. In other words if I had 5 variables when I ran the kNN model, I'd add a new variable with the predictions of the kN... | Combining machine learning models | After looking around for a bit with the help of the above answers, I realized what my problem was. I had been trying to use the predictions of other models in the same model as was used to predict th | Combining machine learning models
After looking around for a bit with the help of the above answers, I realized what my problem was. I had been trying to use the predictions of other models in the same model as was used to predict them. In other words if I had 5 variables when I ran the kNN model, I'd add a new varia... | Combining machine learning models
After looking around for a bit with the help of the above answers, I realized what my problem was. I had been trying to use the predictions of other models in the same model as was used to predict th |
12,634 | Combining machine learning models | Good publication for combining multiple predictors is:
Taraba (2023), "Optimal blending of multiple independent prediction models", Front. Artif. Intell., 6.
It contains formulas for combining the models based on their variances as well as formula for the variance of the final blend. It also provides upper estimate bas... | Combining machine learning models | Good publication for combining multiple predictors is:
Taraba (2023), "Optimal blending of multiple independent prediction models", Front. Artif. Intell., 6.
It contains formulas for combining the mod | Combining machine learning models
Good publication for combining multiple predictors is:
Taraba (2023), "Optimal blending of multiple independent prediction models", Front. Artif. Intell., 6.
It contains formulas for combining the models based on their variances as well as formula for the variance of the final blend. I... | Combining machine learning models
Good publication for combining multiple predictors is:
Taraba (2023), "Optimal blending of multiple independent prediction models", Front. Artif. Intell., 6.
It contains formulas for combining the mod |
12,635 | What is the difference between "testing of hypothesis" and "test of significance"? | Significance testing is what Fisher devised and hypothesis testing is what Neyman and Pearson devised to replace significance testing. They are not the same and are mutually incompatible to an extent that would surprise most users of null hypothesis tests.
Fisher's significance tests yield a p value that represents how... | What is the difference between "testing of hypothesis" and "test of significance"? | Significance testing is what Fisher devised and hypothesis testing is what Neyman and Pearson devised to replace significance testing. They are not the same and are mutually incompatible to an extent | What is the difference between "testing of hypothesis" and "test of significance"?
Significance testing is what Fisher devised and hypothesis testing is what Neyman and Pearson devised to replace significance testing. They are not the same and are mutually incompatible to an extent that would surprise most users of nul... | What is the difference between "testing of hypothesis" and "test of significance"?
Significance testing is what Fisher devised and hypothesis testing is what Neyman and Pearson devised to replace significance testing. They are not the same and are mutually incompatible to an extent |
12,636 | What is the difference between "testing of hypothesis" and "test of significance"? | In many cases, these two statements mean the same thing. However, they can also be quite different.
Testing a hypothesis consists of first saying what you believe will occur with some phenomenon, then developing some kind of test for this phenomenon, and then determining whether or not the phenomenon actually occurred.... | What is the difference between "testing of hypothesis" and "test of significance"? | In many cases, these two statements mean the same thing. However, they can also be quite different.
Testing a hypothesis consists of first saying what you believe will occur with some phenomenon, then | What is the difference between "testing of hypothesis" and "test of significance"?
In many cases, these two statements mean the same thing. However, they can also be quite different.
Testing a hypothesis consists of first saying what you believe will occur with some phenomenon, then developing some kind of test for thi... | What is the difference between "testing of hypothesis" and "test of significance"?
In many cases, these two statements mean the same thing. However, they can also be quite different.
Testing a hypothesis consists of first saying what you believe will occur with some phenomenon, then |
12,637 | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot product or the sum of element-wise multiplication? | Any given layer in a CNN has typically 3 dimensions (we'll call them height, width, depth). The convolution will produce a new layer with a new (or same) height, width and depth. The operation however is performed differently on the height/width and differently on the depth and this is what I think causes confusion.
Le... | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot pr | Any given layer in a CNN has typically 3 dimensions (we'll call them height, width, depth). The convolution will produce a new layer with a new (or same) height, width and depth. The operation however | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot product or the sum of element-wise multiplication?
Any given layer in a CNN has typically 3 dimensions (we'll call them height, width, depth). The convolution will produce a new layer with a new (or same) height, width and... | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot pr
Any given layer in a CNN has typically 3 dimensions (we'll call them height, width, depth). The convolution will produce a new layer with a new (or same) height, width and depth. The operation however |
12,638 | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot product or the sum of element-wise multiplication? | I believe the key is that when the filter is convolving some part of the image (the "receptive field") each number in the filter (i.e. each weight) is first flattened into vector format. Likewise, the pixels of the image are also flattened into vector format. THEN, the dot product is calculated. Which is the exact s... | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot pr | I believe the key is that when the filter is convolving some part of the image (the "receptive field") each number in the filter (i.e. each weight) is first flattened into vector format. Likewise, th | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot product or the sum of element-wise multiplication?
I believe the key is that when the filter is convolving some part of the image (the "receptive field") each number in the filter (i.e. each weight) is first flattened into... | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot pr
I believe the key is that when the filter is convolving some part of the image (the "receptive field") each number in the filter (i.e. each weight) is first flattened into vector format. Likewise, th |
12,639 | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot product or the sum of element-wise multiplication? | The operation is called convolution which involves a sum of element by element multiplication, which in turn is the same as a dot product on multidimensional matrices which ML folks call tensors. If you write it as a loop, it'll look like this pseudo Python code:
for i in 0:3:
for j in 0:3:
s = 0
for k in 0:3... | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot pr | The operation is called convolution which involves a sum of element by element multiplication, which in turn is the same as a dot product on multidimensional matrices which ML folks call tensors. If y | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot product or the sum of element-wise multiplication?
The operation is called convolution which involves a sum of element by element multiplication, which in turn is the same as a dot product on multidimensional matrices whic... | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot pr
The operation is called convolution which involves a sum of element by element multiplication, which in turn is the same as a dot product on multidimensional matrices which ML folks call tensors. If y |
12,640 | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot product or the sum of element-wise multiplication? | Both element-wise and dot product interpretations are correct. When you convolve two tensors, X of shape (h, w, d) and Y of shape (h, w, d), you're doing element-wise multiplication. It's, however, the same as the dot product of X and Y transpose. You can expand the math equation, the shapes and subscripts match. | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot pr | Both element-wise and dot product interpretations are correct. When you convolve two tensors, X of shape (h, w, d) and Y of shape (h, w, d), you're doing element-wise multiplication. It's, however, th | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot product or the sum of element-wise multiplication?
Both element-wise and dot product interpretations are correct. When you convolve two tensors, X of shape (h, w, d) and Y of shape (h, w, d), you're doing element-wise mult... | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot pr
Both element-wise and dot product interpretations are correct. When you convolve two tensors, X of shape (h, w, d) and Y of shape (h, w, d), you're doing element-wise multiplication. It's, however, th |
12,641 | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot product or the sum of element-wise multiplication? | "What operation is actually used (element-by-element multiplication or the dot product?) and what is the primary difference?"
The actual operation is called a convolution defined as:
$$ J(x,y) = K * I = \sum_{n,m}K(n,m)I(x-n,y-m) $$
Where $J$ is the convolved signal, $K$ is the kernel, $I$ is the input signal, and $n,... | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot pr | "What operation is actually used (element-by-element multiplication or the dot product?) and what is the primary difference?"
The actual operation is called a convolution defined as:
$$ J(x,y) = K * I | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot product or the sum of element-wise multiplication?
"What operation is actually used (element-by-element multiplication or the dot product?) and what is the primary difference?"
The actual operation is called a convolution ... | In a convolutional neural network (CNN), when convolving the image, is the operation used the dot pr
"What operation is actually used (element-by-element multiplication or the dot product?) and what is the primary difference?"
The actual operation is called a convolution defined as:
$$ J(x,y) = K * I |
12,642 | Does "curse of dimensionality" really exist in real data? | This paper(1) discusses the blessing of non-uniformity as a counterpoint to the curse of dimensionality. The main idea is that data are not uniformly dispersed within the feature space, so one can gain traction by identifying the ways in which the data are organized.
(1) Pedro Domingos, "A Few Useful Things to Know abo... | Does "curse of dimensionality" really exist in real data? | This paper(1) discusses the blessing of non-uniformity as a counterpoint to the curse of dimensionality. The main idea is that data are not uniformly dispersed within the feature space, so one can gai | Does "curse of dimensionality" really exist in real data?
This paper(1) discusses the blessing of non-uniformity as a counterpoint to the curse of dimensionality. The main idea is that data are not uniformly dispersed within the feature space, so one can gain traction by identifying the ways in which the data are organ... | Does "curse of dimensionality" really exist in real data?
This paper(1) discusses the blessing of non-uniformity as a counterpoint to the curse of dimensionality. The main idea is that data are not uniformly dispersed within the feature space, so one can gai |
12,643 | Does "curse of dimensionality" really exist in real data? | Curse of dimensionality in machine learning is more often the problem of exploding empty space between the few data points that you have. Low manifold data can make it even worse. Here is an example setup with 10000 samples where I try to do kNN with 1 neighbor.
from numpy.random import normal
from sklearn.neighbors im... | Does "curse of dimensionality" really exist in real data? | Curse of dimensionality in machine learning is more often the problem of exploding empty space between the few data points that you have. Low manifold data can make it even worse. Here is an example s | Does "curse of dimensionality" really exist in real data?
Curse of dimensionality in machine learning is more often the problem of exploding empty space between the few data points that you have. Low manifold data can make it even worse. Here is an example setup with 10000 samples where I try to do kNN with 1 neighbor.... | Does "curse of dimensionality" really exist in real data?
Curse of dimensionality in machine learning is more often the problem of exploding empty space between the few data points that you have. Low manifold data can make it even worse. Here is an example s |
12,644 | Does "curse of dimensionality" really exist in real data? | Consider for example time series (and images, and audio). Sensor readings (Internet of Things) are very common.
The curse of dimensionality is much more common than you think. There is a large redundancy there, but also a lot of noise.
The problem is that many people simply avoid these challenges of real data, and only... | Does "curse of dimensionality" really exist in real data? | Consider for example time series (and images, and audio). Sensor readings (Internet of Things) are very common.
The curse of dimensionality is much more common than you think. There is a large redunda | Does "curse of dimensionality" really exist in real data?
Consider for example time series (and images, and audio). Sensor readings (Internet of Things) are very common.
The curse of dimensionality is much more common than you think. There is a large redundancy there, but also a lot of noise.
The problem is that many p... | Does "curse of dimensionality" really exist in real data?
Consider for example time series (and images, and audio). Sensor readings (Internet of Things) are very common.
The curse of dimensionality is much more common than you think. There is a large redunda |
12,645 | Does "curse of dimensionality" really exist in real data? | There is a wonderful article, "Statistical Modeling: the two cultures", by Breiman. He explains the two groups of scientists who deal with data and how each of them look at "dimensionality". The answer to your question is "it depends" in which group you are. Check the paper out. | Does "curse of dimensionality" really exist in real data? | There is a wonderful article, "Statistical Modeling: the two cultures", by Breiman. He explains the two groups of scientists who deal with data and how each of them look at "dimensionality". The answe | Does "curse of dimensionality" really exist in real data?
There is a wonderful article, "Statistical Modeling: the two cultures", by Breiman. He explains the two groups of scientists who deal with data and how each of them look at "dimensionality". The answer to your question is "it depends" in which group you are. Che... | Does "curse of dimensionality" really exist in real data?
There is a wonderful article, "Statistical Modeling: the two cultures", by Breiman. He explains the two groups of scientists who deal with data and how each of them look at "dimensionality". The answe |
12,646 | Deriving the bivariate Poisson distribution | In a slide presentation, Karlis and Ntzoufras define a bivariate Poisson as the distribution of $(X,Y)=(X_1+X_0,X_2+X_0)$ where the $X_i$ independently have Poisson $\theta_i$ distributions. Recall that having such a distribution means
$$\Pr(X_i=k) = e^{-\theta_i}\frac{\theta_i^k}{k!}$$
for $k=0, 1, 2, \ldots.$
The eve... | Deriving the bivariate Poisson distribution | In a slide presentation, Karlis and Ntzoufras define a bivariate Poisson as the distribution of $(X,Y)=(X_1+X_0,X_2+X_0)$ where the $X_i$ independently have Poisson $\theta_i$ distributions. Recall th | Deriving the bivariate Poisson distribution
In a slide presentation, Karlis and Ntzoufras define a bivariate Poisson as the distribution of $(X,Y)=(X_1+X_0,X_2+X_0)$ where the $X_i$ independently have Poisson $\theta_i$ distributions. Recall that having such a distribution means
$$\Pr(X_i=k) = e^{-\theta_i}\frac{\theta... | Deriving the bivariate Poisson distribution
In a slide presentation, Karlis and Ntzoufras define a bivariate Poisson as the distribution of $(X,Y)=(X_1+X_0,X_2+X_0)$ where the $X_i$ independently have Poisson $\theta_i$ distributions. Recall th |
12,647 | Deriving the bivariate Poisson distribution | Here is a way to derive the bivariate poisson distribution.
Let $X_0, X_1, X_2$ be independent poisson random variables with parameters $\theta_0, \theta_1, \theta_2$. Then we define $Y_1=X_0+X_1, Y_2 = X_0+X_2$. The variable $X_0$, common to both $Y_1$ an $Y_2$, causes the pair $(Y_1, Y_2)$ to be correlated. Then we... | Deriving the bivariate Poisson distribution | Here is a way to derive the bivariate poisson distribution.
Let $X_0, X_1, X_2$ be independent poisson random variables with parameters $\theta_0, \theta_1, \theta_2$. Then we define $Y_1=X_0+X_1, Y_ | Deriving the bivariate Poisson distribution
Here is a way to derive the bivariate poisson distribution.
Let $X_0, X_1, X_2$ be independent poisson random variables with parameters $\theta_0, \theta_1, \theta_2$. Then we define $Y_1=X_0+X_1, Y_2 = X_0+X_2$. The variable $X_0$, common to both $Y_1$ an $Y_2$, causes the... | Deriving the bivariate Poisson distribution
Here is a way to derive the bivariate poisson distribution.
Let $X_0, X_1, X_2$ be independent poisson random variables with parameters $\theta_0, \theta_1, \theta_2$. Then we define $Y_1=X_0+X_1, Y_ |
12,648 | Generate pairs of random numbers uniformly distributed and correlated | I'm not aware of a universal method to generate correlated random variables with any given marginal distributions. So, I'll propose an ad hoc method to generate pairs of uniformly distributed random variables with a given (Pearson) correlation.
Without loss of generality, I assume that the desired marginal distribution... | Generate pairs of random numbers uniformly distributed and correlated | I'm not aware of a universal method to generate correlated random variables with any given marginal distributions. So, I'll propose an ad hoc method to generate pairs of uniformly distributed random v | Generate pairs of random numbers uniformly distributed and correlated
I'm not aware of a universal method to generate correlated random variables with any given marginal distributions. So, I'll propose an ad hoc method to generate pairs of uniformly distributed random variables with a given (Pearson) correlation.
Witho... | Generate pairs of random numbers uniformly distributed and correlated
I'm not aware of a universal method to generate correlated random variables with any given marginal distributions. So, I'll propose an ad hoc method to generate pairs of uniformly distributed random v |
12,649 | Generate pairs of random numbers uniformly distributed and correlated | Intuitively, $u_1$ is $U(0,1)$ because $u_1$ equals $w_1$ [which is $U(0,1)$] if $I = 1$, and $u_1$ equals $w_2$ [which is $U(0,1)$] if $I = 0$,
so $u_1$ is $U(0,1)$ in either case. The same for $u_2$. As for the correlation:
$E(u_1 u_2) = E[I w_1 + (1-I) w_2][I w_1 + (1-I) w_3]$
Expanding this, note first that $I(I-... | Generate pairs of random numbers uniformly distributed and correlated | Intuitively, $u_1$ is $U(0,1)$ because $u_1$ equals $w_1$ [which is $U(0,1)$] if $I = 1$, and $u_1$ equals $w_2$ [which is $U(0,1)$] if $I = 0$,
so $u_1$ is $U(0,1)$ in either case. The same for $u_2 | Generate pairs of random numbers uniformly distributed and correlated
Intuitively, $u_1$ is $U(0,1)$ because $u_1$ equals $w_1$ [which is $U(0,1)$] if $I = 1$, and $u_1$ equals $w_2$ [which is $U(0,1)$] if $I = 0$,
so $u_1$ is $U(0,1)$ in either case. The same for $u_2$. As for the correlation:
$E(u_1 u_2) = E[I w_1 ... | Generate pairs of random numbers uniformly distributed and correlated
Intuitively, $u_1$ is $U(0,1)$ because $u_1$ equals $w_1$ [which is $U(0,1)$] if $I = 1$, and $u_1$ equals $w_2$ [which is $U(0,1)$] if $I = 0$,
so $u_1$ is $U(0,1)$ in either case. The same for $u_2 |
12,650 | Generate pairs of random numbers uniformly distributed and correlated | Here is one easy method for positive correlation: Let $(u_1, u_2) = Iw_1 + (1-I) (w_2, w_3)$, where $w_1, w_2,$ and $w_3$ are independent $U(0,1)$ and $I$ is Bernoulli($p$). $u_1$ and $u_2$ will then have $U(0,1)$ distributions with correlation $p$. This extends immediately to $k$-tuples of uniforms with compound sy... | Generate pairs of random numbers uniformly distributed and correlated | Here is one easy method for positive correlation: Let $(u_1, u_2) = Iw_1 + (1-I) (w_2, w_3)$, where $w_1, w_2,$ and $w_3$ are independent $U(0,1)$ and $I$ is Bernoulli($p$). $u_1$ and $u_2$ will the | Generate pairs of random numbers uniformly distributed and correlated
Here is one easy method for positive correlation: Let $(u_1, u_2) = Iw_1 + (1-I) (w_2, w_3)$, where $w_1, w_2,$ and $w_3$ are independent $U(0,1)$ and $I$ is Bernoulli($p$). $u_1$ and $u_2$ will then have $U(0,1)$ distributions with correlation $p$... | Generate pairs of random numbers uniformly distributed and correlated
Here is one easy method for positive correlation: Let $(u_1, u_2) = Iw_1 + (1-I) (w_2, w_3)$, where $w_1, w_2,$ and $w_3$ are independent $U(0,1)$ and $I$ is Bernoulli($p$). $u_1$ and $u_2$ will the |
12,651 | Generate pairs of random numbers uniformly distributed and correlated | From brillant answer to this topic by @QuantIbex some time has passed. Perhaps a fairly new module / library in R will allow someone to get the above a little easier. You can read the detailed documentation of the possibilities that offers simstudy. A definite advantage of this library is that the solution is generaliz... | Generate pairs of random numbers uniformly distributed and correlated | From brillant answer to this topic by @QuantIbex some time has passed. Perhaps a fairly new module / library in R will allow someone to get the above a little easier. You can read the detailed documen | Generate pairs of random numbers uniformly distributed and correlated
From brillant answer to this topic by @QuantIbex some time has passed. Perhaps a fairly new module / library in R will allow someone to get the above a little easier. You can read the detailed documentation of the possibilities that offers simstudy. ... | Generate pairs of random numbers uniformly distributed and correlated
From brillant answer to this topic by @QuantIbex some time has passed. Perhaps a fairly new module / library in R will allow someone to get the above a little easier. You can read the detailed documen |
12,652 | Parameters without defined priors in Stan | From (an earlier version of) the Stan reference manual:
Not specifying a prior is equivalent to specifying a uniform prior.
A uniform prior is only proper if the parameter is bounded[...]
Improper priors are also allowed in Stan programs; they arise from unconstrained parameters without sampling statements. In some ca... | Parameters without defined priors in Stan | From (an earlier version of) the Stan reference manual:
Not specifying a prior is equivalent to specifying a uniform prior.
A uniform prior is only proper if the parameter is bounded[...]
Improper pr | Parameters without defined priors in Stan
From (an earlier version of) the Stan reference manual:
Not specifying a prior is equivalent to specifying a uniform prior.
A uniform prior is only proper if the parameter is bounded[...]
Improper priors are also allowed in Stan programs; they arise from unconstrained paramete... | Parameters without defined priors in Stan
From (an earlier version of) the Stan reference manual:
Not specifying a prior is equivalent to specifying a uniform prior.
A uniform prior is only proper if the parameter is bounded[...]
Improper pr |
12,653 | Parameters without defined priors in Stan | From the Stan reference v1.0.2 (pg 6, footnote 1)
If no prior were specified in the model block, the constraints on theta ensure it falls between 0 and 1, providing theta an implicit uniform prior. For parameters with no prior specified and unbounded support, the result is an improper prior. Stan accepts improper prio... | Parameters without defined priors in Stan | From the Stan reference v1.0.2 (pg 6, footnote 1)
If no prior were specified in the model block, the constraints on theta ensure it falls between 0 and 1, providing theta an implicit uniform prior. F | Parameters without defined priors in Stan
From the Stan reference v1.0.2 (pg 6, footnote 1)
If no prior were specified in the model block, the constraints on theta ensure it falls between 0 and 1, providing theta an implicit uniform prior. For parameters with no prior specified and unbounded support, the result is an ... | Parameters without defined priors in Stan
From the Stan reference v1.0.2 (pg 6, footnote 1)
If no prior were specified in the model block, the constraints on theta ensure it falls between 0 and 1, providing theta an implicit uniform prior. F |
12,654 | How would you design a machine learning system to play Angry Birds? | Assuming you could get the right hooks into the software (or you work with your own mock-up), some things would be easy here, and some less so. This is quite a tough problem I think. As carlosdc mentioned, Reinforcement Learning (RL) is one possible avenue, although I'm not sure it's the right one.
When you begin, you... | How would you design a machine learning system to play Angry Birds? | Assuming you could get the right hooks into the software (or you work with your own mock-up), some things would be easy here, and some less so. This is quite a tough problem I think. As carlosdc menti | How would you design a machine learning system to play Angry Birds?
Assuming you could get the right hooks into the software (or you work with your own mock-up), some things would be easy here, and some less so. This is quite a tough problem I think. As carlosdc mentioned, Reinforcement Learning (RL) is one possible av... | How would you design a machine learning system to play Angry Birds?
Assuming you could get the right hooks into the software (or you work with your own mock-up), some things would be easy here, and some less so. This is quite a tough problem I think. As carlosdc menti |
12,655 | How would you design a machine learning system to play Angry Birds? | Cool question!
It seems like this question is about the natural technique for this type of
problem. I think think the natural technique for this type of problem is
reinforcement learning (RL). RL is about how an agent ought to take actions in
an environment so as to maximize some notion of cumulative reward. Perhaps th... | How would you design a machine learning system to play Angry Birds? | Cool question!
It seems like this question is about the natural technique for this type of
problem. I think think the natural technique for this type of problem is
reinforcement learning (RL). RL is a | How would you design a machine learning system to play Angry Birds?
Cool question!
It seems like this question is about the natural technique for this type of
problem. I think think the natural technique for this type of problem is
reinforcement learning (RL). RL is about how an agent ought to take actions in
an enviro... | How would you design a machine learning system to play Angry Birds?
Cool question!
It seems like this question is about the natural technique for this type of
problem. I think think the natural technique for this type of problem is
reinforcement learning (RL). RL is a |
12,656 | How would you design a machine learning system to play Angry Birds? | Check here how others are doing it or participate yourself:
Angry Birds AI Challenge http://ai2012.web.cse.unsw.edu.au/abc.html | How would you design a machine learning system to play Angry Birds? | Check here how others are doing it or participate yourself:
Angry Birds AI Challenge http://ai2012.web.cse.unsw.edu.au/abc.html | How would you design a machine learning system to play Angry Birds?
Check here how others are doing it or participate yourself:
Angry Birds AI Challenge http://ai2012.web.cse.unsw.edu.au/abc.html | How would you design a machine learning system to play Angry Birds?
Check here how others are doing it or participate yourself:
Angry Birds AI Challenge http://ai2012.web.cse.unsw.edu.au/abc.html |
12,657 | How would you design a machine learning system to play Angry Birds? | just mentioned this over in meta. there was a pioneering use of genetic algorithms by Koza to solve the video game Pacman. he constructed algorithmic primitives that could sense and act. as I recall these were combined in Lisp-like trees to create larger algorithms. crossover with Lisp trees involves substituting or ex... | How would you design a machine learning system to play Angry Birds? | just mentioned this over in meta. there was a pioneering use of genetic algorithms by Koza to solve the video game Pacman. he constructed algorithmic primitives that could sense and act. as I recall t | How would you design a machine learning system to play Angry Birds?
just mentioned this over in meta. there was a pioneering use of genetic algorithms by Koza to solve the video game Pacman. he constructed algorithmic primitives that could sense and act. as I recall these were combined in Lisp-like trees to create larg... | How would you design a machine learning system to play Angry Birds?
just mentioned this over in meta. there was a pioneering use of genetic algorithms by Koza to solve the video game Pacman. he constructed algorithmic primitives that could sense and act. as I recall t |
12,658 | What does "vanilla" mean? | Vanilla means standard, usual, or unmodified version of something. Vanilla gradient descent means the basic gradient descent algorithm without any bells or whistles.
There are many variants on gradient descent. In usual gradient descent (also known as batch gradient descent or vanilla gradient descent), the gradient i... | What does "vanilla" mean? | Vanilla means standard, usual, or unmodified version of something. Vanilla gradient descent means the basic gradient descent algorithm without any bells or whistles.
There are many variants on gradie | What does "vanilla" mean?
Vanilla means standard, usual, or unmodified version of something. Vanilla gradient descent means the basic gradient descent algorithm without any bells or whistles.
There are many variants on gradient descent. In usual gradient descent (also known as batch gradient descent or vanilla gradien... | What does "vanilla" mean?
Vanilla means standard, usual, or unmodified version of something. Vanilla gradient descent means the basic gradient descent algorithm without any bells or whistles.
There are many variants on gradie |
12,659 | Why is skewed data not preferred for modelling? | When removing skewness, transformations are attempting to make the dataset follow the Gaussian distribution. The reason is simply that if the dataset can be transformed to be statistically close enough to a Gaussian dataset, then the largest set of tools possible are available to them to use. Tests such as the ANOVA,... | Why is skewed data not preferred for modelling? | When removing skewness, transformations are attempting to make the dataset follow the Gaussian distribution. The reason is simply that if the dataset can be transformed to be statistically close enou | Why is skewed data not preferred for modelling?
When removing skewness, transformations are attempting to make the dataset follow the Gaussian distribution. The reason is simply that if the dataset can be transformed to be statistically close enough to a Gaussian dataset, then the largest set of tools possible are ava... | Why is skewed data not preferred for modelling?
When removing skewness, transformations are attempting to make the dataset follow the Gaussian distribution. The reason is simply that if the dataset can be transformed to be statistically close enou |
12,660 | Why is skewed data not preferred for modelling? | This is mostly true for parametric models. As Tavrock said, having a response variable that's not skewed makes Gaussian approximation of parameter estimation work better, this because symmetric distribution converge much faster than skewed ones to Gaussian. This means that, if you have skewed data, transforming it will... | Why is skewed data not preferred for modelling? | This is mostly true for parametric models. As Tavrock said, having a response variable that's not skewed makes Gaussian approximation of parameter estimation work better, this because symmetric distri | Why is skewed data not preferred for modelling?
This is mostly true for parametric models. As Tavrock said, having a response variable that's not skewed makes Gaussian approximation of parameter estimation work better, this because symmetric distribution converge much faster than skewed ones to Gaussian. This means tha... | Why is skewed data not preferred for modelling?
This is mostly true for parametric models. As Tavrock said, having a response variable that's not skewed makes Gaussian approximation of parameter estimation work better, this because symmetric distri |
12,661 | Why is skewed data not preferred for modelling? | When is skewness a bad thing to have? Symmetric distributions (generally but not always: e.g., not for the Cauchy distribution) have median, mode and mean very close to each other. So consider, if we want to measure the location of a population, it is useful to have the median, mode and mean close to each other.
For ex... | Why is skewed data not preferred for modelling? | When is skewness a bad thing to have? Symmetric distributions (generally but not always: e.g., not for the Cauchy distribution) have median, mode and mean very close to each other. So consider, if we | Why is skewed data not preferred for modelling?
When is skewness a bad thing to have? Symmetric distributions (generally but not always: e.g., not for the Cauchy distribution) have median, mode and mean very close to each other. So consider, if we want to measure the location of a population, it is useful to have the m... | Why is skewed data not preferred for modelling?
When is skewness a bad thing to have? Symmetric distributions (generally but not always: e.g., not for the Cauchy distribution) have median, mode and mean very close to each other. So consider, if we |
12,662 | Why is skewed data not preferred for modelling? | I believe this is very much an artifact of the tradition to revert to Gaussians due to their nice properties.
But there are nice distributional alternatives, e. g. the generalized gamma that encompasses a host of different skewed distributional shapes and forms | Why is skewed data not preferred for modelling? | I believe this is very much an artifact of the tradition to revert to Gaussians due to their nice properties.
But there are nice distributional alternatives, e. g. the generalized gamma that encompas | Why is skewed data not preferred for modelling?
I believe this is very much an artifact of the tradition to revert to Gaussians due to their nice properties.
But there are nice distributional alternatives, e. g. the generalized gamma that encompasses a host of different skewed distributional shapes and forms | Why is skewed data not preferred for modelling?
I believe this is very much an artifact of the tradition to revert to Gaussians due to their nice properties.
But there are nice distributional alternatives, e. g. the generalized gamma that encompas |
12,663 | Why is skewed data not preferred for modelling? | I think that it's not just modeling but our brains are not used to work with highly skewed data. For instance, it's well known in behavioral finance that we're not good at estimating the very low or high probabilities. | Why is skewed data not preferred for modelling? | I think that it's not just modeling but our brains are not used to work with highly skewed data. For instance, it's well known in behavioral finance that we're not good at estimating the very low or h | Why is skewed data not preferred for modelling?
I think that it's not just modeling but our brains are not used to work with highly skewed data. For instance, it's well known in behavioral finance that we're not good at estimating the very low or high probabilities. | Why is skewed data not preferred for modelling?
I think that it's not just modeling but our brains are not used to work with highly skewed data. For instance, it's well known in behavioral finance that we're not good at estimating the very low or h |
12,664 | Why is skewed data not preferred for modelling? | Like other readers have said, some more background on what you are planning to achieve with your data would be helpful.
That being said, there are two important doctrines in the realm of statistics known as the central limit theorem and the law of large numbers. That is to say, that the more observations one has, the m... | Why is skewed data not preferred for modelling? | Like other readers have said, some more background on what you are planning to achieve with your data would be helpful.
That being said, there are two important doctrines in the realm of statistics kn | Why is skewed data not preferred for modelling?
Like other readers have said, some more background on what you are planning to achieve with your data would be helpful.
That being said, there are two important doctrines in the realm of statistics known as the central limit theorem and the law of large numbers. That is t... | Why is skewed data not preferred for modelling?
Like other readers have said, some more background on what you are planning to achieve with your data would be helpful.
That being said, there are two important doctrines in the realm of statistics kn |
12,665 | Why is skewed data not preferred for modelling? | Mostly of the results are based on Gaussian assumptions. If you have a skewed distribution, you don't have a Gaussian distribution, so maybe you should try desperately to turn it into that.
BUT of course, you can try with GLM. | Why is skewed data not preferred for modelling? | Mostly of the results are based on Gaussian assumptions. If you have a skewed distribution, you don't have a Gaussian distribution, so maybe you should try desperately to turn it into that.
BUT of cou | Why is skewed data not preferred for modelling?
Mostly of the results are based on Gaussian assumptions. If you have a skewed distribution, you don't have a Gaussian distribution, so maybe you should try desperately to turn it into that.
BUT of course, you can try with GLM. | Why is skewed data not preferred for modelling?
Mostly of the results are based on Gaussian assumptions. If you have a skewed distribution, you don't have a Gaussian distribution, so maybe you should try desperately to turn it into that.
BUT of cou |
12,666 | Nystroem Method for Kernel Approximation | Let's derive the Nyström approximation in a way that should make the answers to your questions clearer.
The key assumption in Nyström is that the kernel function is of rank $m$. (Really we assume that it's approximately of rank $m$, but for simplicity let's just pretend it's exactly rank $m$ for now.) That means that a... | Nystroem Method for Kernel Approximation | Let's derive the Nyström approximation in a way that should make the answers to your questions clearer.
The key assumption in Nyström is that the kernel function is of rank $m$. (Really we assume that | Nystroem Method for Kernel Approximation
Let's derive the Nyström approximation in a way that should make the answers to your questions clearer.
The key assumption in Nyström is that the kernel function is of rank $m$. (Really we assume that it's approximately of rank $m$, but for simplicity let's just pretend it's exa... | Nystroem Method for Kernel Approximation
Let's derive the Nyström approximation in a way that should make the answers to your questions clearer.
The key assumption in Nyström is that the kernel function is of rank $m$. (Really we assume that |
12,667 | What is the relationship between the Beta distribution and the logistic regression model? | Beta is a distribution of values in $(0,1)$ range that is very flexible in it's shape, so for almost any unimodal empirical distribution of values in $(0,1)$ you can easily find parameters of such beta distribution that "resembles" shape of the distribution.
Notice that logistic regression provides you with conditional... | What is the relationship between the Beta distribution and the logistic regression model? | Beta is a distribution of values in $(0,1)$ range that is very flexible in it's shape, so for almost any unimodal empirical distribution of values in $(0,1)$ you can easily find parameters of such bet | What is the relationship between the Beta distribution and the logistic regression model?
Beta is a distribution of values in $(0,1)$ range that is very flexible in it's shape, so for almost any unimodal empirical distribution of values in $(0,1)$ you can easily find parameters of such beta distribution that "resembles... | What is the relationship between the Beta distribution and the logistic regression model?
Beta is a distribution of values in $(0,1)$ range that is very flexible in it's shape, so for almost any unimodal empirical distribution of values in $(0,1)$ you can easily find parameters of such bet |
12,668 | What is the relationship between the Beta distribution and the logistic regression model? | Logistic regression is a special case of a Generalized Linear Model (GLM). In this particular case of binary data, the logistic function is the canonical link function that transforms the non-linear regression problem at hand into a linear problem. GLMs are somewhat special, in the sense that they apply only to distrib... | What is the relationship between the Beta distribution and the logistic regression model? | Logistic regression is a special case of a Generalized Linear Model (GLM). In this particular case of binary data, the logistic function is the canonical link function that transforms the non-linear r | What is the relationship between the Beta distribution and the logistic regression model?
Logistic regression is a special case of a Generalized Linear Model (GLM). In this particular case of binary data, the logistic function is the canonical link function that transforms the non-linear regression problem at hand into... | What is the relationship between the Beta distribution and the logistic regression model?
Logistic regression is a special case of a Generalized Linear Model (GLM). In this particular case of binary data, the logistic function is the canonical link function that transforms the non-linear r |
12,669 | What is the relationship between the Beta distribution and the logistic regression model? | Maybe there is no direct connection? The distribution of $P(A=1|X)$ largely depends on your simulation of $X$. If you simulated $X$ with $N(0,1)$, $\exp(-X\beta)$ will have log-normal distribution with $\mu=-1$ given $\beta_0=\beta_1=1$. The distribution of $P(A=1|X)$ can then be found explicitly: with c.d.f. $$F(x)=1-... | What is the relationship between the Beta distribution and the logistic regression model? | Maybe there is no direct connection? The distribution of $P(A=1|X)$ largely depends on your simulation of $X$. If you simulated $X$ with $N(0,1)$, $\exp(-X\beta)$ will have log-normal distribution wit | What is the relationship between the Beta distribution and the logistic regression model?
Maybe there is no direct connection? The distribution of $P(A=1|X)$ largely depends on your simulation of $X$. If you simulated $X$ with $N(0,1)$, $\exp(-X\beta)$ will have log-normal distribution with $\mu=-1$ given $\beta_0=\bet... | What is the relationship between the Beta distribution and the logistic regression model?
Maybe there is no direct connection? The distribution of $P(A=1|X)$ largely depends on your simulation of $X$. If you simulated $X$ with $N(0,1)$, $\exp(-X\beta)$ will have log-normal distribution wit |
12,670 | Are log difference time series models better than growth rates? | One major advantage of log-differences is symmetry: if you have a log difference of $0.1$ today and one of $-0.1$ tomorrow, you are back from where you started. In contrast, 10% growth today and 10% decline tomorrow will not bring you back to the initial value. | Are log difference time series models better than growth rates? | One major advantage of log-differences is symmetry: if you have a log difference of $0.1$ today and one of $-0.1$ tomorrow, you are back from where you started. In contrast, 10% growth today and 10% d | Are log difference time series models better than growth rates?
One major advantage of log-differences is symmetry: if you have a log difference of $0.1$ today and one of $-0.1$ tomorrow, you are back from where you started. In contrast, 10% growth today and 10% decline tomorrow will not bring you back to the initial v... | Are log difference time series models better than growth rates?
One major advantage of log-differences is symmetry: if you have a log difference of $0.1$ today and one of $-0.1$ tomorrow, you are back from where you started. In contrast, 10% growth today and 10% d |
12,671 | Are log difference time series models better than growth rates? | Many macroeconomic indicators are tied to population growth, which is exponential, and thus have an exponential trend themselves. So the process before modelling with ARIMA, VAR or other linear methods is usually:
Take logs to get a series with a linear trend
Then difference to get a stationary series | Are log difference time series models better than growth rates? | Many macroeconomic indicators are tied to population growth, which is exponential, and thus have an exponential trend themselves. So the process before modelling with ARIMA, VAR or other linear method | Are log difference time series models better than growth rates?
Many macroeconomic indicators are tied to population growth, which is exponential, and thus have an exponential trend themselves. So the process before modelling with ARIMA, VAR or other linear methods is usually:
Take logs to get a series with a linear t... | Are log difference time series models better than growth rates?
Many macroeconomic indicators are tied to population growth, which is exponential, and thus have an exponential trend themselves. So the process before modelling with ARIMA, VAR or other linear method |
12,672 | Test a significant difference between two slope values | The following article might be helpfull to you, as it describes how to evaluate if the effect of a given explanatory factor is invariant over persons, time, or organizations:
Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. R. (1998). Using the Correct Statistical Test for the Equality of Regression Coefficient... | Test a significant difference between two slope values | The following article might be helpfull to you, as it describes how to evaluate if the effect of a given explanatory factor is invariant over persons, time, or organizations:
Paternoster, R., Brame, R | Test a significant difference between two slope values
The following article might be helpfull to you, as it describes how to evaluate if the effect of a given explanatory factor is invariant over persons, time, or organizations:
Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. R. (1998). Using the Correct Stat... | Test a significant difference between two slope values
The following article might be helpfull to you, as it describes how to evaluate if the effect of a given explanatory factor is invariant over persons, time, or organizations:
Paternoster, R., Brame, R |
12,673 | Test a significant difference between two slope values | If the slopes come from ordinary least squares regression, it would be good to verify that the year-to-year data which generated these values are indeed independent. Most capture-recapture studies need to account for previous years' volumes using some method of handling the dependence of volume over time.
Using standa... | Test a significant difference between two slope values | If the slopes come from ordinary least squares regression, it would be good to verify that the year-to-year data which generated these values are indeed independent. Most capture-recapture studies nee | Test a significant difference between two slope values
If the slopes come from ordinary least squares regression, it would be good to verify that the year-to-year data which generated these values are indeed independent. Most capture-recapture studies need to account for previous years' volumes using some method of han... | Test a significant difference between two slope values
If the slopes come from ordinary least squares regression, it would be good to verify that the year-to-year data which generated these values are indeed independent. Most capture-recapture studies nee |
12,674 | Test a significant difference between two slope values | The classic (and more statistically powerful) way of testing this is to combine both datasets into a single regression model and then include the area as an interaction term. See, for example, here:
http://www.theanalysisfactor.com/compare-regression-coefficients/ | Test a significant difference between two slope values | The classic (and more statistically powerful) way of testing this is to combine both datasets into a single regression model and then include the area as an interaction term. See, for example, here:
| Test a significant difference between two slope values
The classic (and more statistically powerful) way of testing this is to combine both datasets into a single regression model and then include the area as an interaction term. See, for example, here:
http://www.theanalysisfactor.com/compare-regression-coefficients/ | Test a significant difference between two slope values
The classic (and more statistically powerful) way of testing this is to combine both datasets into a single regression model and then include the area as an interaction term. See, for example, here:
|
12,675 | What are some techniques for sampling two correlated random variables? | I think what you're looking for is a copula. You've got two marginal distributions (specified by either parametric or empirical cdfs) and now you want to specify the dependence between the two. For the bivariate case there are all kinds of choices, but the basic recipe is the same. I'll use a Gaussian copula for ease o... | What are some techniques for sampling two correlated random variables? | I think what you're looking for is a copula. You've got two marginal distributions (specified by either parametric or empirical cdfs) and now you want to specify the dependence between the two. For th | What are some techniques for sampling two correlated random variables?
I think what you're looking for is a copula. You've got two marginal distributions (specified by either parametric or empirical cdfs) and now you want to specify the dependence between the two. For the bivariate case there are all kinds of choices, ... | What are some techniques for sampling two correlated random variables?
I think what you're looking for is a copula. You've got two marginal distributions (specified by either parametric or empirical cdfs) and now you want to specify the dependence between the two. For th |
12,676 | What are some techniques for sampling two correlated random variables? | Another popular method is "trivariate reduction" which samples $X_1 \sim Y+Z$ and $X_2 \sim W+Z$ so that the correlation is induced by the random variate $Z$. Note that this is also generalizable to more than 2 dimensions-but is more complicated than the 2-d case. You might think you can only get positive correlations ... | What are some techniques for sampling two correlated random variables? | Another popular method is "trivariate reduction" which samples $X_1 \sim Y+Z$ and $X_2 \sim W+Z$ so that the correlation is induced by the random variate $Z$. Note that this is also generalizable to m | What are some techniques for sampling two correlated random variables?
Another popular method is "trivariate reduction" which samples $X_1 \sim Y+Z$ and $X_2 \sim W+Z$ so that the correlation is induced by the random variate $Z$. Note that this is also generalizable to more than 2 dimensions-but is more complicated tha... | What are some techniques for sampling two correlated random variables?
Another popular method is "trivariate reduction" which samples $X_1 \sim Y+Z$ and $X_2 \sim W+Z$ so that the correlation is induced by the random variate $Z$. Note that this is also generalizable to m |
12,677 | How to measure/argue the goodness of fit of a trendline to a power law? | See Aaron Clauset's page:
Power-law Distributions in Empirical Data
which has links to code for fitting power laws (Matlab, R, Python, C++) as well as a paper by Clauset and Shalizi you should read first.
You might want to read Clauset's and Shalizi's blogs posts on the paper first:
Power laws and all that jazz
So... | How to measure/argue the goodness of fit of a trendline to a power law? | See Aaron Clauset's page:
Power-law Distributions in Empirical Data
which has links to code for fitting power laws (Matlab, R, Python, C++) as well as a paper by Clauset and Shalizi you should read | How to measure/argue the goodness of fit of a trendline to a power law?
See Aaron Clauset's page:
Power-law Distributions in Empirical Data
which has links to code for fitting power laws (Matlab, R, Python, C++) as well as a paper by Clauset and Shalizi you should read first.
You might want to read Clauset's and Sh... | How to measure/argue the goodness of fit of a trendline to a power law?
See Aaron Clauset's page:
Power-law Distributions in Empirical Data
which has links to code for fitting power laws (Matlab, R, Python, C++) as well as a paper by Clauset and Shalizi you should read |
12,678 | How to measure/argue the goodness of fit of a trendline to a power law? | If you're interested in bivariate power-law functions (as opposed to univariate power-law distributions), then
Warton et al. "Bivariate line-fitting methods for allometry." Biol. Rev. 81, 259-201 (2006)
is an excellent reference. In this case, regression is the right thing to do, although there can be some corrections ... | How to measure/argue the goodness of fit of a trendline to a power law? | If you're interested in bivariate power-law functions (as opposed to univariate power-law distributions), then
Warton et al. "Bivariate line-fitting methods for allometry." Biol. Rev. 81, 259-201 (200 | How to measure/argue the goodness of fit of a trendline to a power law?
If you're interested in bivariate power-law functions (as opposed to univariate power-law distributions), then
Warton et al. "Bivariate line-fitting methods for allometry." Biol. Rev. 81, 259-201 (2006)
is an excellent reference. In this case, regr... | How to measure/argue the goodness of fit of a trendline to a power law?
If you're interested in bivariate power-law functions (as opposed to univariate power-law distributions), then
Warton et al. "Bivariate line-fitting methods for allometry." Biol. Rev. 81, 259-201 (200 |
12,679 | A dynamical systems view of the Central Limit Theorem? | After doing some digging in the literature, encouraged by Kjetil's answer, I've found a few references that do take the geometric/dynamical systems approach to the CLT seriously, besides the book by Y. Sinai. I'm posting what I've found for others who may be interested, but I hope still to hear from an expert about the... | A dynamical systems view of the Central Limit Theorem? | After doing some digging in the literature, encouraged by Kjetil's answer, I've found a few references that do take the geometric/dynamical systems approach to the CLT seriously, besides the book by Y | A dynamical systems view of the Central Limit Theorem?
After doing some digging in the literature, encouraged by Kjetil's answer, I've found a few references that do take the geometric/dynamical systems approach to the CLT seriously, besides the book by Y. Sinai. I'm posting what I've found for others who may be intere... | A dynamical systems view of the Central Limit Theorem?
After doing some digging in the literature, encouraged by Kjetil's answer, I've found a few references that do take the geometric/dynamical systems approach to the CLT seriously, besides the book by Y |
12,680 | A dynamical systems view of the Central Limit Theorem? | The text "Probability Theory An Introductory Course" by Y Sinai (Springer)
discusses the CLT in this way.
The idea is (from memory ...) that
The normal distribution maximizes entropy (among distributions with fixed variance)
The averaging operator $A(x_1,x_2) = \frac{x_1+x_2}{\sqrt{2}}$ maintains variance and increa... | A dynamical systems view of the Central Limit Theorem? | The text "Probability Theory An Introductory Course" by Y Sinai (Springer)
discusses the CLT in this way.
The idea is (from memory ...) that
The normal distribution maximizes entropy (among distribu | A dynamical systems view of the Central Limit Theorem?
The text "Probability Theory An Introductory Course" by Y Sinai (Springer)
discusses the CLT in this way.
The idea is (from memory ...) that
The normal distribution maximizes entropy (among distributions with fixed variance)
The averaging operator $A(x_1,x_2) = ... | A dynamical systems view of the Central Limit Theorem?
The text "Probability Theory An Introductory Course" by Y Sinai (Springer)
discusses the CLT in this way.
The idea is (from memory ...) that
The normal distribution maximizes entropy (among distribu |
12,681 | A dynamical systems view of the Central Limit Theorem? | Great question; I've often wondered about that.
A somewhat related idea is explained in our paper
Dynamical attraction to stable processes, Ann. Inst. H. Poincaré Probab. Statist. Volume 48, Number 2, 2012, pp 551-578 (Albert Fisher and Marina Talet)
see https://www.ime.usp.br/~afisher/
The idea is to turn Levy's prob... | A dynamical systems view of the Central Limit Theorem? | Great question; I've often wondered about that.
A somewhat related idea is explained in our paper
Dynamical attraction to stable processes, Ann. Inst. H. Poincaré Probab. Statist. Volume 48, Number 2, | A dynamical systems view of the Central Limit Theorem?
Great question; I've often wondered about that.
A somewhat related idea is explained in our paper
Dynamical attraction to stable processes, Ann. Inst. H. Poincaré Probab. Statist. Volume 48, Number 2, 2012, pp 551-578 (Albert Fisher and Marina Talet)
see https://w... | A dynamical systems view of the Central Limit Theorem?
Great question; I've often wondered about that.
A somewhat related idea is explained in our paper
Dynamical attraction to stable processes, Ann. Inst. H. Poincaré Probab. Statist. Volume 48, Number 2, |
12,682 | What does "degree of freedom" mean in neural networks? | I suspect this is what Bishop means:
If you think of a neural net as a function that maps inputs to an output, then when you first initialize a neural net with small random weights, the neural net looks a lot like a linear function. The sigmoid activation function is close to linear around zero (just do a Taylor expan... | What does "degree of freedom" mean in neural networks? | I suspect this is what Bishop means:
If you think of a neural net as a function that maps inputs to an output, then when you first initialize a neural net with small random weights, the neural net loo | What does "degree of freedom" mean in neural networks?
I suspect this is what Bishop means:
If you think of a neural net as a function that maps inputs to an output, then when you first initialize a neural net with small random weights, the neural net looks a lot like a linear function. The sigmoid activation function... | What does "degree of freedom" mean in neural networks?
I suspect this is what Bishop means:
If you think of a neural net as a function that maps inputs to an output, then when you first initialize a neural net with small random weights, the neural net loo |
12,683 | What does "degree of freedom" mean in neural networks? | The phrase "sometimes explained qualitatively" suggests that he is merely making a analogy to simple linear regression. Each time we add a term to a linear regression model we add a degree of freedom to the model and subtract a degree of freedom from those associated with the error term. If we put enough independent ... | What does "degree of freedom" mean in neural networks? | The phrase "sometimes explained qualitatively" suggests that he is merely making a analogy to simple linear regression. Each time we add a term to a linear regression model we add a degree of freedom | What does "degree of freedom" mean in neural networks?
The phrase "sometimes explained qualitatively" suggests that he is merely making a analogy to simple linear regression. Each time we add a term to a linear regression model we add a degree of freedom to the model and subtract a degree of freedom from those associa... | What does "degree of freedom" mean in neural networks?
The phrase "sometimes explained qualitatively" suggests that he is merely making a analogy to simple linear regression. Each time we add a term to a linear regression model we add a degree of freedom |
12,684 | What does "degree of freedom" mean in neural networks? | The issue of the degrees of freedom on complicated statistical learning models has been discussed in Ye 1998 JASA. Basically, the idea is to see by how much the output of a complicated model, such as the neural network, responds to a unit change in inputs. For linear models, the relation is unsurpisingly one-to-one, so... | What does "degree of freedom" mean in neural networks? | The issue of the degrees of freedom on complicated statistical learning models has been discussed in Ye 1998 JASA. Basically, the idea is to see by how much the output of a complicated model, such as | What does "degree of freedom" mean in neural networks?
The issue of the degrees of freedom on complicated statistical learning models has been discussed in Ye 1998 JASA. Basically, the idea is to see by how much the output of a complicated model, such as the neural network, responds to a unit change in inputs. For line... | What does "degree of freedom" mean in neural networks?
The issue of the degrees of freedom on complicated statistical learning models has been discussed in Ye 1998 JASA. Basically, the idea is to see by how much the output of a complicated model, such as |
12,685 | What does "degree of freedom" mean in neural networks? | He says the "effective complexity of the network". He actually refers to the size of the weights of the network. This can be understood in terms of the minimum description length principle. But before I get into that, the intuition is that the bigger the weights, the more different sort of functions your network can fi... | What does "degree of freedom" mean in neural networks? | He says the "effective complexity of the network". He actually refers to the size of the weights of the network. This can be understood in terms of the minimum description length principle. But before | What does "degree of freedom" mean in neural networks?
He says the "effective complexity of the network". He actually refers to the size of the weights of the network. This can be understood in terms of the minimum description length principle. But before I get into that, the intuition is that the bigger the weights, t... | What does "degree of freedom" mean in neural networks?
He says the "effective complexity of the network". He actually refers to the size of the weights of the network. This can be understood in terms of the minimum description length principle. But before |
12,686 | Confirming the distribution of residuals in linear regression | It all depends on how you estimate the parameters. Usually, the estimators are linear, which implies the residuals are linear functions of the data. When the errors $u_i$ have a Normal distribution, then so do the data, whence so do the residuals $\hat{u}_i$ ($i$ indexes the data cases, of course).
It's conceivable (... | Confirming the distribution of residuals in linear regression | It all depends on how you estimate the parameters. Usually, the estimators are linear, which implies the residuals are linear functions of the data. When the errors $u_i$ have a Normal distribution, | Confirming the distribution of residuals in linear regression
It all depends on how you estimate the parameters. Usually, the estimators are linear, which implies the residuals are linear functions of the data. When the errors $u_i$ have a Normal distribution, then so do the data, whence so do the residuals $\hat{u}_... | Confirming the distribution of residuals in linear regression
It all depends on how you estimate the parameters. Usually, the estimators are linear, which implies the residuals are linear functions of the data. When the errors $u_i$ have a Normal distribution, |
12,687 | Confirming the distribution of residuals in linear regression | Let us recall the geometry of the least squares: we have the basic equation
$$ y_i = x_i'\beta + \epsilon_i $$
written in the matrix form as
$$ \mathbf{y} = \mathbf{X}\beta + \mathbf{\epsilon} $$
from which we derive the residuals
$$ \mathbf{e} = (I-H) \mathbf{y} $$
where $$ H = X(X'X)^{-1} X'$$ is the projection matri... | Confirming the distribution of residuals in linear regression | Let us recall the geometry of the least squares: we have the basic equation
$$ y_i = x_i'\beta + \epsilon_i $$
written in the matrix form as
$$ \mathbf{y} = \mathbf{X}\beta + \mathbf{\epsilon} $$
from | Confirming the distribution of residuals in linear regression
Let us recall the geometry of the least squares: we have the basic equation
$$ y_i = x_i'\beta + \epsilon_i $$
written in the matrix form as
$$ \mathbf{y} = \mathbf{X}\beta + \mathbf{\epsilon} $$
from which we derive the residuals
$$ \mathbf{e} = (I-H) \math... | Confirming the distribution of residuals in linear regression
Let us recall the geometry of the least squares: we have the basic equation
$$ y_i = x_i'\beta + \epsilon_i $$
written in the matrix form as
$$ \mathbf{y} = \mathbf{X}\beta + \mathbf{\epsilon} $$
from |
12,688 | Confirming the distribution of residuals in linear regression | If we get something which looks like a familiar distribution, can we
assume that our error term has this distribution?
I would argue that you can't, since the model you have just fit is invalid if the normality assumption about the errors does not hold. (in the sense that the shape of the distribution is distinctly ... | Confirming the distribution of residuals in linear regression | If we get something which looks like a familiar distribution, can we
assume that our error term has this distribution?
I would argue that you can't, since the model you have just fit is invalid if | Confirming the distribution of residuals in linear regression
If we get something which looks like a familiar distribution, can we
assume that our error term has this distribution?
I would argue that you can't, since the model you have just fit is invalid if the normality assumption about the errors does not hold. (... | Confirming the distribution of residuals in linear regression
If we get something which looks like a familiar distribution, can we
assume that our error term has this distribution?
I would argue that you can't, since the model you have just fit is invalid if |
12,689 | Confirming the distribution of residuals in linear regression | 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.
Yes it is sensible. The residuals are the errors. You ... | Confirming the distribution of residuals in linear regression | 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.
| Confirming the distribution of residuals in linear regression
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.
... | Confirming the distribution of residuals in linear regression
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.
|
12,690 | What is the relation between estimator and estimate? | E. L. Lehmann, in his classic Theory of Point Estimation, answers this question on pp 1-2.
The observations are now postulated to be the values taken on by random variables which are assumed to follow a joint probability distribution, $P$, belonging to some known class...
...let us now specialize to point estimation..... | What is the relation between estimator and estimate? | E. L. Lehmann, in his classic Theory of Point Estimation, answers this question on pp 1-2.
The observations are now postulated to be the values taken on by random variables which are assumed to follo | What is the relation between estimator and estimate?
E. L. Lehmann, in his classic Theory of Point Estimation, answers this question on pp 1-2.
The observations are now postulated to be the values taken on by random variables which are assumed to follow a joint probability distribution, $P$, belonging to some known cl... | What is the relation between estimator and estimate?
E. L. Lehmann, in his classic Theory of Point Estimation, answers this question on pp 1-2.
The observations are now postulated to be the values taken on by random variables which are assumed to follo |
12,691 | What is the relation between estimator and estimate? | In short: an estimator is a function and an estimate is a value that summarizes an observed sample.
An estimator is a function that maps a random sample to the parameter estimate:
$$
\hat{\Theta}=t(X_1,X_2,...,X_n)
$$
Note that an estimator of n random variables $X_1,X_2,...,X_n$ is a random variable $\hat{\Theta}$. Fo... | What is the relation between estimator and estimate? | In short: an estimator is a function and an estimate is a value that summarizes an observed sample.
An estimator is a function that maps a random sample to the parameter estimate:
$$
\hat{\Theta}=t(X_ | What is the relation between estimator and estimate?
In short: an estimator is a function and an estimate is a value that summarizes an observed sample.
An estimator is a function that maps a random sample to the parameter estimate:
$$
\hat{\Theta}=t(X_1,X_2,...,X_n)
$$
Note that an estimator of n random variables $X_1... | What is the relation between estimator and estimate?
In short: an estimator is a function and an estimate is a value that summarizes an observed sample.
An estimator is a function that maps a random sample to the parameter estimate:
$$
\hat{\Theta}=t(X_ |
12,692 | What is the relation between estimator and estimate? | It might be helpful to illustrate whuber's answer in the context of a linear regression model. Let's say you have some bivariate data and you use Ordinary Least Squares to come up with the following model:
Y = 6X + 1
At this point, you can take any value of X, plug it into the model and predict the outcome, Y. In thi... | What is the relation between estimator and estimate? | It might be helpful to illustrate whuber's answer in the context of a linear regression model. Let's say you have some bivariate data and you use Ordinary Least Squares to come up with the following m | What is the relation between estimator and estimate?
It might be helpful to illustrate whuber's answer in the context of a linear regression model. Let's say you have some bivariate data and you use Ordinary Least Squares to come up with the following model:
Y = 6X + 1
At this point, you can take any value of X, plug... | What is the relation between estimator and estimate?
It might be helpful to illustrate whuber's answer in the context of a linear regression model. Let's say you have some bivariate data and you use Ordinary Least Squares to come up with the following m |
12,693 | What is the relation between estimator and estimate? | Suppose you received some data, and you had some observed variable called theta. Now your data can be from a distribution of data, for this distribution, there is a corresponding value of theta that you infer which is a random variable. You can use the MAP or mean for calculating the estimate of this random variable wh... | What is the relation between estimator and estimate? | Suppose you received some data, and you had some observed variable called theta. Now your data can be from a distribution of data, for this distribution, there is a corresponding value of theta that y | What is the relation between estimator and estimate?
Suppose you received some data, and you had some observed variable called theta. Now your data can be from a distribution of data, for this distribution, there is a corresponding value of theta that you infer which is a random variable. You can use the MAP or mean fo... | What is the relation between estimator and estimate?
Suppose you received some data, and you had some observed variable called theta. Now your data can be from a distribution of data, for this distribution, there is a corresponding value of theta that y |
12,694 | Probability formula for a multivariate-bernoulli distribution | The random variable taking values in $\{0,1\}^n$ is a discrete random variable. Its distribution is fully described by probabilities
$p_{\mathbf{i}}=P(X=\mathbf{i})$ with $\mathbf{i}\in\{0,1\}^n$. The probabilities $p_{i}$ and $p_{ij}$ you give are sums of $p_{\mathbf{i}}$ for certain indexes $\mathbf{i}$.
Now it se... | Probability formula for a multivariate-bernoulli distribution | The random variable taking values in $\{0,1\}^n$ is a discrete random variable. Its distribution is fully described by probabilities
$p_{\mathbf{i}}=P(X=\mathbf{i})$ with $\mathbf{i}\in\{0,1\}^n$. T | Probability formula for a multivariate-bernoulli distribution
The random variable taking values in $\{0,1\}^n$ is a discrete random variable. Its distribution is fully described by probabilities
$p_{\mathbf{i}}=P(X=\mathbf{i})$ with $\mathbf{i}\in\{0,1\}^n$. The probabilities $p_{i}$ and $p_{ij}$ you give are sums of... | Probability formula for a multivariate-bernoulli distribution
The random variable taking values in $\{0,1\}^n$ is a discrete random variable. Its distribution is fully described by probabilities
$p_{\mathbf{i}}=P(X=\mathbf{i})$ with $\mathbf{i}\in\{0,1\}^n$. T |
12,695 | Probability formula for a multivariate-bernoulli distribution | See the following paper:
J. L. Teugels, Some representations of the multivariate Bernoulli and binomial
distributions, Journal of Multivariate Analysis, vol. 32, no. 2, Feb. 1990, 256–268.
Here is the abstract:
Multivariate but vectorized versions for Bernoulli and binomial distributions are established using the ... | Probability formula for a multivariate-bernoulli distribution | See the following paper:
J. L. Teugels, Some representations of the multivariate Bernoulli and binomial
distributions, Journal of Multivariate Analysis, vol. 32, no. 2, Feb. 1990, 256–268.
Here is | Probability formula for a multivariate-bernoulli distribution
See the following paper:
J. L. Teugels, Some representations of the multivariate Bernoulli and binomial
distributions, Journal of Multivariate Analysis, vol. 32, no. 2, Feb. 1990, 256–268.
Here is the abstract:
Multivariate but vectorized versions for B... | Probability formula for a multivariate-bernoulli distribution
See the following paper:
J. L. Teugels, Some representations of the multivariate Bernoulli and binomial
distributions, Journal of Multivariate Analysis, vol. 32, no. 2, Feb. 1990, 256–268.
Here is |
12,696 | Probability formula for a multivariate-bernoulli distribution | An $n$-dimensional Bernoulli distribution can be expressed in terms of an $n$ by $n$ matrix $\Sigma$, which is a matrix analogous to the covariance matrix of the Gaussian distribution, but not necessarily a symmetric matrix.
For example, the diagonal elements of $\Sigma$ represent probabilities for a single element $p(... | Probability formula for a multivariate-bernoulli distribution | An $n$-dimensional Bernoulli distribution can be expressed in terms of an $n$ by $n$ matrix $\Sigma$, which is a matrix analogous to the covariance matrix of the Gaussian distribution, but not necessa | Probability formula for a multivariate-bernoulli distribution
An $n$-dimensional Bernoulli distribution can be expressed in terms of an $n$ by $n$ matrix $\Sigma$, which is a matrix analogous to the covariance matrix of the Gaussian distribution, but not necessarily a symmetric matrix.
For example, the diagonal element... | Probability formula for a multivariate-bernoulli distribution
An $n$-dimensional Bernoulli distribution can be expressed in terms of an $n$ by $n$ matrix $\Sigma$, which is a matrix analogous to the covariance matrix of the Gaussian distribution, but not necessa |
12,697 | Probability formula for a multivariate-bernoulli distribution | I don't know what the resulting distribution is called, or if it even has a name, but it strikes me the obvious way to set this up is to think of the model you'd use to model a 2×2×2×…×2 table using a log-linear (Poisson regression) model. As you know the 1st-order interactions only, it's then natural to assume that al... | Probability formula for a multivariate-bernoulli distribution | I don't know what the resulting distribution is called, or if it even has a name, but it strikes me the obvious way to set this up is to think of the model you'd use to model a 2×2×2×…×2 table using a | Probability formula for a multivariate-bernoulli distribution
I don't know what the resulting distribution is called, or if it even has a name, but it strikes me the obvious way to set this up is to think of the model you'd use to model a 2×2×2×…×2 table using a log-linear (Poisson regression) model. As you know the 1s... | Probability formula for a multivariate-bernoulli distribution
I don't know what the resulting distribution is called, or if it even has a name, but it strikes me the obvious way to set this up is to think of the model you'd use to model a 2×2×2×…×2 table using a |
12,698 | Why the name "kernel" in stats and ML? | You can find some information on this matter by checking the website for earliest known uses for some of the words of mathematics maintained by mathematician Jeff Miller. You can also find information on the etymology of the word "kernel" in standard dictionary sources.
Writing in French, Fredholm (1903) used the word... | Why the name "kernel" in stats and ML? | You can find some information on this matter by checking the website for earliest known uses for some of the words of mathematics maintained by mathematician Jeff Miller. You can also find informatio | Why the name "kernel" in stats and ML?
You can find some information on this matter by checking the website for earliest known uses for some of the words of mathematics maintained by mathematician Jeff Miller. You can also find information on the etymology of the word "kernel" in standard dictionary sources.
Writing i... | Why the name "kernel" in stats and ML?
You can find some information on this matter by checking the website for earliest known uses for some of the words of mathematics maintained by mathematician Jeff Miller. You can also find informatio |
12,699 | Why the name "kernel" in stats and ML? | A kernel is used a multitude of times in Machine Learning and statistics. A few examples are:
In Support Vector Machines a kernel is a function that maps the data to a higher-dimensional space where the problem becomes linearly solvable (watch this).
Kernel Density Estimation
Kernel Density Estimation is a non-para... | Why the name "kernel" in stats and ML? | A kernel is used a multitude of times in Machine Learning and statistics. A few examples are:
In Support Vector Machines a kernel is a function that maps the data to a higher-dimensional space where | Why the name "kernel" in stats and ML?
A kernel is used a multitude of times in Machine Learning and statistics. A few examples are:
In Support Vector Machines a kernel is a function that maps the data to a higher-dimensional space where the problem becomes linearly solvable (watch this).
Kernel Density Estimation
... | Why the name "kernel" in stats and ML?
A kernel is used a multitude of times in Machine Learning and statistics. A few examples are:
In Support Vector Machines a kernel is a function that maps the data to a higher-dimensional space where |
12,700 | Showing that 100 measurements for 5 subjects provide much less information than 5 measurements for 100 subjects | The short answer is that your conjecture is true when and only when there is a positive intra-class correlation in the data. Empirically speaking, most clustered datasets most of the time show a positive intra-class correlation, which means that in practice your conjecture is usually true. But if the intra-class correl... | Showing that 100 measurements for 5 subjects provide much less information than 5 measurements for 1 | The short answer is that your conjecture is true when and only when there is a positive intra-class correlation in the data. Empirically speaking, most clustered datasets most of the time show a posit | Showing that 100 measurements for 5 subjects provide much less information than 5 measurements for 100 subjects
The short answer is that your conjecture is true when and only when there is a positive intra-class correlation in the data. Empirically speaking, most clustered datasets most of the time show a positive intr... | Showing that 100 measurements for 5 subjects provide much less information than 5 measurements for 1
The short answer is that your conjecture is true when and only when there is a positive intra-class correlation in the data. Empirically speaking, most clustered datasets most of the time show a posit |
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