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 |
|---|---|---|---|---|---|---|
3,501 | Why do neural networks need so many training examples to perform? | We don't learn to "see cars" until we learn to see
It takes quite a long time and lots of examples for a child to learn how to see objects as such. After that, a child can learn to identify a particular type of object from just a few examples. If you compare a two year old child with a learning system that literally st... | Why do neural networks need so many training examples to perform? | We don't learn to "see cars" until we learn to see
It takes quite a long time and lots of examples for a child to learn how to see objects as such. After that, a child can learn to identify a particul | Why do neural networks need so many training examples to perform?
We don't learn to "see cars" until we learn to see
It takes quite a long time and lots of examples for a child to learn how to see objects as such. After that, a child can learn to identify a particular type of object from just a few examples. If you com... | Why do neural networks need so many training examples to perform?
We don't learn to "see cars" until we learn to see
It takes quite a long time and lots of examples for a child to learn how to see objects as such. After that, a child can learn to identify a particul |
3,502 | Why do neural networks need so many training examples to perform? | I would argue the performance is not that different as you might expect, but you ask a great question (see the last paragraph).
As you mention transfer learning: To compare apples with apples we have to look how many pictures in total and how many pictures of the class of interest a human / neural net "sees".
1. How ma... | Why do neural networks need so many training examples to perform? | I would argue the performance is not that different as you might expect, but you ask a great question (see the last paragraph).
As you mention transfer learning: To compare apples with apples we have | Why do neural networks need so many training examples to perform?
I would argue the performance is not that different as you might expect, but you ask a great question (see the last paragraph).
As you mention transfer learning: To compare apples with apples we have to look how many pictures in total and how many pictur... | Why do neural networks need so many training examples to perform?
I would argue the performance is not that different as you might expect, but you ask a great question (see the last paragraph).
As you mention transfer learning: To compare apples with apples we have |
3,503 | Why do neural networks need so many training examples to perform? | I am an expert in this. I am human, I was a baby, I have a car, and I do AI.
The reason why babies pick up cars with far more limited examples is intuition. The human brain already has structures to deal with 3D rotations. Also, there are two eyes which provide parallax for depth mapping which really helps. You can in... | Why do neural networks need so many training examples to perform? | I am an expert in this. I am human, I was a baby, I have a car, and I do AI.
The reason why babies pick up cars with far more limited examples is intuition. The human brain already has structures to | Why do neural networks need so many training examples to perform?
I am an expert in this. I am human, I was a baby, I have a car, and I do AI.
The reason why babies pick up cars with far more limited examples is intuition. The human brain already has structures to deal with 3D rotations. Also, there are two eyes which... | Why do neural networks need so many training examples to perform?
I am an expert in this. I am human, I was a baby, I have a car, and I do AI.
The reason why babies pick up cars with far more limited examples is intuition. The human brain already has structures to |
3,504 | Find expected value using CDF | Edited for the comment from probabilityislogic
Note that $F(1)=0$ in this case so the distribution has probability $0$ of being less than $1$, so $x \ge 1$, and you will also need $\alpha > 0$ for an increasing cdf.
If you have the cdf then you want the anti-integral or derivative which with a continuous distribution ... | Find expected value using CDF | Edited for the comment from probabilityislogic
Note that $F(1)=0$ in this case so the distribution has probability $0$ of being less than $1$, so $x \ge 1$, and you will also need $\alpha > 0$ for an | Find expected value using CDF
Edited for the comment from probabilityislogic
Note that $F(1)=0$ in this case so the distribution has probability $0$ of being less than $1$, so $x \ge 1$, and you will also need $\alpha > 0$ for an increasing cdf.
If you have the cdf then you want the anti-integral or derivative which w... | Find expected value using CDF
Edited for the comment from probabilityislogic
Note that $F(1)=0$ in this case so the distribution has probability $0$ of being less than $1$, so $x \ge 1$, and you will also need $\alpha > 0$ for an |
3,505 | Find expected value using CDF | Usage of the density function is not necessary
Integrate 1 minus the CDF
When you have a random variable $X$ that has a support that is non-negative (that is, the variable has nonzero density/probability for only positive values), you can use the following property:
$$
E(X) = \int_0^\infty \left( 1 - F_X(x) \right) \,... | Find expected value using CDF | Usage of the density function is not necessary
Integrate 1 minus the CDF
When you have a random variable $X$ that has a support that is non-negative (that is, the variable has nonzero density/probabil | Find expected value using CDF
Usage of the density function is not necessary
Integrate 1 minus the CDF
When you have a random variable $X$ that has a support that is non-negative (that is, the variable has nonzero density/probability for only positive values), you can use the following property:
$$
E(X) = \int_0^\inft... | Find expected value using CDF
Usage of the density function is not necessary
Integrate 1 minus the CDF
When you have a random variable $X$ that has a support that is non-negative (that is, the variable has nonzero density/probabil |
3,506 | Find expected value using CDF | The result extends to the $k$th moment of $X$ as well. Here is a graphical representation: | Find expected value using CDF | The result extends to the $k$th moment of $X$ as well. Here is a graphical representation: | Find expected value using CDF
The result extends to the $k$th moment of $X$ as well. Here is a graphical representation: | Find expected value using CDF
The result extends to the $k$th moment of $X$ as well. Here is a graphical representation: |
3,507 | Find expected value using CDF | I think you actually mean $x\geq 1$, otherwise the CDF is vacuous, as $F(1)=1-1^{-\alpha}=1-1=0$.
What you "know" about CDFs is that they eventually approach zero as the argument $x$ decreases without bound and eventually approach one as $x \to \infty$. They are also non-decreasing, so this means $0\leq F(y)\leq F(x)\... | Find expected value using CDF | I think you actually mean $x\geq 1$, otherwise the CDF is vacuous, as $F(1)=1-1^{-\alpha}=1-1=0$.
What you "know" about CDFs is that they eventually approach zero as the argument $x$ decreases without | Find expected value using CDF
I think you actually mean $x\geq 1$, otherwise the CDF is vacuous, as $F(1)=1-1^{-\alpha}=1-1=0$.
What you "know" about CDFs is that they eventually approach zero as the argument $x$ decreases without bound and eventually approach one as $x \to \infty$. They are also non-decreasing, so th... | Find expected value using CDF
I think you actually mean $x\geq 1$, otherwise the CDF is vacuous, as $F(1)=1-1^{-\alpha}=1-1=0$.
What you "know" about CDFs is that they eventually approach zero as the argument $x$ decreases without |
3,508 | Find expected value using CDF | The Answer requiring change of order is unnecessarily ugly. Here's a more elegant 2 line proof.
$\int udv = uv - \int vdu$
Now take $du = dx$ and $v = 1- F(x)$
$\int_{0}^{\infty} [ 1- F(x)] dx = [x(1-F(x)) ]_{0}^{\infty} + \int_{0}^{\infty} x f(x)dx$
$= 0 + \int_{0}^{\infty} x f(x)dx$
$= \mathbb{E}[X] \qquad \blacksqu... | Find expected value using CDF | The Answer requiring change of order is unnecessarily ugly. Here's a more elegant 2 line proof.
$\int udv = uv - \int vdu$
Now take $du = dx$ and $v = 1- F(x)$
$\int_{0}^{\infty} [ 1- F(x)] dx = [x(1 | Find expected value using CDF
The Answer requiring change of order is unnecessarily ugly. Here's a more elegant 2 line proof.
$\int udv = uv - \int vdu$
Now take $du = dx$ and $v = 1- F(x)$
$\int_{0}^{\infty} [ 1- F(x)] dx = [x(1-F(x)) ]_{0}^{\infty} + \int_{0}^{\infty} x f(x)dx$
$= 0 + \int_{0}^{\infty} x f(x)dx$
$= ... | Find expected value using CDF
The Answer requiring change of order is unnecessarily ugly. Here's a more elegant 2 line proof.
$\int udv = uv - \int vdu$
Now take $du = dx$ and $v = 1- F(x)$
$\int_{0}^{\infty} [ 1- F(x)] dx = [x(1 |
3,509 | Find expected value using CDF | In case when a conditional expectation using only CDF is needed, we can formulate two cases,
$\mathbb{E}\left(x|x\geq y\right)=y+\frac{\int_{y}^{\infty}\left(1-F(x)\right)dx}{\left(1-F(y)\right)}$
$\mathbb{E}\left(x|x\leq y\right)=y-\frac{\int_{-\infty}^{y}F(x)dx}{F(y)}$
The derivation leverages on previous post such t... | Find expected value using CDF | In case when a conditional expectation using only CDF is needed, we can formulate two cases,
$\mathbb{E}\left(x|x\geq y\right)=y+\frac{\int_{y}^{\infty}\left(1-F(x)\right)dx}{\left(1-F(y)\right)}$
$\m | Find expected value using CDF
In case when a conditional expectation using only CDF is needed, we can formulate two cases,
$\mathbb{E}\left(x|x\geq y\right)=y+\frac{\int_{y}^{\infty}\left(1-F(x)\right)dx}{\left(1-F(y)\right)}$
$\mathbb{E}\left(x|x\leq y\right)=y-\frac{\int_{-\infty}^{y}F(x)dx}{F(y)}$
The derivation lev... | Find expected value using CDF
In case when a conditional expectation using only CDF is needed, we can formulate two cases,
$\mathbb{E}\left(x|x\geq y\right)=y+\frac{\int_{y}^{\infty}\left(1-F(x)\right)dx}{\left(1-F(y)\right)}$
$\m |
3,510 | Is the R language reliable for the field of economics? | Let me share a contrasting view point. I'm an economist. I was trained in econometrics using SAS. I work in financial services and just tonight I updated R based models which we will use tomorrow to put millions of dollars at risk.
Your professor is just plain wrong. But the mistake he's making is VERY common and is wo... | Is the R language reliable for the field of economics? | Let me share a contrasting view point. I'm an economist. I was trained in econometrics using SAS. I work in financial services and just tonight I updated R based models which we will use tomorrow to p | Is the R language reliable for the field of economics?
Let me share a contrasting view point. I'm an economist. I was trained in econometrics using SAS. I work in financial services and just tonight I updated R based models which we will use tomorrow to put millions of dollars at risk.
Your professor is just plain wron... | Is the R language reliable for the field of economics?
Let me share a contrasting view point. I'm an economist. I was trained in econometrics using SAS. I work in financial services and just tonight I updated R based models which we will use tomorrow to p |
3,511 | Is the R language reliable for the field of economics? | It is not more or less reliable than other software. Base and recommended R is probably less prone to errors than contributed packages might be, but it depends on the authors.
But R's biggest advantage is that you can check yourself whether it is! It is free software, not like Stata or SPSS or similar. Hence even if i... | Is the R language reliable for the field of economics? | It is not more or less reliable than other software. Base and recommended R is probably less prone to errors than contributed packages might be, but it depends on the authors.
But R's biggest advanta | Is the R language reliable for the field of economics?
It is not more or less reliable than other software. Base and recommended R is probably less prone to errors than contributed packages might be, but it depends on the authors.
But R's biggest advantage is that you can check yourself whether it is! It is free softw... | Is the R language reliable for the field of economics?
It is not more or less reliable than other software. Base and recommended R is probably less prone to errors than contributed packages might be, but it depends on the authors.
But R's biggest advanta |
3,512 | Is the R language reliable for the field of economics? | Your professor makes some bold claims. I suspect that the problem was unfamiliarity with R language, not the actual results produced. I work in a company which does a lot of econometric modeling and we do everything in R. I also converted my economist colleague into using R.
Concerning field of economics in my persona... | Is the R language reliable for the field of economics? | Your professor makes some bold claims. I suspect that the problem was unfamiliarity with R language, not the actual results produced. I work in a company which does a lot of econometric modeling and w | Is the R language reliable for the field of economics?
Your professor makes some bold claims. I suspect that the problem was unfamiliarity with R language, not the actual results produced. I work in a company which does a lot of econometric modeling and we do everything in R. I also converted my economist colleague int... | Is the R language reliable for the field of economics?
Your professor makes some bold claims. I suspect that the problem was unfamiliarity with R language, not the actual results produced. I work in a company which does a lot of econometric modeling and w |
3,513 | Is the R language reliable for the field of economics? | I am an economist and I have been working in research for 4 years now, mostly doing applied econometrics. There are plenty of econometrics packages out there, and there is room for all of them. In my view, in economics, Stata is used for almost everything but time series, Rats, Eviews and Ox are used for time series, M... | Is the R language reliable for the field of economics? | I am an economist and I have been working in research for 4 years now, mostly doing applied econometrics. There are plenty of econometrics packages out there, and there is room for all of them. In my | Is the R language reliable for the field of economics?
I am an economist and I have been working in research for 4 years now, mostly doing applied econometrics. There are plenty of econometrics packages out there, and there is room for all of them. In my view, in economics, Stata is used for almost everything but time ... | Is the R language reliable for the field of economics?
I am an economist and I have been working in research for 4 years now, mostly doing applied econometrics. There are plenty of econometrics packages out there, and there is room for all of them. In my |
3,514 | Is the R language reliable for the field of economics? | When I was teaching graduate level statistics, I was telling my students: "I don't care what package you use, and you can use anything for your homework, as I expect you to provide substantive explanations, and will take points off if I see tr23y5m variable names in your submissions. I can support your learning very we... | Is the R language reliable for the field of economics? | When I was teaching graduate level statistics, I was telling my students: "I don't care what package you use, and you can use anything for your homework, as I expect you to provide substantive explana | Is the R language reliable for the field of economics?
When I was teaching graduate level statistics, I was telling my students: "I don't care what package you use, and you can use anything for your homework, as I expect you to provide substantive explanations, and will take points off if I see tr23y5m variable names i... | Is the R language reliable for the field of economics?
When I was teaching graduate level statistics, I was telling my students: "I don't care what package you use, and you can use anything for your homework, as I expect you to provide substantive explana |
3,515 | Is the R language reliable for the field of economics? | I'd be very careful of anyone who claims a fact but never backs it up with anything substantial.
You can easily turn his arguments around.
For example, people getting paid to write code could have LESS incentive to get it right because there is an expectation that their code will be correct, whereas the typical baseme... | Is the R language reliable for the field of economics? | I'd be very careful of anyone who claims a fact but never backs it up with anything substantial.
You can easily turn his arguments around.
For example, people getting paid to write code could have LE | Is the R language reliable for the field of economics?
I'd be very careful of anyone who claims a fact but never backs it up with anything substantial.
You can easily turn his arguments around.
For example, people getting paid to write code could have LESS incentive to get it right because there is an expectation that... | Is the R language reliable for the field of economics?
I'd be very careful of anyone who claims a fact but never backs it up with anything substantial.
You can easily turn his arguments around.
For example, people getting paid to write code could have LE |
3,516 | Is the R language reliable for the field of economics? | In the ReplicationWiki (that I work on) you can see that R was one of the software packages used most often for some 2000 empirical studies published in some well established journals already in the years 2000-2013. It seems that it was more used in more recent years. Stata was used by far most often (>900 times), foll... | Is the R language reliable for the field of economics? | In the ReplicationWiki (that I work on) you can see that R was one of the software packages used most often for some 2000 empirical studies published in some well established journals already in the y | Is the R language reliable for the field of economics?
In the ReplicationWiki (that I work on) you can see that R was one of the software packages used most often for some 2000 empirical studies published in some well established journals already in the years 2000-2013. It seems that it was more used in more recent yea... | Is the R language reliable for the field of economics?
In the ReplicationWiki (that I work on) you can see that R was one of the software packages used most often for some 2000 empirical studies published in some well established journals already in the y |
3,517 | Is the R language reliable for the field of economics? | I have been using R for half a decade and also use SAS, SPSS, Calc, WEKA and a couple of other tools. I never enjoyed with any tool as much as it was through R. Basically R is for those who think independently and try something on their own learning. When it comes to statistics it is all about methods. Users might not ... | Is the R language reliable for the field of economics? | I have been using R for half a decade and also use SAS, SPSS, Calc, WEKA and a couple of other tools. I never enjoyed with any tool as much as it was through R. Basically R is for those who think inde | Is the R language reliable for the field of economics?
I have been using R for half a decade and also use SAS, SPSS, Calc, WEKA and a couple of other tools. I never enjoyed with any tool as much as it was through R. Basically R is for those who think independently and try something on their own learning. When it comes ... | Is the R language reliable for the field of economics?
I have been using R for half a decade and also use SAS, SPSS, Calc, WEKA and a couple of other tools. I never enjoyed with any tool as much as it was through R. Basically R is for those who think inde |
3,518 | A generalization of the Law of Iterated Expectations | INFORMAL TREATMENT
We should remember that the notation where we condition on random variables is inaccurate, although economical, as notation. In reality we condition on the sigma-algebra that these random variables generate. In other words $E[Y\mid X]$ is meant to mean $E[Y\mid \sigma(X)]$. This remark may seem out ... | A generalization of the Law of Iterated Expectations | INFORMAL TREATMENT
We should remember that the notation where we condition on random variables is inaccurate, although economical, as notation. In reality we condition on the sigma-algebra that these | A generalization of the Law of Iterated Expectations
INFORMAL TREATMENT
We should remember that the notation where we condition on random variables is inaccurate, although economical, as notation. In reality we condition on the sigma-algebra that these random variables generate. In other words $E[Y\mid X]$ is meant to... | A generalization of the Law of Iterated Expectations
INFORMAL TREATMENT
We should remember that the notation where we condition on random variables is inaccurate, although economical, as notation. In reality we condition on the sigma-algebra that these |
3,519 | A generalization of the Law of Iterated Expectations | The way I understand conditional expectation and teach my students is the following:
conditional expectation $E[Y|\sigma(X)]$ is a picture taken by a camera with resolution $\sigma(X)$
As mentioned by Alecos Papadopoulos, the notation $E[Y|\sigma(X)]$ is more precise than $E[Y|X]$. Along the line of camera, one can th... | A generalization of the Law of Iterated Expectations | The way I understand conditional expectation and teach my students is the following:
conditional expectation $E[Y|\sigma(X)]$ is a picture taken by a camera with resolution $\sigma(X)$
As mentioned b | A generalization of the Law of Iterated Expectations
The way I understand conditional expectation and teach my students is the following:
conditional expectation $E[Y|\sigma(X)]$ is a picture taken by a camera with resolution $\sigma(X)$
As mentioned by Alecos Papadopoulos, the notation $E[Y|\sigma(X)]$ is more precis... | A generalization of the Law of Iterated Expectations
The way I understand conditional expectation and teach my students is the following:
conditional expectation $E[Y|\sigma(X)]$ is a picture taken by a camera with resolution $\sigma(X)$
As mentioned b |
3,520 | A generalization of the Law of Iterated Expectations | In the Law of Iterated Expectation (LIE), $E\left[E[Y \mid X]\right] = E[Y]$, that inner expectation is a random variable which happens to be a function of $X$,
say $g(X)$, and not a function of $Y$. That the expectation of this
function of $X$ happens to equal the expectation of $Y$ is a consequence of
a LIE.
All tha... | A generalization of the Law of Iterated Expectations | In the Law of Iterated Expectation (LIE), $E\left[E[Y \mid X]\right] = E[Y]$, that inner expectation is a random variable which happens to be a function of $X$,
say $g(X)$, and not a function of $Y$. | A generalization of the Law of Iterated Expectations
In the Law of Iterated Expectation (LIE), $E\left[E[Y \mid X]\right] = E[Y]$, that inner expectation is a random variable which happens to be a function of $X$,
say $g(X)$, and not a function of $Y$. That the expectation of this
function of $X$ happens to equal the e... | A generalization of the Law of Iterated Expectations
In the Law of Iterated Expectation (LIE), $E\left[E[Y \mid X]\right] = E[Y]$, that inner expectation is a random variable which happens to be a function of $X$,
say $g(X)$, and not a function of $Y$. |
3,521 | Wald test for logistic regression | The estimates of the coefficients and the intercepts in logistic regression (and any GLM) are found via maximum-likelihood estimation (MLE). These estimates are denoted with a hat over the parameters, something like $\hat{\theta}$. Our parameter of interest is denoted $\theta_{0}$ and this is usually 0 as we want to te... | Wald test for logistic regression | The estimates of the coefficients and the intercepts in logistic regression (and any GLM) are found via maximum-likelihood estimation (MLE). These estimates are denoted with a hat over the parameters, | Wald test for logistic regression
The estimates of the coefficients and the intercepts in logistic regression (and any GLM) are found via maximum-likelihood estimation (MLE). These estimates are denoted with a hat over the parameters, something like $\hat{\theta}$. Our parameter of interest is denoted $\theta_{0}$ and ... | Wald test for logistic regression
The estimates of the coefficients and the intercepts in logistic regression (and any GLM) are found via maximum-likelihood estimation (MLE). These estimates are denoted with a hat over the parameters, |
3,522 | Warning in R - Chi-squared approximation may be incorrect | It gave the warning because many of the expected values will be very small and therefore the approximations of p may not be right.
In R you can use chisq.test(a, simulate.p.value = TRUE) to use simulate p values.
However, with such small cell sizes, all estimates will be poor. It might be good to just test pass vs. fa... | Warning in R - Chi-squared approximation may be incorrect | It gave the warning because many of the expected values will be very small and therefore the approximations of p may not be right.
In R you can use chisq.test(a, simulate.p.value = TRUE) to use simula | Warning in R - Chi-squared approximation may be incorrect
It gave the warning because many of the expected values will be very small and therefore the approximations of p may not be right.
In R you can use chisq.test(a, simulate.p.value = TRUE) to use simulate p values.
However, with such small cell sizes, all estimat... | Warning in R - Chi-squared approximation may be incorrect
It gave the warning because many of the expected values will be very small and therefore the approximations of p may not be right.
In R you can use chisq.test(a, simulate.p.value = TRUE) to use simula |
3,523 | Warning in R - Chi-squared approximation may be incorrect | The issue is that the chi-square approximation to the distribution of the test statistic relies on the counts being roughly normally distributed. If many of the expected counts are very small, the approximation may be poor.
Note that the actual distribution of the chi-square statistic for independence in contingency ta... | Warning in R - Chi-squared approximation may be incorrect | The issue is that the chi-square approximation to the distribution of the test statistic relies on the counts being roughly normally distributed. If many of the expected counts are very small, the app | Warning in R - Chi-squared approximation may be incorrect
The issue is that the chi-square approximation to the distribution of the test statistic relies on the counts being roughly normally distributed. If many of the expected counts are very small, the approximation may be poor.
Note that the actual distribution of t... | Warning in R - Chi-squared approximation may be incorrect
The issue is that the chi-square approximation to the distribution of the test statistic relies on the counts being roughly normally distributed. If many of the expected counts are very small, the app |
3,524 | Warning in R - Chi-squared approximation may be incorrect | For such small counts, you could use Fisher's exact test:
> fisher.test(a)
Fisher's Exact Test for Count Data
data: a
p-value = 0.02618
alternative hypothesis: two.sided | Warning in R - Chi-squared approximation may be incorrect | For such small counts, you could use Fisher's exact test:
> fisher.test(a)
Fisher's Exact Test for Count Data
data: a
p-value = 0.02618
alternative hypothesis: two.sided | Warning in R - Chi-squared approximation may be incorrect
For such small counts, you could use Fisher's exact test:
> fisher.test(a)
Fisher's Exact Test for Count Data
data: a
p-value = 0.02618
alternative hypothesis: two.sided | Warning in R - Chi-squared approximation may be incorrect
For such small counts, you could use Fisher's exact test:
> fisher.test(a)
Fisher's Exact Test for Count Data
data: a
p-value = 0.02618
alternative hypothesis: two.sided |
3,525 | Warning in R - Chi-squared approximation may be incorrect | Please see the "Assumptions" section of Pearson's chi-squared test article.
In a nutshell, when counts in any of the cells in your table are fewer than 5 then one of the assumptions is broken. I think that's what the error message is referring to. In the article linked you can also find about the correction that can be... | Warning in R - Chi-squared approximation may be incorrect | Please see the "Assumptions" section of Pearson's chi-squared test article.
In a nutshell, when counts in any of the cells in your table are fewer than 5 then one of the assumptions is broken. I think | Warning in R - Chi-squared approximation may be incorrect
Please see the "Assumptions" section of Pearson's chi-squared test article.
In a nutshell, when counts in any of the cells in your table are fewer than 5 then one of the assumptions is broken. I think that's what the error message is referring to. In the article... | Warning in R - Chi-squared approximation may be incorrect
Please see the "Assumptions" section of Pearson's chi-squared test article.
In a nutshell, when counts in any of the cells in your table are fewer than 5 then one of the assumptions is broken. I think |
3,526 | Warning in R - Chi-squared approximation may be incorrect | Your main question talks about the sample size, but I see that more than two groups are compared. If the p-value from the test is 0.05 or less, it would be difficult to interpret the results. Therefore, I am sharing a brief script that I use in such situations:
# Load the required packages:
library(MASS) # for chisq
li... | Warning in R - Chi-squared approximation may be incorrect | Your main question talks about the sample size, but I see that more than two groups are compared. If the p-value from the test is 0.05 or less, it would be difficult to interpret the results. Therefor | Warning in R - Chi-squared approximation may be incorrect
Your main question talks about the sample size, but I see that more than two groups are compared. If the p-value from the test is 0.05 or less, it would be difficult to interpret the results. Therefore, I am sharing a brief script that I use in such situations:
... | Warning in R - Chi-squared approximation may be incorrect
Your main question talks about the sample size, but I see that more than two groups are compared. If the p-value from the test is 0.05 or less, it would be difficult to interpret the results. Therefor |
3,527 | Warning in R - Chi-squared approximation may be incorrect | Your counts per cell are too low. The general rule of thumb is, if the count is bellow 5, use fisher.test.
> fisher.test(a)
The Fisher exact test extends well to small and large counts, while the chisq.test is generally used for larger counts. You have several values that are 0 and all are below 5, so the Fisher test... | Warning in R - Chi-squared approximation may be incorrect | Your counts per cell are too low. The general rule of thumb is, if the count is bellow 5, use fisher.test.
> fisher.test(a)
The Fisher exact test extends well to small and large counts, while the ch | Warning in R - Chi-squared approximation may be incorrect
Your counts per cell are too low. The general rule of thumb is, if the count is bellow 5, use fisher.test.
> fisher.test(a)
The Fisher exact test extends well to small and large counts, while the chisq.test is generally used for larger counts. You have several... | Warning in R - Chi-squared approximation may be incorrect
Your counts per cell are too low. The general rule of thumb is, if the count is bellow 5, use fisher.test.
> fisher.test(a)
The Fisher exact test extends well to small and large counts, while the ch |
3,528 | Cost function of neural network is non-convex? | The cost function of a neural network is in general neither convex nor concave. This means that the matrix of all second partial derivatives (the Hessian) is neither positive semidefinite, nor negative semidefinite. Since the second derivative is a matrix, it's possible that it's neither one or the other.
To make this ... | Cost function of neural network is non-convex? | The cost function of a neural network is in general neither convex nor concave. This means that the matrix of all second partial derivatives (the Hessian) is neither positive semidefinite, nor negativ | Cost function of neural network is non-convex?
The cost function of a neural network is in general neither convex nor concave. This means that the matrix of all second partial derivatives (the Hessian) is neither positive semidefinite, nor negative semidefinite. Since the second derivative is a matrix, it's possible th... | Cost function of neural network is non-convex?
The cost function of a neural network is in general neither convex nor concave. This means that the matrix of all second partial derivatives (the Hessian) is neither positive semidefinite, nor negativ |
3,529 | Cost function of neural network is non-convex? | If you permute the neurons in the hidden layer and do the same permutation on the weights of the adjacent layers then the loss doesn't change. Hence if there is a non-zero global minimum as a function of weights, then it can't be unique since the permutation of weights gives another minimum. Hence the function is not c... | Cost function of neural network is non-convex? | If you permute the neurons in the hidden layer and do the same permutation on the weights of the adjacent layers then the loss doesn't change. Hence if there is a non-zero global minimum as a function | Cost function of neural network is non-convex?
If you permute the neurons in the hidden layer and do the same permutation on the weights of the adjacent layers then the loss doesn't change. Hence if there is a non-zero global minimum as a function of weights, then it can't be unique since the permutation of weights giv... | Cost function of neural network is non-convex?
If you permute the neurons in the hidden layer and do the same permutation on the weights of the adjacent layers then the loss doesn't change. Hence if there is a non-zero global minimum as a function |
3,530 | Cost function of neural network is non-convex? | Whether the objective function is convex or not depends on the details of the network. In the case where multiple local minima exist, you ask whether they're all equivalent. In general, the answer is no, but the chance of finding a local minimum with good generalization performance appears to increase with network size... | Cost function of neural network is non-convex? | Whether the objective function is convex or not depends on the details of the network. In the case where multiple local minima exist, you ask whether they're all equivalent. In general, the answer is | Cost function of neural network is non-convex?
Whether the objective function is convex or not depends on the details of the network. In the case where multiple local minima exist, you ask whether they're all equivalent. In general, the answer is no, but the chance of finding a local minimum with good generalization pe... | Cost function of neural network is non-convex?
Whether the objective function is convex or not depends on the details of the network. In the case where multiple local minima exist, you ask whether they're all equivalent. In general, the answer is |
3,531 | Cost function of neural network is non-convex? | Some answers for your updates:
Yes, there are in general multiple local minima. (If there was only one, it would be called the global minimum.) The local minima will not necessarily be of the same value. In general, there may be no local minima sharing the same value.
No, it's not convex unless it's a one-layer networ... | Cost function of neural network is non-convex? | Some answers for your updates:
Yes, there are in general multiple local minima. (If there was only one, it would be called the global minimum.) The local minima will not necessarily be of the same va | Cost function of neural network is non-convex?
Some answers for your updates:
Yes, there are in general multiple local minima. (If there was only one, it would be called the global minimum.) The local minima will not necessarily be of the same value. In general, there may be no local minima sharing the same value.
No,... | Cost function of neural network is non-convex?
Some answers for your updates:
Yes, there are in general multiple local minima. (If there was only one, it would be called the global minimum.) The local minima will not necessarily be of the same va |
3,532 | Cost function of neural network is non-convex? | You will have one global minimum if problem is convex or quasiconvex.
About convex "building blocks" during building neural networks (Computer Science version)
I think there are several of them which can be mentioned:
max(0,x) - convex and increasing
log-sum-exp - convex and increasing in each parameter
y = Ax is aff... | Cost function of neural network is non-convex? | You will have one global minimum if problem is convex or quasiconvex.
About convex "building blocks" during building neural networks (Computer Science version)
I think there are several of them which | Cost function of neural network is non-convex?
You will have one global minimum if problem is convex or quasiconvex.
About convex "building blocks" during building neural networks (Computer Science version)
I think there are several of them which can be mentioned:
max(0,x) - convex and increasing
log-sum-exp - convex... | Cost function of neural network is non-convex?
You will have one global minimum if problem is convex or quasiconvex.
About convex "building blocks" during building neural networks (Computer Science version)
I think there are several of them which |
3,533 | Cost function of neural network is non-convex? | The composition of multiple layers is what makes the cross-entropy or least-squares loss function of multi-layer neural networks non-convex with respect to the set of all weights and biases. The composition is via multiplications of functions of the weights/biases and that is the main culprit for non-convexity, not the... | Cost function of neural network is non-convex? | The composition of multiple layers is what makes the cross-entropy or least-squares loss function of multi-layer neural networks non-convex with respect to the set of all weights and biases. The compo | Cost function of neural network is non-convex?
The composition of multiple layers is what makes the cross-entropy or least-squares loss function of multi-layer neural networks non-convex with respect to the set of all weights and biases. The composition is via multiplications of functions of the weights/biases and that... | Cost function of neural network is non-convex?
The composition of multiple layers is what makes the cross-entropy or least-squares loss function of multi-layer neural networks non-convex with respect to the set of all weights and biases. The compo |
3,534 | Cost function of neural network is non-convex? | By definition, a function $f(x)$ is convex over a convex set $S$ if for all $x, y \in S$ and $t \in [0, 1]$, $tf(x) + (1-t)f(y) \geq f(tx + (1-t)y)$. Think of this as a straight line connecting two points of $y = x^2$ always being above the curve itself.
In the general case, $f$ can be shown to be convex if its Hessian... | Cost function of neural network is non-convex? | By definition, a function $f(x)$ is convex over a convex set $S$ if for all $x, y \in S$ and $t \in [0, 1]$, $tf(x) + (1-t)f(y) \geq f(tx + (1-t)y)$. Think of this as a straight line connecting two po | Cost function of neural network is non-convex?
By definition, a function $f(x)$ is convex over a convex set $S$ if for all $x, y \in S$ and $t \in [0, 1]$, $tf(x) + (1-t)f(y) \geq f(tx + (1-t)y)$. Think of this as a straight line connecting two points of $y = x^2$ always being above the curve itself.
In the general cas... | Cost function of neural network is non-convex?
By definition, a function $f(x)$ is convex over a convex set $S$ if for all $x, y \in S$ and $t \in [0, 1]$, $tf(x) + (1-t)f(y) \geq f(tx + (1-t)y)$. Think of this as a straight line connecting two po |
3,535 | Is chi-squared always a one-sided test? | The chi-squared test is essentially always a one-sided test. Here is a loose way to think about it: the chi-squared test is basically a 'goodness of fit' test. Sometimes it is explicitly referred to as such, but even when it's not, it is still often in essence a goodness of fit. For example, the chi-squared test of ... | Is chi-squared always a one-sided test? | The chi-squared test is essentially always a one-sided test. Here is a loose way to think about it: the chi-squared test is basically a 'goodness of fit' test. Sometimes it is explicitly referred to | Is chi-squared always a one-sided test?
The chi-squared test is essentially always a one-sided test. Here is a loose way to think about it: the chi-squared test is basically a 'goodness of fit' test. Sometimes it is explicitly referred to as such, but even when it's not, it is still often in essence a goodness of fit... | Is chi-squared always a one-sided test?
The chi-squared test is essentially always a one-sided test. Here is a loose way to think about it: the chi-squared test is basically a 'goodness of fit' test. Sometimes it is explicitly referred to |
3,536 | Is chi-squared always a one-sided test? | Is chi-squared always a one-sided test?
That really depends on two things:
what hypothesis is being tested. If you're testing variance of normal data against a specified value, it's quite possible to be dealing with the upper or lower tails of the chi-square (one-tailed), or both tails of the distribution. We have to... | Is chi-squared always a one-sided test? | Is chi-squared always a one-sided test?
That really depends on two things:
what hypothesis is being tested. If you're testing variance of normal data against a specified value, it's quite possible t | Is chi-squared always a one-sided test?
Is chi-squared always a one-sided test?
That really depends on two things:
what hypothesis is being tested. If you're testing variance of normal data against a specified value, it's quite possible to be dealing with the upper or lower tails of the chi-square (one-tailed), or bo... | Is chi-squared always a one-sided test?
Is chi-squared always a one-sided test?
That really depends on two things:
what hypothesis is being tested. If you're testing variance of normal data against a specified value, it's quite possible t |
3,537 | Is chi-squared always a one-sided test? | The chi-square test $(n-1)s^2/\sigma^2$ of the hypothesis that the variance is $\sigma^2$ can be either one- or two-tailed in exactly the same sense that the t-test $(m-\mu)\sqrt{n}/s$ of the hypothesis that the mean is $\mu$ can be either one- or two-tailed. | Is chi-squared always a one-sided test? | The chi-square test $(n-1)s^2/\sigma^2$ of the hypothesis that the variance is $\sigma^2$ can be either one- or two-tailed in exactly the same sense that the t-test $(m-\mu)\sqrt{n}/s$ of the hypothes | Is chi-squared always a one-sided test?
The chi-square test $(n-1)s^2/\sigma^2$ of the hypothesis that the variance is $\sigma^2$ can be either one- or two-tailed in exactly the same sense that the t-test $(m-\mu)\sqrt{n}/s$ of the hypothesis that the mean is $\mu$ can be either one- or two-tailed. | Is chi-squared always a one-sided test?
The chi-square test $(n-1)s^2/\sigma^2$ of the hypothesis that the variance is $\sigma^2$ can be either one- or two-tailed in exactly the same sense that the t-test $(m-\mu)\sqrt{n}/s$ of the hypothes |
3,538 | Is chi-squared always a one-sided test? | I also have had some problems to come to grips with this question as well, but after some experimentation it seemed as if my problem was simply in how the tests are named.
In SPSS as an example, a 2x2 table can have an addition of a chisquare-test. There there are two columns for p-values, one for the "Pearson Chi-Sqa... | Is chi-squared always a one-sided test? | I also have had some problems to come to grips with this question as well, but after some experimentation it seemed as if my problem was simply in how the tests are named.
In SPSS as an example, a 2x | Is chi-squared always a one-sided test?
I also have had some problems to come to grips with this question as well, but after some experimentation it seemed as if my problem was simply in how the tests are named.
In SPSS as an example, a 2x2 table can have an addition of a chisquare-test. There there are two columns fo... | Is chi-squared always a one-sided test?
I also have had some problems to come to grips with this question as well, but after some experimentation it seemed as if my problem was simply in how the tests are named.
In SPSS as an example, a 2x |
3,539 | Is chi-squared always a one-sided test? | @gung's answer is correct and is the way discussion of $\chi^2$ should be read. However, confusion may arise from another reading:
It would be easy to interpret a $\chi^2$ as 'two-sided' in the sense that the test statistic is typically composed of a sum of squared differences from both sides of an original distributio... | Is chi-squared always a one-sided test? | @gung's answer is correct and is the way discussion of $\chi^2$ should be read. However, confusion may arise from another reading:
It would be easy to interpret a $\chi^2$ as 'two-sided' in the sense | Is chi-squared always a one-sided test?
@gung's answer is correct and is the way discussion of $\chi^2$ should be read. However, confusion may arise from another reading:
It would be easy to interpret a $\chi^2$ as 'two-sided' in the sense that the test statistic is typically composed of a sum of squared differences fr... | Is chi-squared always a one-sided test?
@gung's answer is correct and is the way discussion of $\chi^2$ should be read. However, confusion may arise from another reading:
It would be easy to interpret a $\chi^2$ as 'two-sided' in the sense |
3,540 | Is chi-squared always a one-sided test? | $\chi^2$ test of variance can be one or two sided: The test statistic is $(n-1)\frac{s^2}{\sigma^2}$, and the null hypothesis is: s (sample deviation)= $\sigma$ (a reference value). The alternative hypothesis could be: (a) $ s> \sigma$, (b) $s < \sigma$, (c) $s \neq \sigma$. p-value caculation involves the asymmetry of... | Is chi-squared always a one-sided test? | $\chi^2$ test of variance can be one or two sided: The test statistic is $(n-1)\frac{s^2}{\sigma^2}$, and the null hypothesis is: s (sample deviation)= $\sigma$ (a reference value). The alternative hy | Is chi-squared always a one-sided test?
$\chi^2$ test of variance can be one or two sided: The test statistic is $(n-1)\frac{s^2}{\sigma^2}$, and the null hypothesis is: s (sample deviation)= $\sigma$ (a reference value). The alternative hypothesis could be: (a) $ s> \sigma$, (b) $s < \sigma$, (c) $s \neq \sigma$. p-va... | Is chi-squared always a one-sided test?
$\chi^2$ test of variance can be one or two sided: The test statistic is $(n-1)\frac{s^2}{\sigma^2}$, and the null hypothesis is: s (sample deviation)= $\sigma$ (a reference value). The alternative hy |
3,541 | Is chi-squared always a one-sided test? | The $\chi^2$ and F tests are one sided tests because we never have negative values of $\chi^2$ and F. For $\chi^2$, the sum of the difference of observed and expected squared is divided by the expected ( a proportion), thus chi-square is always a positive number or it may be close to zero on the right side when there i... | Is chi-squared always a one-sided test? | The $\chi^2$ and F tests are one sided tests because we never have negative values of $\chi^2$ and F. For $\chi^2$, the sum of the difference of observed and expected squared is divided by the expecte | Is chi-squared always a one-sided test?
The $\chi^2$ and F tests are one sided tests because we never have negative values of $\chi^2$ and F. For $\chi^2$, the sum of the difference of observed and expected squared is divided by the expected ( a proportion), thus chi-square is always a positive number or it may be clos... | Is chi-squared always a one-sided test?
The $\chi^2$ and F tests are one sided tests because we never have negative values of $\chi^2$ and F. For $\chi^2$, the sum of the difference of observed and expected squared is divided by the expecte |
3,542 | Are mean normalization and feature scaling needed for k-means clustering? | If your variables are of incomparable units (e.g. height in cm and weight in kg) then you should standardize variables, of course. Even if variables are of the same units but show quite different variances it is still a good idea to standardize before K-means. You see, K-means clustering is "isotropic" in all direction... | Are mean normalization and feature scaling needed for k-means clustering? | If your variables are of incomparable units (e.g. height in cm and weight in kg) then you should standardize variables, of course. Even if variables are of the same units but show quite different vari | Are mean normalization and feature scaling needed for k-means clustering?
If your variables are of incomparable units (e.g. height in cm and weight in kg) then you should standardize variables, of course. Even if variables are of the same units but show quite different variances it is still a good idea to standardize b... | Are mean normalization and feature scaling needed for k-means clustering?
If your variables are of incomparable units (e.g. height in cm and weight in kg) then you should standardize variables, of course. Even if variables are of the same units but show quite different vari |
3,543 | Are mean normalization and feature scaling needed for k-means clustering? | Depends on your data I guess. If you would like trends in your data to cluster together regardless of the magnitude, you should center. eg. say you have some gene expression profile, and want to see trends in gene expression, then without mean centering, your low expression genes will cluster together and away from hig... | Are mean normalization and feature scaling needed for k-means clustering? | Depends on your data I guess. If you would like trends in your data to cluster together regardless of the magnitude, you should center. eg. say you have some gene expression profile, and want to see t | Are mean normalization and feature scaling needed for k-means clustering?
Depends on your data I guess. If you would like trends in your data to cluster together regardless of the magnitude, you should center. eg. say you have some gene expression profile, and want to see trends in gene expression, then without mean ce... | Are mean normalization and feature scaling needed for k-means clustering?
Depends on your data I guess. If you would like trends in your data to cluster together regardless of the magnitude, you should center. eg. say you have some gene expression profile, and want to see t |
3,544 | Why only three partitions? (training, validation, test) | First, I think you're mistaken about what the three partitions do. You don't make any choices based on the test data. Your algorithms adjust their parameters based on the training data. You then run them on the validation data to compare your algorithms (and their trained parameters) and decide on a winner. You then ru... | Why only three partitions? (training, validation, test) | First, I think you're mistaken about what the three partitions do. You don't make any choices based on the test data. Your algorithms adjust their parameters based on the training data. You then run t | Why only three partitions? (training, validation, test)
First, I think you're mistaken about what the three partitions do. You don't make any choices based on the test data. Your algorithms adjust their parameters based on the training data. You then run them on the validation data to compare your algorithms (and their... | Why only three partitions? (training, validation, test)
First, I think you're mistaken about what the three partitions do. You don't make any choices based on the test data. Your algorithms adjust their parameters based on the training data. You then run t |
3,545 | Why only three partitions? (training, validation, test) | This is interesting question, and I found it is helpful with the answer from @Wayne.
From my understanding, dividing the dataset into different partition depends on the purpose of the author, and the requirement of the model in real world application.
Normally we have two datsets: training and testing. The training o... | Why only three partitions? (training, validation, test) | This is interesting question, and I found it is helpful with the answer from @Wayne.
From my understanding, dividing the dataset into different partition depends on the purpose of the author, and the | Why only three partitions? (training, validation, test)
This is interesting question, and I found it is helpful with the answer from @Wayne.
From my understanding, dividing the dataset into different partition depends on the purpose of the author, and the requirement of the model in real world application.
Normally w... | Why only three partitions? (training, validation, test)
This is interesting question, and I found it is helpful with the answer from @Wayne.
From my understanding, dividing the dataset into different partition depends on the purpose of the author, and the |
3,546 | Won't highly-correlated variables in random forest distort accuracy and feature-selection? | That is correct, but therefore in most of those sub-samplings where variable Y was available it would produce the best possible split.
You may try to increase mtry, to make sure this happens more often.
You may try either recursive correlation pruning, that is in turns to remove one of two variables whom together have ... | Won't highly-correlated variables in random forest distort accuracy and feature-selection? | That is correct, but therefore in most of those sub-samplings where variable Y was available it would produce the best possible split.
You may try to increase mtry, to make sure this happens more ofte | Won't highly-correlated variables in random forest distort accuracy and feature-selection?
That is correct, but therefore in most of those sub-samplings where variable Y was available it would produce the best possible split.
You may try to increase mtry, to make sure this happens more often.
You may try either recursi... | Won't highly-correlated variables in random forest distort accuracy and feature-selection?
That is correct, but therefore in most of those sub-samplings where variable Y was available it would produce the best possible split.
You may try to increase mtry, to make sure this happens more ofte |
3,547 | Won't highly-correlated variables in random forest distort accuracy and feature-selection? | Old thread, but I don't agree with a blanket statement that collinearity is not an issue with random forest models. When the dataset has two (or more) correlated features, then from the point of view of the model, any of these correlated features can be used as the predictor, with no concrete preference of one over th... | Won't highly-correlated variables in random forest distort accuracy and feature-selection? | Old thread, but I don't agree with a blanket statement that collinearity is not an issue with random forest models. When the dataset has two (or more) correlated features, then from the point of view | Won't highly-correlated variables in random forest distort accuracy and feature-selection?
Old thread, but I don't agree with a blanket statement that collinearity is not an issue with random forest models. When the dataset has two (or more) correlated features, then from the point of view of the model, any of these co... | Won't highly-correlated variables in random forest distort accuracy and feature-selection?
Old thread, but I don't agree with a blanket statement that collinearity is not an issue with random forest models. When the dataset has two (or more) correlated features, then from the point of view |
3,548 | Won't highly-correlated variables in random forest distort accuracy and feature-selection? | One thing to add to above explanations: based on the experiments in Genuer et al, 2010:
Robin Genuer, Jean-Michel Poggi, Christine Tuleau-Malot. Variable selection using Random Forests. Pattern Recognition Letters, Elsevier, 2010, 31 (14), pp.2225-2236.
When the number of variables were more than the number of observat... | Won't highly-correlated variables in random forest distort accuracy and feature-selection? | One thing to add to above explanations: based on the experiments in Genuer et al, 2010:
Robin Genuer, Jean-Michel Poggi, Christine Tuleau-Malot. Variable selection using Random Forests. Pattern Recogn | Won't highly-correlated variables in random forest distort accuracy and feature-selection?
One thing to add to above explanations: based on the experiments in Genuer et al, 2010:
Robin Genuer, Jean-Michel Poggi, Christine Tuleau-Malot. Variable selection using Random Forests. Pattern Recognition Letters, Elsevier, 2010... | Won't highly-correlated variables in random forest distort accuracy and feature-selection?
One thing to add to above explanations: based on the experiments in Genuer et al, 2010:
Robin Genuer, Jean-Michel Poggi, Christine Tuleau-Malot. Variable selection using Random Forests. Pattern Recogn |
3,549 | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network? | A feature map, or activation map, is the output activations for a given filter (a1 in your case) and the definition is the same regardless of what layer you are on.
Feature map and activation map mean exactly the same thing. It is called an activation map because it is a mapping that corresponds to the activation of d... | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network? | A feature map, or activation map, is the output activations for a given filter (a1 in your case) and the definition is the same regardless of what layer you are on.
Feature map and activation map mea | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network?
A feature map, or activation map, is the output activations for a given filter (a1 in your case) and the definition is the same regardless of what layer you are on.
Feature map and activation map mean exactly the same t... | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network?
A feature map, or activation map, is the output activations for a given filter (a1 in your case) and the definition is the same regardless of what layer you are on.
Feature map and activation map mea |
3,550 | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network? | In CNN terminology, the 3×3 matrix is called a ‘filter‘ or ‘kernel’ or ‘feature detector’ and the matrix formed by sliding the filter over the image and computing the dot product is called the ‘Convolved Feature’ or ‘Activation Map’ or the ‘Feature Map‘. It is important to note that filters acts as feature detectors fr... | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network? | In CNN terminology, the 3×3 matrix is called a ‘filter‘ or ‘kernel’ or ‘feature detector’ and the matrix formed by sliding the filter over the image and computing the dot product is called the ‘Convol | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network?
In CNN terminology, the 3×3 matrix is called a ‘filter‘ or ‘kernel’ or ‘feature detector’ and the matrix formed by sliding the filter over the image and computing the dot product is called the ‘Convolved Feature’ or ‘Act... | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network?
In CNN terminology, the 3×3 matrix is called a ‘filter‘ or ‘kernel’ or ‘feature detector’ and the matrix formed by sliding the filter over the image and computing the dot product is called the ‘Convol |
3,551 | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network? | before talk about what feature map means, let just define the term of feature vector.
feature vector is vectorial representation of objects. For example, a car can be represented by [number of wheels, door. windows, age ..etc].
feature map is a function that takes feature vectors in one space and transforms them into f... | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network? | before talk about what feature map means, let just define the term of feature vector.
feature vector is vectorial representation of objects. For example, a car can be represented by [number of wheels, | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network?
before talk about what feature map means, let just define the term of feature vector.
feature vector is vectorial representation of objects. For example, a car can be represented by [number of wheels, door. windows, age ... | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network?
before talk about what feature map means, let just define the term of feature vector.
feature vector is vectorial representation of objects. For example, a car can be represented by [number of wheels, |
3,552 | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network? | To give a complete answer, we need some definitions:
Background Definitions:
For us, an "input space" $\mathcal{X}$ is just a metric space.
A model class $\mathcal{F}$ (of continuous functions) is universal from $\mathcal{X}$ to $\mathcal{R}^D$ if $\mathcal{F}$ is dense in $C(\mathcal{X},\mathbb{R}^D)$ for the uniform... | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network? | To give a complete answer, we need some definitions:
Background Definitions:
For us, an "input space" $\mathcal{X}$ is just a metric space.
A model class $\mathcal{F}$ (of continuous functions) is un | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network?
To give a complete answer, we need some definitions:
Background Definitions:
For us, an "input space" $\mathcal{X}$ is just a metric space.
A model class $\mathcal{F}$ (of continuous functions) is universal from $\mathc... | What is the definition of a "feature map" (aka "activation map") in a convolutional neural network?
To give a complete answer, we need some definitions:
Background Definitions:
For us, an "input space" $\mathcal{X}$ is just a metric space.
A model class $\mathcal{F}$ (of continuous functions) is un |
3,553 | 40,000 neuroscience papers might be wrong | On the 40000 figure
The news are really sensationalist, but the paper is really well founded. Discussions raged for days in my laboratory, all in all a really necessary critique that makes researchers introspect their work. I recommend the reading of the following commentary by Thomas Nichols, one of the authors of the... | 40,000 neuroscience papers might be wrong | On the 40000 figure
The news are really sensationalist, but the paper is really well founded. Discussions raged for days in my laboratory, all in all a really necessary critique that makes researchers | 40,000 neuroscience papers might be wrong
On the 40000 figure
The news are really sensationalist, but the paper is really well founded. Discussions raged for days in my laboratory, all in all a really necessary critique that makes researchers introspect their work. I recommend the reading of the following commentary by... | 40,000 neuroscience papers might be wrong
On the 40000 figure
The news are really sensationalist, but the paper is really well founded. Discussions raged for days in my laboratory, all in all a really necessary critique that makes researchers |
3,554 | How much to pay? A practical problem | I would be interested in feedback on the paragraph beginning "Upon reflection...", since particular part of the model has been keeping me up at night.
The Bayesian model
The revised question makes me think that we can develop the model explicitly, without using simulation. Simulation introduced additional variability d... | How much to pay? A practical problem | I would be interested in feedback on the paragraph beginning "Upon reflection...", since particular part of the model has been keeping me up at night.
The Bayesian model
The revised question makes me | How much to pay? A practical problem
I would be interested in feedback on the paragraph beginning "Upon reflection...", since particular part of the model has been keeping me up at night.
The Bayesian model
The revised question makes me think that we can develop the model explicitly, without using simulation. Simulatio... | How much to pay? A practical problem
I would be interested in feedback on the paragraph beginning "Upon reflection...", since particular part of the model has been keeping me up at night.
The Bayesian model
The revised question makes me |
3,555 | How much to pay? A practical problem | EDIT: Tragedy! My initial assumptions were incorrect! (Or in doubt, at least -- do you trust what the seller is telling you? Still, hat tip to Morten, as well.) Which I guess is another good introduction to statistics, but The Partial Sheet Approach is now added below (since people seemed to like the Whole Sheet one, a... | How much to pay? A practical problem | EDIT: Tragedy! My initial assumptions were incorrect! (Or in doubt, at least -- do you trust what the seller is telling you? Still, hat tip to Morten, as well.) Which I guess is another good introduct | How much to pay? A practical problem
EDIT: Tragedy! My initial assumptions were incorrect! (Or in doubt, at least -- do you trust what the seller is telling you? Still, hat tip to Morten, as well.) Which I guess is another good introduction to statistics, but The Partial Sheet Approach is now added below (since people ... | How much to pay? A practical problem
EDIT: Tragedy! My initial assumptions were incorrect! (Or in doubt, at least -- do you trust what the seller is telling you? Still, hat tip to Morten, as well.) Which I guess is another good introduct |
3,556 | How much to pay? A practical problem | This is a fairly limited sample. (Code snippets are in R)
> sample <- c(97,98,96,100,95,97)
For an initial guess at expected number in the total population and a 95% confidence value for price we can start with the mean and the 5% quantile
> 100*mean(sample)
[1] 9716.667
> 100*quantile(sample,0.05)
5%
9525
To go ... | How much to pay? A practical problem | This is a fairly limited sample. (Code snippets are in R)
> sample <- c(97,98,96,100,95,97)
For an initial guess at expected number in the total population and a 95% confidence value for price we can | How much to pay? A practical problem
This is a fairly limited sample. (Code snippets are in R)
> sample <- c(97,98,96,100,95,97)
For an initial guess at expected number in the total population and a 95% confidence value for price we can start with the mean and the 5% quantile
> 100*mean(sample)
[1] 9716.667
> 100*quan... | How much to pay? A practical problem
This is a fairly limited sample. (Code snippets are in R)
> sample <- c(97,98,96,100,95,97)
For an initial guess at expected number in the total population and a 95% confidence value for price we can |
3,557 | How much to pay? A practical problem | In a pinch, my first inclination would be to calculate a 95% confidence interval for your sample mean over a truncated normal distribution falling between the lower and upper bounds of 90 and 100 labels.
The R package truncnorm allows you to find confidence intervals for a truncated normal distribution given a specifie... | How much to pay? A practical problem | In a pinch, my first inclination would be to calculate a 95% confidence interval for your sample mean over a truncated normal distribution falling between the lower and upper bounds of 90 and 100 labe | How much to pay? A practical problem
In a pinch, my first inclination would be to calculate a 95% confidence interval for your sample mean over a truncated normal distribution falling between the lower and upper bounds of 90 and 100 labels.
The R package truncnorm allows you to find confidence intervals for a truncated... | How much to pay? A practical problem
In a pinch, my first inclination would be to calculate a 95% confidence interval for your sample mean over a truncated normal distribution falling between the lower and upper bounds of 90 and 100 labe |
3,558 | How much to pay? A practical problem | A quick and simple approach is to consider all possible resamples of size 6. There are only 15,625 permutations. Looking at these and taking the average for each case, and then sorting the averages and extracting the 5% quantile, we get a value of 96.
So the estimated amount you should be willing to pay is about 9600.... | How much to pay? A practical problem | A quick and simple approach is to consider all possible resamples of size 6. There are only 15,625 permutations. Looking at these and taking the average for each case, and then sorting the averages an | How much to pay? A practical problem
A quick and simple approach is to consider all possible resamples of size 6. There are only 15,625 permutations. Looking at these and taking the average for each case, and then sorting the averages and extracting the 5% quantile, we get a value of 96.
So the estimated amount you sh... | How much to pay? A practical problem
A quick and simple approach is to consider all possible resamples of size 6. There are only 15,625 permutations. Looking at these and taking the average for each case, and then sorting the averages an |
3,559 | How much to pay? A practical problem | It seems like you have already concluded that the error was done intentionally, but a statistician would not jump to such conclusions (even though the evidence seems to support this).
One could set this up as an hypothesis test:
H0: The dealer is honest but quite sloppy
H1: The dealer is fraudulent, and the shortfall ... | How much to pay? A practical problem | It seems like you have already concluded that the error was done intentionally, but a statistician would not jump to such conclusions (even though the evidence seems to support this).
One could set th | How much to pay? A practical problem
It seems like you have already concluded that the error was done intentionally, but a statistician would not jump to such conclusions (even though the evidence seems to support this).
One could set this up as an hypothesis test:
H0: The dealer is honest but quite sloppy
H1: The dea... | How much to pay? A practical problem
It seems like you have already concluded that the error was done intentionally, but a statistician would not jump to such conclusions (even though the evidence seems to support this).
One could set th |
3,560 | How much to pay? A practical problem | How about something like a multinomial model.
Prob of each outcome is estimated as 1/6, 1/6, .... (based on the 6 observations) and so E(x)=97.16 and Var(x)=sum(95^2*1/6+...)-E(x)^2=2.47 so the 95% CI would be [94, 100] | How much to pay? A practical problem | How about something like a multinomial model.
Prob of each outcome is estimated as 1/6, 1/6, .... (based on the 6 observations) and so E(x)=97.16 and Var(x)=sum(95^2*1/6+...)-E(x)^2=2.47 so the 95% C | How much to pay? A practical problem
How about something like a multinomial model.
Prob of each outcome is estimated as 1/6, 1/6, .... (based on the 6 observations) and so E(x)=97.16 and Var(x)=sum(95^2*1/6+...)-E(x)^2=2.47 so the 95% CI would be [94, 100] | How much to pay? A practical problem
How about something like a multinomial model.
Prob of each outcome is estimated as 1/6, 1/6, .... (based on the 6 observations) and so E(x)=97.16 and Var(x)=sum(95^2*1/6+...)-E(x)^2=2.47 so the 95% C |
3,561 | Is it important to scale data before clustering? | The issue is what represents a good measure of distance between cases.
If you have two features, one where the differences between cases is large and the other small, are you prepared to have the former as almost the only driver of distance?
So for example if you clustered people on their weights in kilograms and h... | Is it important to scale data before clustering? | The issue is what represents a good measure of distance between cases.
If you have two features, one where the differences between cases is large and the other small, are you prepared to have the fo | Is it important to scale data before clustering?
The issue is what represents a good measure of distance between cases.
If you have two features, one where the differences between cases is large and the other small, are you prepared to have the former as almost the only driver of distance?
So for example if you clu... | Is it important to scale data before clustering?
The issue is what represents a good measure of distance between cases.
If you have two features, one where the differences between cases is large and the other small, are you prepared to have the fo |
3,562 | Is it important to scale data before clustering? | Other answers are correct, but it might help to get an intuitive grasp of the problem by seeing an example. Below, I generate a dataset that has two clear clusters, but the non-clustered dimension is much larger than the clustered dimension (note the different scales on the axes). Clustering on the non-normalised data ... | Is it important to scale data before clustering? | Other answers are correct, but it might help to get an intuitive grasp of the problem by seeing an example. Below, I generate a dataset that has two clear clusters, but the non-clustered dimension is | Is it important to scale data before clustering?
Other answers are correct, but it might help to get an intuitive grasp of the problem by seeing an example. Below, I generate a dataset that has two clear clusters, but the non-clustered dimension is much larger than the clustered dimension (note the different scales on ... | Is it important to scale data before clustering?
Other answers are correct, but it might help to get an intuitive grasp of the problem by seeing an example. Below, I generate a dataset that has two clear clusters, but the non-clustered dimension is |
3,563 | Is it important to scale data before clustering? | It depends on your data.
If you have attributes with a well-defined meaning. Say, latitude and longitude, then you should not scale your data, because this will cause distortion. (K-means might be a bad choice, too - you need something that can handle lat/lon naturally)
If you have mixed numerical data, where each attr... | Is it important to scale data before clustering? | It depends on your data.
If you have attributes with a well-defined meaning. Say, latitude and longitude, then you should not scale your data, because this will cause distortion. (K-means might be a b | Is it important to scale data before clustering?
It depends on your data.
If you have attributes with a well-defined meaning. Say, latitude and longitude, then you should not scale your data, because this will cause distortion. (K-means might be a bad choice, too - you need something that can handle lat/lon naturally)
... | Is it important to scale data before clustering?
It depends on your data.
If you have attributes with a well-defined meaning. Say, latitude and longitude, then you should not scale your data, because this will cause distortion. (K-means might be a b |
3,564 | Is it important to scale data before clustering? | Standardization is an important step of Data preprocessing.
it controls the variability of the dataset, it convert data into specific range using a linear transformation which generate good quality clusters and improve the accuracy of clustering algorithms, check out the link below to view its effects on k-means analys... | Is it important to scale data before clustering? | Standardization is an important step of Data preprocessing.
it controls the variability of the dataset, it convert data into specific range using a linear transformation which generate good quality cl | Is it important to scale data before clustering?
Standardization is an important step of Data preprocessing.
it controls the variability of the dataset, it convert data into specific range using a linear transformation which generate good quality clusters and improve the accuracy of clustering algorithms, check out the... | Is it important to scale data before clustering?
Standardization is an important step of Data preprocessing.
it controls the variability of the dataset, it convert data into specific range using a linear transformation which generate good quality cl |
3,565 | Is it important to scale data before clustering? | As explained in this paper, the k-means minimizes the error function using the Newton algorithm, i.e. a gradient-based optimization algorithm. Normalizing the data improves convergence of such algorithms. See here for some details on it.
The idea is that if different components of data (features) have different scales,... | Is it important to scale data before clustering? | As explained in this paper, the k-means minimizes the error function using the Newton algorithm, i.e. a gradient-based optimization algorithm. Normalizing the data improves convergence of such algorit | Is it important to scale data before clustering?
As explained in this paper, the k-means minimizes the error function using the Newton algorithm, i.e. a gradient-based optimization algorithm. Normalizing the data improves convergence of such algorithms. See here for some details on it.
The idea is that if different com... | Is it important to scale data before clustering?
As explained in this paper, the k-means minimizes the error function using the Newton algorithm, i.e. a gradient-based optimization algorithm. Normalizing the data improves convergence of such algorit |
3,566 | Is it important to scale data before clustering? | Standardization (Z-cscore normalization) is to bring the data to a mean of 0 and std dev of 1. This can be accomplished by (x-xmean)/std dev
Normalization is to bring the data to a scale of [0,1]. This can be accomplished by (x-xmin)/(xmax-xmin).
For algorithms such as clustering, each feature range can differ. Let's s... | Is it important to scale data before clustering? | Standardization (Z-cscore normalization) is to bring the data to a mean of 0 and std dev of 1. This can be accomplished by (x-xmean)/std dev
Normalization is to bring the data to a scale of [0,1]. Thi | Is it important to scale data before clustering?
Standardization (Z-cscore normalization) is to bring the data to a mean of 0 and std dev of 1. This can be accomplished by (x-xmean)/std dev
Normalization is to bring the data to a scale of [0,1]. This can be accomplished by (x-xmin)/(xmax-xmin).
For algorithms such as c... | Is it important to scale data before clustering?
Standardization (Z-cscore normalization) is to bring the data to a mean of 0 and std dev of 1. This can be accomplished by (x-xmean)/std dev
Normalization is to bring the data to a scale of [0,1]. Thi |
3,567 | Is this chart showing the likelihood of a terrorist attack statistically useful? | Imagine your job is to forecast the number of Americans that will die from various causes next year.
A reasonable place to start your analysis might be the National Vital Statistics Data final death data for 2014. The assumption is that 2017 might look roughly like 2014. You'll find that approximately 2,626,000 America... | Is this chart showing the likelihood of a terrorist attack statistically useful? | Imagine your job is to forecast the number of Americans that will die from various causes next year.
A reasonable place to start your analysis might be the National Vital Statistics Data final death d | Is this chart showing the likelihood of a terrorist attack statistically useful?
Imagine your job is to forecast the number of Americans that will die from various causes next year.
A reasonable place to start your analysis might be the National Vital Statistics Data final death data for 2014. The assumption is that 20... | Is this chart showing the likelihood of a terrorist attack statistically useful?
Imagine your job is to forecast the number of Americans that will die from various causes next year.
A reasonable place to start your analysis might be the National Vital Statistics Data final death d |
3,568 | Is this chart showing the likelihood of a terrorist attack statistically useful? | Problems with the chart:
It implies refugees are more likely than other groups of people to commit acts of terror. Why not frame it in terms of migrants in general? And what about acts of terror committed by a country's own citizens?
How does it define a refugee?
The comparative groups don't make sense. If we are goin... | Is this chart showing the likelihood of a terrorist attack statistically useful? | Problems with the chart:
It implies refugees are more likely than other groups of people to commit acts of terror. Why not frame it in terms of migrants in general? And what about acts of terror comm | Is this chart showing the likelihood of a terrorist attack statistically useful?
Problems with the chart:
It implies refugees are more likely than other groups of people to commit acts of terror. Why not frame it in terms of migrants in general? And what about acts of terror committed by a country's own citizens?
How ... | Is this chart showing the likelihood of a terrorist attack statistically useful?
Problems with the chart:
It implies refugees are more likely than other groups of people to commit acts of terror. Why not frame it in terms of migrants in general? And what about acts of terror comm |
3,569 | Is this chart showing the likelihood of a terrorist attack statistically useful? | This chart is definitely incomplete without at least the following information: how "terrorism" is defined for these purposes, how "refugee" is defined for these purposes, what time-span this data covers, and which people are included--for instance, does the lighting strike data include people who live in nursing homes... | Is this chart showing the likelihood of a terrorist attack statistically useful? | This chart is definitely incomplete without at least the following information: how "terrorism" is defined for these purposes, how "refugee" is defined for these purposes, what time-span this data cov | Is this chart showing the likelihood of a terrorist attack statistically useful?
This chart is definitely incomplete without at least the following information: how "terrorism" is defined for these purposes, how "refugee" is defined for these purposes, what time-span this data covers, and which people are included--for... | Is this chart showing the likelihood of a terrorist attack statistically useful?
This chart is definitely incomplete without at least the following information: how "terrorism" is defined for these purposes, how "refugee" is defined for these purposes, what time-span this data cov |
3,570 | Is this chart showing the likelihood of a terrorist attack statistically useful? | On the Frequency of Severe Terrorist Events
This paper attempts to model the likelihood that a terrorist attack of any given severity occurs. The conclusion is that terrorist events follow a power law distribution, which is 'tail heavy'. What this means is that most terrorism related deaths happen due to things like 9/... | Is this chart showing the likelihood of a terrorist attack statistically useful? | On the Frequency of Severe Terrorist Events
This paper attempts to model the likelihood that a terrorist attack of any given severity occurs. The conclusion is that terrorist events follow a power law | Is this chart showing the likelihood of a terrorist attack statistically useful?
On the Frequency of Severe Terrorist Events
This paper attempts to model the likelihood that a terrorist attack of any given severity occurs. The conclusion is that terrorist events follow a power law distribution, which is 'tail heavy'. W... | Is this chart showing the likelihood of a terrorist attack statistically useful?
On the Frequency of Severe Terrorist Events
This paper attempts to model the likelihood that a terrorist attack of any given severity occurs. The conclusion is that terrorist events follow a power law |
3,571 | Is this chart showing the likelihood of a terrorist attack statistically useful? | This chart is only useful if you want to know the probability of being killed by a person with a particular status in particular circumstances over the time of the study, which is 35 years (1975 to 2015). What it's useless for includes:
knowing how probable it is to be killed by a refugee. Cases of homicide performed ... | Is this chart showing the likelihood of a terrorist attack statistically useful? | This chart is only useful if you want to know the probability of being killed by a person with a particular status in particular circumstances over the time of the study, which is 35 years (1975 to 20 | Is this chart showing the likelihood of a terrorist attack statistically useful?
This chart is only useful if you want to know the probability of being killed by a person with a particular status in particular circumstances over the time of the study, which is 35 years (1975 to 2015). What it's useless for includes:
k... | Is this chart showing the likelihood of a terrorist attack statistically useful?
This chart is only useful if you want to know the probability of being killed by a person with a particular status in particular circumstances over the time of the study, which is 35 years (1975 to 20 |
3,572 | Is this chart showing the likelihood of a terrorist attack statistically useful? | Your intuition is correct that the statistic above doesn't tell the whole story. Yes, past refugee terrorist behaviour isn't necessarily a good indicator of future refugee terrorist behaviour, but that isn't the problem. The problem is that even one or two large-scale terrorist attacks would be awful, and statistics is... | Is this chart showing the likelihood of a terrorist attack statistically useful? | Your intuition is correct that the statistic above doesn't tell the whole story. Yes, past refugee terrorist behaviour isn't necessarily a good indicator of future refugee terrorist behaviour, but tha | Is this chart showing the likelihood of a terrorist attack statistically useful?
Your intuition is correct that the statistic above doesn't tell the whole story. Yes, past refugee terrorist behaviour isn't necessarily a good indicator of future refugee terrorist behaviour, but that isn't the problem. The problem is tha... | Is this chart showing the likelihood of a terrorist attack statistically useful?
Your intuition is correct that the statistic above doesn't tell the whole story. Yes, past refugee terrorist behaviour isn't necessarily a good indicator of future refugee terrorist behaviour, but tha |
3,573 | Is this chart showing the likelihood of a terrorist attack statistically useful? | Others have answered in a great deal more detail than I will, but here's my 2 cents:
The details just don't matter. You can quibble about the definition of terrorism, migrants, etc, but when the deaths due to terrorism are multiple orders of magnitude smaller than other causes of death, the difference between the broad... | Is this chart showing the likelihood of a terrorist attack statistically useful? | Others have answered in a great deal more detail than I will, but here's my 2 cents:
The details just don't matter. You can quibble about the definition of terrorism, migrants, etc, but when the death | Is this chart showing the likelihood of a terrorist attack statistically useful?
Others have answered in a great deal more detail than I will, but here's my 2 cents:
The details just don't matter. You can quibble about the definition of terrorism, migrants, etc, but when the deaths due to terrorism are multiple orders ... | Is this chart showing the likelihood of a terrorist attack statistically useful?
Others have answered in a great deal more detail than I will, but here's my 2 cents:
The details just don't matter. You can quibble about the definition of terrorism, migrants, etc, but when the death |
3,574 | Is this chart showing the likelihood of a terrorist attack statistically useful? | My feeling is that the question is about blatant political activism, is not evidence of anything relevant, and my concern is that such things should not be posted on this site. The chart shown, is propaganda, and propaganda is problematic no matter who is presenting it for whatever reason.
Does that mean that we shoul... | Is this chart showing the likelihood of a terrorist attack statistically useful? | My feeling is that the question is about blatant political activism, is not evidence of anything relevant, and my concern is that such things should not be posted on this site. The chart shown, is pro | Is this chart showing the likelihood of a terrorist attack statistically useful?
My feeling is that the question is about blatant political activism, is not evidence of anything relevant, and my concern is that such things should not be posted on this site. The chart shown, is propaganda, and propaganda is problematic ... | Is this chart showing the likelihood of a terrorist attack statistically useful?
My feeling is that the question is about blatant political activism, is not evidence of anything relevant, and my concern is that such things should not be posted on this site. The chart shown, is pro |
3,575 | Is this chart showing the likelihood of a terrorist attack statistically useful? | This is a picture representation of numbers for people who are too lazy to look at the numbers. This is almost statistically useless. | Is this chart showing the likelihood of a terrorist attack statistically useful? | This is a picture representation of numbers for people who are too lazy to look at the numbers. This is almost statistically useless. | Is this chart showing the likelihood of a terrorist attack statistically useful?
This is a picture representation of numbers for people who are too lazy to look at the numbers. This is almost statistically useless. | Is this chart showing the likelihood of a terrorist attack statistically useful?
This is a picture representation of numbers for people who are too lazy to look at the numbers. This is almost statistically useless. |
3,576 | Rule of thumb for number of bootstrap samples | My experience is that statisticians won't take simulations or bootstraps seriously unless the number of iterations exceeds 1,000. MC error is a big issue that's a little under appreciated. For instance, this paper used Niter=50 to demonstrate LASSO as a feature selection tool. My thesis would have taken a lot less time... | Rule of thumb for number of bootstrap samples | My experience is that statisticians won't take simulations or bootstraps seriously unless the number of iterations exceeds 1,000. MC error is a big issue that's a little under appreciated. For instanc | Rule of thumb for number of bootstrap samples
My experience is that statisticians won't take simulations or bootstraps seriously unless the number of iterations exceeds 1,000. MC error is a big issue that's a little under appreciated. For instance, this paper used Niter=50 to demonstrate LASSO as a feature selection to... | Rule of thumb for number of bootstrap samples
My experience is that statisticians won't take simulations or bootstraps seriously unless the number of iterations exceeds 1,000. MC error is a big issue that's a little under appreciated. For instanc |
3,577 | Rule of thumb for number of bootstrap samples | edit:
If you are serious about having enough samples, what you should do is to run your bootstrap procedure with, what you hope are, enough samples a number of times and see how much the bootstrap estimates "jump around". If the repeated estimates does not differ much (where "much" depends on your specific situation) y... | Rule of thumb for number of bootstrap samples | edit:
If you are serious about having enough samples, what you should do is to run your bootstrap procedure with, what you hope are, enough samples a number of times and see how much the bootstrap est | Rule of thumb for number of bootstrap samples
edit:
If you are serious about having enough samples, what you should do is to run your bootstrap procedure with, what you hope are, enough samples a number of times and see how much the bootstrap estimates "jump around". If the repeated estimates does not differ much (wher... | Rule of thumb for number of bootstrap samples
edit:
If you are serious about having enough samples, what you should do is to run your bootstrap procedure with, what you hope are, enough samples a number of times and see how much the bootstrap est |
3,578 | Rule of thumb for number of bootstrap samples | I start by responding to something raised in another answer: why such a strange number as "$599$" (number of bootstrap samples)?
This applies also to Monte Carlo tests (to which bootstrapping is equivalent when the underlying statistic is pivotal), and comes from the following: if the test is to be exact, then, if $\... | Rule of thumb for number of bootstrap samples | I start by responding to something raised in another answer: why such a strange number as "$599$" (number of bootstrap samples)?
This applies also to Monte Carlo tests (to which bootstrapping is equ | Rule of thumb for number of bootstrap samples
I start by responding to something raised in another answer: why such a strange number as "$599$" (number of bootstrap samples)?
This applies also to Monte Carlo tests (to which bootstrapping is equivalent when the underlying statistic is pivotal), and comes from the foll... | Rule of thumb for number of bootstrap samples
I start by responding to something raised in another answer: why such a strange number as "$599$" (number of bootstrap samples)?
This applies also to Monte Carlo tests (to which bootstrapping is equ |
3,579 | Rule of thumb for number of bootstrap samples | There are a some situations where you can tell either beforehand or after a few iterations that huge numbers of bootstrap iterations won't help in the end.
You hopefully have an idea beforehand on the order of magnitude of precision that is required for meaningful interpretation of the results. If you don't maybe it i... | Rule of thumb for number of bootstrap samples | There are a some situations where you can tell either beforehand or after a few iterations that huge numbers of bootstrap iterations won't help in the end.
You hopefully have an idea beforehand on th | Rule of thumb for number of bootstrap samples
There are a some situations where you can tell either beforehand or after a few iterations that huge numbers of bootstrap iterations won't help in the end.
You hopefully have an idea beforehand on the order of magnitude of precision that is required for meaningful interpre... | Rule of thumb for number of bootstrap samples
There are a some situations where you can tell either beforehand or after a few iterations that huge numbers of bootstrap iterations won't help in the end.
You hopefully have an idea beforehand on th |
3,580 | Rule of thumb for number of bootstrap samples | TLDR. 10,000 seems to be a good rule of thumb, e.g. p-values from this large or larger of bootstrap samples will be within 0.01 of the "true p-value" for the method about 95% of the time.
I only consider the percentile bootstrap approach below, which is the most commonly used method (to my knowledge) but also admittedl... | Rule of thumb for number of bootstrap samples | TLDR. 10,000 seems to be a good rule of thumb, e.g. p-values from this large or larger of bootstrap samples will be within 0.01 of the "true p-value" for the method about 95% of the time.
I only consi | Rule of thumb for number of bootstrap samples
TLDR. 10,000 seems to be a good rule of thumb, e.g. p-values from this large or larger of bootstrap samples will be within 0.01 of the "true p-value" for the method about 95% of the time.
I only consider the percentile bootstrap approach below, which is the most commonly us... | Rule of thumb for number of bootstrap samples
TLDR. 10,000 seems to be a good rule of thumb, e.g. p-values from this large or larger of bootstrap samples will be within 0.01 of the "true p-value" for the method about 95% of the time.
I only consi |
3,581 | Rule of thumb for number of bootstrap samples | Most bootstrapping applications I have seen reported around 2,000 to 100k iterations. In modern practice with adequate software, the salient issues with bootstrap are the statistical ones, more so than time and computing capacity. For novice users with Excel, one could perform only several hundreds before requiring the... | Rule of thumb for number of bootstrap samples | Most bootstrapping applications I have seen reported around 2,000 to 100k iterations. In modern practice with adequate software, the salient issues with bootstrap are the statistical ones, more so tha | Rule of thumb for number of bootstrap samples
Most bootstrapping applications I have seen reported around 2,000 to 100k iterations. In modern practice with adequate software, the salient issues with bootstrap are the statistical ones, more so than time and computing capacity. For novice users with Excel, one could perf... | Rule of thumb for number of bootstrap samples
Most bootstrapping applications I have seen reported around 2,000 to 100k iterations. In modern practice with adequate software, the salient issues with bootstrap are the statistical ones, more so tha |
3,582 | Rule of thumb for number of bootstrap samples | Data-driven theory-backed procedure
If you want a formal treatment of the subject, a good method comes from a pioneering paper by Andrews & Buchinsky (2000, Econometrica): do some small number of bootstrap replications, see how stable or noisy the estimator is, and then, based on some target accuracy measure, increase ... | Rule of thumb for number of bootstrap samples | Data-driven theory-backed procedure
If you want a formal treatment of the subject, a good method comes from a pioneering paper by Andrews & Buchinsky (2000, Econometrica): do some small number of boot | Rule of thumb for number of bootstrap samples
Data-driven theory-backed procedure
If you want a formal treatment of the subject, a good method comes from a pioneering paper by Andrews & Buchinsky (2000, Econometrica): do some small number of bootstrap replications, see how stable or noisy the estimator is, and then, ba... | Rule of thumb for number of bootstrap samples
Data-driven theory-backed procedure
If you want a formal treatment of the subject, a good method comes from a pioneering paper by Andrews & Buchinsky (2000, Econometrica): do some small number of boot |
3,583 | Effect of switching response and explanatory variable in simple linear regression | Given $n$ data points $(x_i,y_i), i = 1,2,\ldots n$, in the plane,
let us draw a straight line
$y = ax+b$. If we predict $ax_i+b$ as the value $\hat{y}_i$ of $y_i$, then
the error is $(y_i-\hat{y}_i) = (y_i-ax_i-b)$, the squared error is
$(y_i-ax_i-b)^2$, and the total squared error $\sum_{i=1}^n (y_i-ax_i-b)^2$.
We ... | Effect of switching response and explanatory variable in simple linear regression | Given $n$ data points $(x_i,y_i), i = 1,2,\ldots n$, in the plane,
let us draw a straight line
$y = ax+b$. If we predict $ax_i+b$ as the value $\hat{y}_i$ of $y_i$, then
the error is $(y_i-\hat{y}_i | Effect of switching response and explanatory variable in simple linear regression
Given $n$ data points $(x_i,y_i), i = 1,2,\ldots n$, in the plane,
let us draw a straight line
$y = ax+b$. If we predict $ax_i+b$ as the value $\hat{y}_i$ of $y_i$, then
the error is $(y_i-\hat{y}_i) = (y_i-ax_i-b)$, the squared error i... | Effect of switching response and explanatory variable in simple linear regression
Given $n$ data points $(x_i,y_i), i = 1,2,\ldots n$, in the plane,
let us draw a straight line
$y = ax+b$. If we predict $ax_i+b$ as the value $\hat{y}_i$ of $y_i$, then
the error is $(y_i-\hat{y}_i |
3,584 | Effect of switching response and explanatory variable in simple linear regression | Just to illustrate Dilip’s answer: on the following pictures,
the black dots are data points ;
on the left, the black line is the regression line obtained by y ~ x, which minimize the squares of the length of the red segments;
on the right, the black line is the regression line obtained by x ~ y, which minimize the s... | Effect of switching response and explanatory variable in simple linear regression | Just to illustrate Dilip’s answer: on the following pictures,
the black dots are data points ;
on the left, the black line is the regression line obtained by y ~ x, which minimize the squares of the | Effect of switching response and explanatory variable in simple linear regression
Just to illustrate Dilip’s answer: on the following pictures,
the black dots are data points ;
on the left, the black line is the regression line obtained by y ~ x, which minimize the squares of the length of the red segments;
on the ri... | Effect of switching response and explanatory variable in simple linear regression
Just to illustrate Dilip’s answer: on the following pictures,
the black dots are data points ;
on the left, the black line is the regression line obtained by y ~ x, which minimize the squares of the |
3,585 | Effect of switching response and explanatory variable in simple linear regression | Just a brief note on why you see the slope smaller for one regression. Both slopes depend on three numbers: standard deviations of $x$ and $y$ ($s_{x}$ and $s_{y}$), and correlation between $x$ and $y$ ($r$). The regression with $y$ as response has slope $r\frac{s_{y}}{s_{x}}$ and the regression with $x$ as response ... | Effect of switching response and explanatory variable in simple linear regression | Just a brief note on why you see the slope smaller for one regression. Both slopes depend on three numbers: standard deviations of $x$ and $y$ ($s_{x}$ and $s_{y}$), and correlation between $x$ and $ | Effect of switching response and explanatory variable in simple linear regression
Just a brief note on why you see the slope smaller for one regression. Both slopes depend on three numbers: standard deviations of $x$ and $y$ ($s_{x}$ and $s_{y}$), and correlation between $x$ and $y$ ($r$). The regression with $y$ as ... | Effect of switching response and explanatory variable in simple linear regression
Just a brief note on why you see the slope smaller for one regression. Both slopes depend on three numbers: standard deviations of $x$ and $y$ ($s_{x}$ and $s_{y}$), and correlation between $x$ and $ |
3,586 | Effect of switching response and explanatory variable in simple linear regression | Regression line is not (always) the same as true relationship
You may have some 'true' causal relationship with an equation in a linear form $a+bx$ like
$$y := a + bx + \epsilon$$
Where the $:=$ means that the value of $a+bx$ with some added noise $\epsilon$ is assigned to $y$.
The fitted regression lines y ~ x or x ~ ... | Effect of switching response and explanatory variable in simple linear regression | Regression line is not (always) the same as true relationship
You may have some 'true' causal relationship with an equation in a linear form $a+bx$ like
$$y := a + bx + \epsilon$$
Where the $:=$ means | Effect of switching response and explanatory variable in simple linear regression
Regression line is not (always) the same as true relationship
You may have some 'true' causal relationship with an equation in a linear form $a+bx$ like
$$y := a + bx + \epsilon$$
Where the $:=$ means that the value of $a+bx$ with some ad... | Effect of switching response and explanatory variable in simple linear regression
Regression line is not (always) the same as true relationship
You may have some 'true' causal relationship with an equation in a linear form $a+bx$ like
$$y := a + bx + \epsilon$$
Where the $:=$ means |
3,587 | Effect of switching response and explanatory variable in simple linear regression | A simple way to look at this is to note that, if for the true model $y=\alpha+\beta x+\epsilon$, you run two regressions:
$y=a_{y\sim x}+b_{y\sim x} x$
$x=a_{x\sim y}+b_{x\sim y} y$
Then we have, using $b_{y\sim x}=\frac{cov(x,y)}{var(x)}=\frac{cov(x,y)}{var(y)}\frac{var(y)}{var(x)}$:
$$b_{y\sim x}=b_{x\sim y}\frac... | Effect of switching response and explanatory variable in simple linear regression | A simple way to look at this is to note that, if for the true model $y=\alpha+\beta x+\epsilon$, you run two regressions:
$y=a_{y\sim x}+b_{y\sim x} x$
$x=a_{x\sim y}+b_{x\sim y} y$
Then we have, u | Effect of switching response and explanatory variable in simple linear regression
A simple way to look at this is to note that, if for the true model $y=\alpha+\beta x+\epsilon$, you run two regressions:
$y=a_{y\sim x}+b_{y\sim x} x$
$x=a_{x\sim y}+b_{x\sim y} y$
Then we have, using $b_{y\sim x}=\frac{cov(x,y)}{var(... | Effect of switching response and explanatory variable in simple linear regression
A simple way to look at this is to note that, if for the true model $y=\alpha+\beta x+\epsilon$, you run two regressions:
$y=a_{y\sim x}+b_{y\sim x} x$
$x=a_{x\sim y}+b_{x\sim y} y$
Then we have, u |
3,588 | Effect of switching response and explanatory variable in simple linear regression | It becomes interesting when there is also noise on your inputs (which we could argue is always the case, no command or observation is ever perfect).
I have built some simulations to observe the phenomenon, based on a simple linear relationship $x = y$, with Gaussian noise on both x and y. I generated the observations a... | Effect of switching response and explanatory variable in simple linear regression | It becomes interesting when there is also noise on your inputs (which we could argue is always the case, no command or observation is ever perfect).
I have built some simulations to observe the phenom | Effect of switching response and explanatory variable in simple linear regression
It becomes interesting when there is also noise on your inputs (which we could argue is always the case, no command or observation is ever perfect).
I have built some simulations to observe the phenomenon, based on a simple linear relatio... | Effect of switching response and explanatory variable in simple linear regression
It becomes interesting when there is also noise on your inputs (which we could argue is always the case, no command or observation is ever perfect).
I have built some simulations to observe the phenom |
3,589 | Effect of switching response and explanatory variable in simple linear regression | The short answer
The goal of a simple linear regression is to come up with the best predictions of the y variable, given values of the x variable. This is a different goal than trying to come up with the best prediction of the x variable, given values of the y variable.
Simple linear regression of y ~ x gives you the '... | Effect of switching response and explanatory variable in simple linear regression | The short answer
The goal of a simple linear regression is to come up with the best predictions of the y variable, given values of the x variable. This is a different goal than trying to come up with | Effect of switching response and explanatory variable in simple linear regression
The short answer
The goal of a simple linear regression is to come up with the best predictions of the y variable, given values of the x variable. This is a different goal than trying to come up with the best prediction of the x variable,... | Effect of switching response and explanatory variable in simple linear regression
The short answer
The goal of a simple linear regression is to come up with the best predictions of the y variable, given values of the x variable. This is a different goal than trying to come up with |
3,590 | Backpropagation with Softmax / Cross Entropy | Note: I am not an expert on backprop, but now having read a bit, I think the following caveat is appropriate. When reading papers or books on neural nets, it is not uncommon for derivatives to be written using a mix of the standard summation/index notation, matrix notation, and multi-index notation (include a hybrid of... | Backpropagation with Softmax / Cross Entropy | Note: I am not an expert on backprop, but now having read a bit, I think the following caveat is appropriate. When reading papers or books on neural nets, it is not uncommon for derivatives to be writ | Backpropagation with Softmax / Cross Entropy
Note: I am not an expert on backprop, but now having read a bit, I think the following caveat is appropriate. When reading papers or books on neural nets, it is not uncommon for derivatives to be written using a mix of the standard summation/index notation, matrix notation, ... | Backpropagation with Softmax / Cross Entropy
Note: I am not an expert on backprop, but now having read a bit, I think the following caveat is appropriate. When reading papers or books on neural nets, it is not uncommon for derivatives to be writ |
3,591 | Backpropagation with Softmax / Cross Entropy | While @GeoMatt22's answer is correct, I personally found it very useful to reduce the problem to a toy example and draw a picture:
I then defined the operations each node was computing, treating the $h$'s and $w$'s as inputs to a "network" ($\mathbf{t}$ is a one-hot vector representing the class label of the data poin... | Backpropagation with Softmax / Cross Entropy | While @GeoMatt22's answer is correct, I personally found it very useful to reduce the problem to a toy example and draw a picture:
I then defined the operations each node was computing, treating the | Backpropagation with Softmax / Cross Entropy
While @GeoMatt22's answer is correct, I personally found it very useful to reduce the problem to a toy example and draw a picture:
I then defined the operations each node was computing, treating the $h$'s and $w$'s as inputs to a "network" ($\mathbf{t}$ is a one-hot vector ... | Backpropagation with Softmax / Cross Entropy
While @GeoMatt22's answer is correct, I personally found it very useful to reduce the problem to a toy example and draw a picture:
I then defined the operations each node was computing, treating the |
3,592 | Backpropagation with Softmax / Cross Entropy | In place of the $\{o_i\},\,$ I want a letter whose uppercase is visually distinct from its lowercase. So let me substitute $\{y_i\}$. Also, let's use the variable $\{p_i\}$ to designate the $\{o_i\}$ from the previous layer.
Let $Y$ be the diagonal matrix whose diagonal equals the vector $y$, i.e.
$$Y={\rm Diag}(y)$$... | Backpropagation with Softmax / Cross Entropy | In place of the $\{o_i\},\,$ I want a letter whose uppercase is visually distinct from its lowercase. So let me substitute $\{y_i\}$. Also, let's use the variable $\{p_i\}$ to designate the $\{o_i\}$ | Backpropagation with Softmax / Cross Entropy
In place of the $\{o_i\},\,$ I want a letter whose uppercase is visually distinct from its lowercase. So let me substitute $\{y_i\}$. Also, let's use the variable $\{p_i\}$ to designate the $\{o_i\}$ from the previous layer.
Let $Y$ be the diagonal matrix whose diagonal eq... | Backpropagation with Softmax / Cross Entropy
In place of the $\{o_i\},\,$ I want a letter whose uppercase is visually distinct from its lowercase. So let me substitute $\{y_i\}$. Also, let's use the variable $\{p_i\}$ to designate the $\{o_i\}$ |
3,593 | Backpropagation with Softmax / Cross Entropy | The original question is answered by this post Derivative of Softmax Activation -Alijah Ahmed.
However writing this out for those who have come here for the general question of Backpropagation with Softmax and Cross-Entropy.
$$
\mathbf {
\bbox[10px, border:2px solid red] { \color{red}{
\begin{aligned}
a^0 \rightarrow
... | Backpropagation with Softmax / Cross Entropy | The original question is answered by this post Derivative of Softmax Activation -Alijah Ahmed.
However writing this out for those who have come here for the general question of Backpropagation with So | Backpropagation with Softmax / Cross Entropy
The original question is answered by this post Derivative of Softmax Activation -Alijah Ahmed.
However writing this out for those who have come here for the general question of Backpropagation with Softmax and Cross-Entropy.
$$
\mathbf {
\bbox[10px, border:2px solid red] { \... | Backpropagation with Softmax / Cross Entropy
The original question is answered by this post Derivative of Softmax Activation -Alijah Ahmed.
However writing this out for those who have come here for the general question of Backpropagation with So |
3,594 | Backpropagation with Softmax / Cross Entropy | Other answers have provided the correct way of calculating the derivative, but they do not point out where you have gone wrong. In fact, $t_j$ is always 1 in your last equation, cause you have assumed that $o_j$ takes that node of target 1 in your output; $o_j$ of other nodes have different forms of probability functio... | Backpropagation with Softmax / Cross Entropy | Other answers have provided the correct way of calculating the derivative, but they do not point out where you have gone wrong. In fact, $t_j$ is always 1 in your last equation, cause you have assumed | Backpropagation with Softmax / Cross Entropy
Other answers have provided the correct way of calculating the derivative, but they do not point out where you have gone wrong. In fact, $t_j$ is always 1 in your last equation, cause you have assumed that $o_j$ takes that node of target 1 in your output; $o_j$ of other node... | Backpropagation with Softmax / Cross Entropy
Other answers have provided the correct way of calculating the derivative, but they do not point out where you have gone wrong. In fact, $t_j$ is always 1 in your last equation, cause you have assumed |
3,595 | Logistic Regression - Error Term and its Distribution | In linear regression observations are assumed to follow a Gaussian distribution with a mean parameter conditional on the predictor values. If you subtract the mean from the observations you get the error: a Gaussian distribution with mean zero, & independent of predictor values—that is errors at any set of predictor va... | Logistic Regression - Error Term and its Distribution | In linear regression observations are assumed to follow a Gaussian distribution with a mean parameter conditional on the predictor values. If you subtract the mean from the observations you get the er | Logistic Regression - Error Term and its Distribution
In linear regression observations are assumed to follow a Gaussian distribution with a mean parameter conditional on the predictor values. If you subtract the mean from the observations you get the error: a Gaussian distribution with mean zero, & independent of pred... | Logistic Regression - Error Term and its Distribution
In linear regression observations are assumed to follow a Gaussian distribution with a mean parameter conditional on the predictor values. If you subtract the mean from the observations you get the er |
3,596 | Logistic Regression - Error Term and its Distribution | This has been covered before. A model that is constrained to have predicted values in $[0,1]$ cannot possibly have an additive error term that would make the predictions go outside $[0,1]$. Think of the simplest example of a binary logistic model -- a model containing only an intercept. This is equivalent to the Ber... | Logistic Regression - Error Term and its Distribution | This has been covered before. A model that is constrained to have predicted values in $[0,1]$ cannot possibly have an additive error term that would make the predictions go outside $[0,1]$. Think of | Logistic Regression - Error Term and its Distribution
This has been covered before. A model that is constrained to have predicted values in $[0,1]$ cannot possibly have an additive error term that would make the predictions go outside $[0,1]$. Think of the simplest example of a binary logistic model -- a model contai... | Logistic Regression - Error Term and its Distribution
This has been covered before. A model that is constrained to have predicted values in $[0,1]$ cannot possibly have an additive error term that would make the predictions go outside $[0,1]$. Think of |
3,597 | Logistic Regression - Error Term and its Distribution | To me the unification of logistic, linear, poisson regression etc... has always been in terms of specification of the mean and variance in the Generalized Linear Model framework. We start by specifying a probability distribution for our data, normal for continuous data, Bernoulli for dichotomous, Poisson for counts, et... | Logistic Regression - Error Term and its Distribution | To me the unification of logistic, linear, poisson regression etc... has always been in terms of specification of the mean and variance in the Generalized Linear Model framework. We start by specifyin | Logistic Regression - Error Term and its Distribution
To me the unification of logistic, linear, poisson regression etc... has always been in terms of specification of the mean and variance in the Generalized Linear Model framework. We start by specifying a probability distribution for our data, normal for continuous d... | Logistic Regression - Error Term and its Distribution
To me the unification of logistic, linear, poisson regression etc... has always been in terms of specification of the mean and variance in the Generalized Linear Model framework. We start by specifyin |
3,598 | Logistic Regression - Error Term and its Distribution | No errors exist. We are modeling the mean! The mean is just a true number.
This doesn't make sense to me.
Think the response variable as a latent variable. If you assume the error term is normally distributed, then the model becomes a probit model. If you assume the distribution of the error term is logistic, then the... | Logistic Regression - Error Term and its Distribution | No errors exist. We are modeling the mean! The mean is just a true number.
This doesn't make sense to me.
Think the response variable as a latent variable. If you assume the error term is normally di | Logistic Regression - Error Term and its Distribution
No errors exist. We are modeling the mean! The mean is just a true number.
This doesn't make sense to me.
Think the response variable as a latent variable. If you assume the error term is normally distributed, then the model becomes a probit model. If you assume th... | Logistic Regression - Error Term and its Distribution
No errors exist. We are modeling the mean! The mean is just a true number.
This doesn't make sense to me.
Think the response variable as a latent variable. If you assume the error term is normally di |
3,599 | How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics? | Summary: the "random-effects model" in econometrics and a "random intercept mixed model" are indeed the same models, but they are estimated in different ways. The econometrics way is to use FGLS, and the mixed model way is to use ML. There are different algorithms of doing FGLS, and some of them (on this dataset) produ... | How exactly does a "random effects model" in econometrics relate to mixed models outside of economet | Summary: the "random-effects model" in econometrics and a "random intercept mixed model" are indeed the same models, but they are estimated in different ways. The econometrics way is to use FGLS, and | How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics?
Summary: the "random-effects model" in econometrics and a "random intercept mixed model" are indeed the same models, but they are estimated in different ways. The econometrics way is to use FGLS, and the mixed mode... | How exactly does a "random effects model" in econometrics relate to mixed models outside of economet
Summary: the "random-effects model" in econometrics and a "random intercept mixed model" are indeed the same models, but they are estimated in different ways. The econometrics way is to use FGLS, and |
3,600 | How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics? | This answer doesn't comment on mixed models, but I can explain what the random-effects estimator does and why it screws up on that graph.
Summary: the random-effects estimator assumes $E[u_i \mid x ] = 0$, which is not true in this example.
What is the random effects estimator doing?
Assume we have the model:
$$ y_{i... | How exactly does a "random effects model" in econometrics relate to mixed models outside of economet | This answer doesn't comment on mixed models, but I can explain what the random-effects estimator does and why it screws up on that graph.
Summary: the random-effects estimator assumes $E[u_i \mid x ] | How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics?
This answer doesn't comment on mixed models, but I can explain what the random-effects estimator does and why it screws up on that graph.
Summary: the random-effects estimator assumes $E[u_i \mid x ] = 0$, which is... | How exactly does a "random effects model" in econometrics relate to mixed models outside of economet
This answer doesn't comment on mixed models, but I can explain what the random-effects estimator does and why it screws up on that graph.
Summary: the random-effects estimator assumes $E[u_i \mid x ] |
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