idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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44,301 | Why we always put log() before the joint pdf when we use MLE(Maximum likelihood Estimation)? | Apart from the reasons mentioned in the comments to your question, there is another important one: in applying maximum likelihood estimation, we essentially solve a maximization problem with respect to the unknown coefficients. Recall that finding the global maximum of a function is not a simple matter, in case where w... | Why we always put log() before the joint pdf when we use MLE(Maximum likelihood Estimation)? | Apart from the reasons mentioned in the comments to your question, there is another important one: in applying maximum likelihood estimation, we essentially solve a maximization problem with respect t | Why we always put log() before the joint pdf when we use MLE(Maximum likelihood Estimation)?
Apart from the reasons mentioned in the comments to your question, there is another important one: in applying maximum likelihood estimation, we essentially solve a maximization problem with respect to the unknown coefficients.... | Why we always put log() before the joint pdf when we use MLE(Maximum likelihood Estimation)?
Apart from the reasons mentioned in the comments to your question, there is another important one: in applying maximum likelihood estimation, we essentially solve a maximization problem with respect t |
44,302 | Why we always put log() before the joint pdf when we use MLE(Maximum likelihood Estimation)? | In addition to the mathematical reason that Alecos wrote, let me give you a computational reason. Remember that the likelihood function is nothing but the joint density of random variables (expressed as a function of the parameters), i.e.
$$
Pr(\mathbf{x}) = Pr(x_{1})\cdot Pr(x_{2})\cdot\ldots\cdot Pr(x_{n}) = \prod_{i... | Why we always put log() before the joint pdf when we use MLE(Maximum likelihood Estimation)? | In addition to the mathematical reason that Alecos wrote, let me give you a computational reason. Remember that the likelihood function is nothing but the joint density of random variables (expressed | Why we always put log() before the joint pdf when we use MLE(Maximum likelihood Estimation)?
In addition to the mathematical reason that Alecos wrote, let me give you a computational reason. Remember that the likelihood function is nothing but the joint density of random variables (expressed as a function of the parame... | Why we always put log() before the joint pdf when we use MLE(Maximum likelihood Estimation)?
In addition to the mathematical reason that Alecos wrote, let me give you a computational reason. Remember that the likelihood function is nothing but the joint density of random variables (expressed |
44,303 | Can PCA be extended to account for nonlinear dependencies? | There is a technique invented by Trevor Hastie and Werner Stuetzle called principal curves, which is a nonlinear generalisation of principal components.
From the abstract for the original paper:
Principal curves are smooth one-dimensional curves that pass through the middle of a p-dimensional data set, providing a non... | Can PCA be extended to account for nonlinear dependencies? | There is a technique invented by Trevor Hastie and Werner Stuetzle called principal curves, which is a nonlinear generalisation of principal components.
From the abstract for the original paper:
Prin | Can PCA be extended to account for nonlinear dependencies?
There is a technique invented by Trevor Hastie and Werner Stuetzle called principal curves, which is a nonlinear generalisation of principal components.
From the abstract for the original paper:
Principal curves are smooth one-dimensional curves that pass thro... | Can PCA be extended to account for nonlinear dependencies?
There is a technique invented by Trevor Hastie and Werner Stuetzle called principal curves, which is a nonlinear generalisation of principal components.
From the abstract for the original paper:
Prin |
44,304 | Can PCA be extended to account for nonlinear dependencies? | The nonlinear dependencies you describe are Mercer kernels. A valid kernel is any function taking two observations that is continuous, symmetric and has a positive definite gram matrix. Gram and covariance are interchangeable in this context. The observations needn't be fixed-length vectors. They could be graphs, strin... | Can PCA be extended to account for nonlinear dependencies? | The nonlinear dependencies you describe are Mercer kernels. A valid kernel is any function taking two observations that is continuous, symmetric and has a positive definite gram matrix. Gram and covar | Can PCA be extended to account for nonlinear dependencies?
The nonlinear dependencies you describe are Mercer kernels. A valid kernel is any function taking two observations that is continuous, symmetric and has a positive definite gram matrix. Gram and covariance are interchangeable in this context. The observations n... | Can PCA be extended to account for nonlinear dependencies?
The nonlinear dependencies you describe are Mercer kernels. A valid kernel is any function taking two observations that is continuous, symmetric and has a positive definite gram matrix. Gram and covar |
44,305 | Can PCA be extended to account for nonlinear dependencies? | Nonlinear principal components are readily obtained using the MGV and MTV methods, implemented in SAS PROC PRINQUAL and the R Hmisc package's transcan function. The basic idea is to expand each continuous variable with regression spline basis functions, and to expand categorical variables into indicator variables. Th... | Can PCA be extended to account for nonlinear dependencies? | Nonlinear principal components are readily obtained using the MGV and MTV methods, implemented in SAS PROC PRINQUAL and the R Hmisc package's transcan function. The basic idea is to expand each conti | Can PCA be extended to account for nonlinear dependencies?
Nonlinear principal components are readily obtained using the MGV and MTV methods, implemented in SAS PROC PRINQUAL and the R Hmisc package's transcan function. The basic idea is to expand each continuous variable with regression spline basis functions, and to... | Can PCA be extended to account for nonlinear dependencies?
Nonlinear principal components are readily obtained using the MGV and MTV methods, implemented in SAS PROC PRINQUAL and the R Hmisc package's transcan function. The basic idea is to expand each conti |
44,306 | Exception for sum of deviations from mean being 0 | When a mean is computed, it's not computed to infinite precision. As a result, the computed sum of deviations around a mean can be a little different from zero.
We can see this, for example, in R, like so:
x <- rnorm(1000) # generates 1000 standard normal random numbers, puts them in x
d <- x - mean(x) # compute th... | Exception for sum of deviations from mean being 0 | When a mean is computed, it's not computed to infinite precision. As a result, the computed sum of deviations around a mean can be a little different from zero.
We can see this, for example, in R, lik | Exception for sum of deviations from mean being 0
When a mean is computed, it's not computed to infinite precision. As a result, the computed sum of deviations around a mean can be a little different from zero.
We can see this, for example, in R, like so:
x <- rnorm(1000) # generates 1000 standard normal random numbe... | Exception for sum of deviations from mean being 0
When a mean is computed, it's not computed to infinite precision. As a result, the computed sum of deviations around a mean can be a little different from zero.
We can see this, for example, in R, lik |
44,307 | Exception for sum of deviations from mean being 0 | I want to add something to the previous answer, with which I completely agree.
It happens that I am working on implementing a statistical library in Java and I use as a reference point the computed values from R. A few days ago I studied algorithms for implementing mean and variance. And what I found is that the C code... | Exception for sum of deviations from mean being 0 | I want to add something to the previous answer, with which I completely agree.
It happens that I am working on implementing a statistical library in Java and I use as a reference point the computed va | Exception for sum of deviations from mean being 0
I want to add something to the previous answer, with which I completely agree.
It happens that I am working on implementing a statistical library in Java and I use as a reference point the computed values from R. A few days ago I studied algorithms for implementing mean... | Exception for sum of deviations from mean being 0
I want to add something to the previous answer, with which I completely agree.
It happens that I am working on implementing a statistical library in Java and I use as a reference point the computed va |
44,308 | Why are the residuals in this model so linearly skewed? | You shouldn't plot the residuals against the predicator values because they are correlated, instead we plot against the fitted values, i.e. $\hat Y$. To see this, consider this simple data set:
x = runif(20)
y = rnorm(20)
Clearly $x$ and $y$ are unrelated. Now, we fitted a simple linear regression model
m = lm(y ~ x)
... | Why are the residuals in this model so linearly skewed? | You shouldn't plot the residuals against the predicator values because they are correlated, instead we plot against the fitted values, i.e. $\hat Y$. To see this, consider this simple data set:
x = ru | Why are the residuals in this model so linearly skewed?
You shouldn't plot the residuals against the predicator values because they are correlated, instead we plot against the fitted values, i.e. $\hat Y$. To see this, consider this simple data set:
x = runif(20)
y = rnorm(20)
Clearly $x$ and $y$ are unrelated. Now, w... | Why are the residuals in this model so linearly skewed?
You shouldn't plot the residuals against the predicator values because they are correlated, instead we plot against the fitted values, i.e. $\hat Y$. To see this, consider this simple data set:
x = ru |
44,309 | Why are the residuals in this model so linearly skewed? | What you are seeing is called "Regression towards the Mean" and is completely expected. Any time that there is variability in the data (and yours looks like it has a bunch) then the prediction values will on average be between the overall mean and the observed values. The plot you created, of the outcome vs the predi... | Why are the residuals in this model so linearly skewed? | What you are seeing is called "Regression towards the Mean" and is completely expected. Any time that there is variability in the data (and yours looks like it has a bunch) then the prediction values | Why are the residuals in this model so linearly skewed?
What you are seeing is called "Regression towards the Mean" and is completely expected. Any time that there is variability in the data (and yours looks like it has a bunch) then the prediction values will on average be between the overall mean and the observed va... | Why are the residuals in this model so linearly skewed?
What you are seeing is called "Regression towards the Mean" and is completely expected. Any time that there is variability in the data (and yours looks like it has a bunch) then the prediction values |
44,310 | Resources or methods for determining if a technique is in current use? | There's no shortcut for experience, but one way to get a hint is to look up the method's original references on google scholar and see the number of citations. | Resources or methods for determining if a technique is in current use? | There's no shortcut for experience, but one way to get a hint is to look up the method's original references on google scholar and see the number of citations. | Resources or methods for determining if a technique is in current use?
There's no shortcut for experience, but one way to get a hint is to look up the method's original references on google scholar and see the number of citations. | Resources or methods for determining if a technique is in current use?
There's no shortcut for experience, but one way to get a hint is to look up the method's original references on google scholar and see the number of citations. |
44,311 | Resources or methods for determining if a technique is in current use? | Many techniques are not so popular, however they may be useful for specific research purposes. If a statistical methodology is supported by Monte Carlo simulations, and if it was published on prestigious journals, so I think you can take it in consideration, even though it was little used by researchers. For example, I... | Resources or methods for determining if a technique is in current use? | Many techniques are not so popular, however they may be useful for specific research purposes. If a statistical methodology is supported by Monte Carlo simulations, and if it was published on prestigi | Resources or methods for determining if a technique is in current use?
Many techniques are not so popular, however they may be useful for specific research purposes. If a statistical methodology is supported by Monte Carlo simulations, and if it was published on prestigious journals, so I think you can take it in consi... | Resources or methods for determining if a technique is in current use?
Many techniques are not so popular, however they may be useful for specific research purposes. If a statistical methodology is supported by Monte Carlo simulations, and if it was published on prestigi |
44,312 | Resources or methods for determining if a technique is in current use? | I agree with use4733. My planned answer was to be "ask the experts". Regarding this particular technique I personally can't say much because I hadn't heard of it before even though I have some expertise in time series analysis. However, since the references seem to all be over the most recent three years it could jus... | Resources or methods for determining if a technique is in current use? | I agree with use4733. My planned answer was to be "ask the experts". Regarding this particular technique I personally can't say much because I hadn't heard of it before even though I have some exper | Resources or methods for determining if a technique is in current use?
I agree with use4733. My planned answer was to be "ask the experts". Regarding this particular technique I personally can't say much because I hadn't heard of it before even though I have some expertise in time series analysis. However, since the ... | Resources or methods for determining if a technique is in current use?
I agree with use4733. My planned answer was to be "ask the experts". Regarding this particular technique I personally can't say much because I hadn't heard of it before even though I have some exper |
44,313 | Is there a software package designed to automatically check the assumptions of various statistical tests? | I think you should look at applied statistics texts. An easy one to read the is one of my favorites was written by the late Rupert Miller (I took the applied statistics sequence that he taught when I was a graduate student at Stanford). At that time we had notes. His book was not finished but it is a marvel. He was a... | Is there a software package designed to automatically check the assumptions of various statistical t | I think you should look at applied statistics texts. An easy one to read the is one of my favorites was written by the late Rupert Miller (I took the applied statistics sequence that he taught when I | Is there a software package designed to automatically check the assumptions of various statistical tests?
I think you should look at applied statistics texts. An easy one to read the is one of my favorites was written by the late Rupert Miller (I took the applied statistics sequence that he taught when I was a gradua... | Is there a software package designed to automatically check the assumptions of various statistical t
I think you should look at applied statistics texts. An easy one to read the is one of my favorites was written by the late Rupert Miller (I took the applied statistics sequence that he taught when I |
44,314 | Is there a software package designed to automatically check the assumptions of various statistical tests? | The information needed to decide if the assumptions about a statistical test are reasonable are often exterior to the data itself. This means that an automated program would not have the information needed. For example it is usually assumed that the data was collected independently (or conditionally independently), b... | Is there a software package designed to automatically check the assumptions of various statistical t | The information needed to decide if the assumptions about a statistical test are reasonable are often exterior to the data itself. This means that an automated program would not have the information | Is there a software package designed to automatically check the assumptions of various statistical tests?
The information needed to decide if the assumptions about a statistical test are reasonable are often exterior to the data itself. This means that an automated program would not have the information needed. For ... | Is there a software package designed to automatically check the assumptions of various statistical t
The information needed to decide if the assumptions about a statistical test are reasonable are often exterior to the data itself. This means that an automated program would not have the information |
44,315 | Is there a software package designed to automatically check the assumptions of various statistical tests? | This is old but your library may have it:
"A guide for selecting statistical techniques for analyzing social science data"
2nd ed 1981; institute for social research,university of michigan
Andrews, FM; Klem, L; Davidson, TN; O'Malley, PM; rodgers, WL
Laurence | Is there a software package designed to automatically check the assumptions of various statistical t | This is old but your library may have it:
"A guide for selecting statistical techniques for analyzing social science data"
2nd ed 1981; institute for social research,university of michigan
Andrews, FM | Is there a software package designed to automatically check the assumptions of various statistical tests?
This is old but your library may have it:
"A guide for selecting statistical techniques for analyzing social science data"
2nd ed 1981; institute for social research,university of michigan
Andrews, FM; Klem, L; Da... | Is there a software package designed to automatically check the assumptions of various statistical t
This is old but your library may have it:
"A guide for selecting statistical techniques for analyzing social science data"
2nd ed 1981; institute for social research,university of michigan
Andrews, FM |
44,316 | How to select best parameter for polynomial kernel? | Grid search is a sensible procedure as @JohnSmith suggests, however it is not the only stable technique. I generally use the Nelder-Mead simplex algortihm, which I have found to be very reliable and more efficient than grid search as less time is spent investigating areas of hyper-parameter space that give poor models... | How to select best parameter for polynomial kernel? | Grid search is a sensible procedure as @JohnSmith suggests, however it is not the only stable technique. I generally use the Nelder-Mead simplex algortihm, which I have found to be very reliable and | How to select best parameter for polynomial kernel?
Grid search is a sensible procedure as @JohnSmith suggests, however it is not the only stable technique. I generally use the Nelder-Mead simplex algortihm, which I have found to be very reliable and more efficient than grid search as less time is spent investigating ... | How to select best parameter for polynomial kernel?
Grid search is a sensible procedure as @JohnSmith suggests, however it is not the only stable technique. I generally use the Nelder-Mead simplex algortihm, which I have found to be very reliable and |
44,317 | How to select best parameter for polynomial kernel? | Why don't you want to use grid search? It seems to me the only stable technique for SVM parameter estimation. Of course you can use adaptive search, but it can save you not so much time, but lead you to some strange results.
And the implementation for CV procedure is pretty standart:
Divide your dataset into two parts:... | How to select best parameter for polynomial kernel? | Why don't you want to use grid search? It seems to me the only stable technique for SVM parameter estimation. Of course you can use adaptive search, but it can save you not so much time, but lead you | How to select best parameter for polynomial kernel?
Why don't you want to use grid search? It seems to me the only stable technique for SVM parameter estimation. Of course you can use adaptive search, but it can save you not so much time, but lead you to some strange results.
And the implementation for CV procedure is ... | How to select best parameter for polynomial kernel?
Why don't you want to use grid search? It seems to me the only stable technique for SVM parameter estimation. Of course you can use adaptive search, but it can save you not so much time, but lead you |
44,318 | How to select best parameter for polynomial kernel? | You can try using a random search algorithm to get near equivalent results as grid search with a lot less work depending on the granularity of your grid. You can read more about it at Dato Blog along with other hyperparameter tuning techniques. This method is relatively quick if you set it up to run in parallel. | How to select best parameter for polynomial kernel? | You can try using a random search algorithm to get near equivalent results as grid search with a lot less work depending on the granularity of your grid. You can read more about it at Dato Blog along | How to select best parameter for polynomial kernel?
You can try using a random search algorithm to get near equivalent results as grid search with a lot less work depending on the granularity of your grid. You can read more about it at Dato Blog along with other hyperparameter tuning techniques. This method is relative... | How to select best parameter for polynomial kernel?
You can try using a random search algorithm to get near equivalent results as grid search with a lot less work depending on the granularity of your grid. You can read more about it at Dato Blog along |
44,319 | how to add second order terms into the model in R? | The formula documentation for R shows how to do this. In short, you use poly(). For example, make some quadratic data:
x <- rnorm(100)
y <- x + x**2 * 0.5 + rnorm(100)
Now fit this using a second order polynomial (i.e x and x**2) like this
mod <- lm(y ~ poly(x, 2))
Note that this will fit an orthogonal polynomial... | how to add second order terms into the model in R? | The formula documentation for R shows how to do this. In short, you use poly(). For example, make some quadratic data:
x <- rnorm(100)
y <- x + x**2 * 0.5 + rnorm(100)
Now fit this using a second | how to add second order terms into the model in R?
The formula documentation for R shows how to do this. In short, you use poly(). For example, make some quadratic data:
x <- rnorm(100)
y <- x + x**2 * 0.5 + rnorm(100)
Now fit this using a second order polynomial (i.e x and x**2) like this
mod <- lm(y ~ poly(x, 2)... | how to add second order terms into the model in R?
The formula documentation for R shows how to do this. In short, you use poly(). For example, make some quadratic data:
x <- rnorm(100)
y <- x + x**2 * 0.5 + rnorm(100)
Now fit this using a second |
44,320 | how to add second order terms into the model in R? | Type :
lm(y ~ x1 + x2 + I(x1*x2) + I(x1^2) + ...) | how to add second order terms into the model in R? | Type :
lm(y ~ x1 + x2 + I(x1*x2) + I(x1^2) + ...) | how to add second order terms into the model in R?
Type :
lm(y ~ x1 + x2 + I(x1*x2) + I(x1^2) + ...) | how to add second order terms into the model in R?
Type :
lm(y ~ x1 + x2 + I(x1*x2) + I(x1^2) + ...) |
44,321 | how to add second order terms into the model in R? | Here's how to do it in principle, illustrated on a smaller dataset with only 10 predictors:
# Make fake data
mydata = as.data.frame(matrix(rnorm(1100), 100))
names(mydata) = c(paste0("x", 1:10), "y")
# Form a matrix containing all predictor columns but not y
x = as.matrix(mydata[, 1:10])
# Use poly() to form all 2-way... | how to add second order terms into the model in R? | Here's how to do it in principle, illustrated on a smaller dataset with only 10 predictors:
# Make fake data
mydata = as.data.frame(matrix(rnorm(1100), 100))
names(mydata) = c(paste0("x", 1:10), "y")
| how to add second order terms into the model in R?
Here's how to do it in principle, illustrated on a smaller dataset with only 10 predictors:
# Make fake data
mydata = as.data.frame(matrix(rnorm(1100), 100))
names(mydata) = c(paste0("x", 1:10), "y")
# Form a matrix containing all predictor columns but not y
x = as.ma... | how to add second order terms into the model in R?
Here's how to do it in principle, illustrated on a smaller dataset with only 10 predictors:
# Make fake data
mydata = as.data.frame(matrix(rnorm(1100), 100))
names(mydata) = c(paste0("x", 1:10), "y")
|
44,322 | Kendall's tau and independence | I am going to interpret your question as one regarding a hypothesis on the population quantity $\tau$. If this is not what you intended, please comment to that effect and I will revise the answer accordingly.
Definition and equivalent expressions
Let $(X,Y)$ by a bivariate random vector with a continuous joint distrib... | Kendall's tau and independence | I am going to interpret your question as one regarding a hypothesis on the population quantity $\tau$. If this is not what you intended, please comment to that effect and I will revise the answer acc | Kendall's tau and independence
I am going to interpret your question as one regarding a hypothesis on the population quantity $\tau$. If this is not what you intended, please comment to that effect and I will revise the answer accordingly.
Definition and equivalent expressions
Let $(X,Y)$ by a bivariate random vector ... | Kendall's tau and independence
I am going to interpret your question as one regarding a hypothesis on the population quantity $\tau$. If this is not what you intended, please comment to that effect and I will revise the answer acc |
44,323 | Calculating proportions by age in R | Your approach seems way too complicated to me. Let's start with some data:
## make up some data
status <- factor(rbinom(1000, 1, 0.3), labels = c("single", "married"))
age <- sample(20:50, 1000, replace = TRUE)
df <- data.frame(status, age)
head(df)
Print the first six cases:
> head(df)
status age
1 married 21
2 ... | Calculating proportions by age in R | Your approach seems way too complicated to me. Let's start with some data:
## make up some data
status <- factor(rbinom(1000, 1, 0.3), labels = c("single", "married"))
age <- sample(20:50, 1000, repla | Calculating proportions by age in R
Your approach seems way too complicated to me. Let's start with some data:
## make up some data
status <- factor(rbinom(1000, 1, 0.3), labels = c("single", "married"))
age <- sample(20:50, 1000, replace = TRUE)
df <- data.frame(status, age)
head(df)
Print the first six cases:
> head... | Calculating proportions by age in R
Your approach seems way too complicated to me. Let's start with some data:
## make up some data
status <- factor(rbinom(1000, 1, 0.3), labels = c("single", "married"))
age <- sample(20:50, 1000, repla |
44,324 | Calculating proportions by age in R | I did something similar recently. There are quite a few ways to aggregate data like this in R, but the ddply function from the package plyr is my security blanket, and I turn to it for things like this.
I'm assuming that you have individual records for each person in your dataset, with age, sex, and marital status. T... | Calculating proportions by age in R | I did something similar recently. There are quite a few ways to aggregate data like this in R, but the ddply function from the package plyr is my security blanket, and I turn to it for things like th | Calculating proportions by age in R
I did something similar recently. There are quite a few ways to aggregate data like this in R, but the ddply function from the package plyr is my security blanket, and I turn to it for things like this.
I'm assuming that you have individual records for each person in your dataset, w... | Calculating proportions by age in R
I did something similar recently. There are quite a few ways to aggregate data like this in R, but the ddply function from the package plyr is my security blanket, and I turn to it for things like th |
44,325 | Calculating proportions by age in R | Probably what you need is table or aggregate. If you add more details I can give you a more in-depth explanation. | Calculating proportions by age in R | Probably what you need is table or aggregate. If you add more details I can give you a more in-depth explanation. | Calculating proportions by age in R
Probably what you need is table or aggregate. If you add more details I can give you a more in-depth explanation. | Calculating proportions by age in R
Probably what you need is table or aggregate. If you add more details I can give you a more in-depth explanation. |
44,326 | Is there a verifiable way to generate discrete random variables on the basis of an external event? | Just as another source of verifiable randomness: random.org generates random numbers from atmospheric noise. They publish a daily file (most days) of random bits; the first digit of each day's file might prove suitably verifiable to your parties.
Update 2013-11-12: Access to these files is now restricted, but it look... | Is there a verifiable way to generate discrete random variables on the basis of an external event? | Just as another source of verifiable randomness: random.org generates random numbers from atmospheric noise. They publish a daily file (most days) of random bits; the first digit of each day's file m | Is there a verifiable way to generate discrete random variables on the basis of an external event?
Just as another source of verifiable randomness: random.org generates random numbers from atmospheric noise. They publish a daily file (most days) of random bits; the first digit of each day's file might prove suitably v... | Is there a verifiable way to generate discrete random variables on the basis of an external event?
Just as another source of verifiable randomness: random.org generates random numbers from atmospheric noise. They publish a daily file (most days) of random bits; the first digit of each day's file m |
44,327 | Is there a verifiable way to generate discrete random variables on the basis of an external event? | Many countries have state lottery which is regularly audited, and whose results are announced online: e.g. UK national lottery. You just need to construct an appropriate function which maps this output space to your desired output.
A continuous distribution would be more tricky, but you could obtain a discrete approxi... | Is there a verifiable way to generate discrete random variables on the basis of an external event? | Many countries have state lottery which is regularly audited, and whose results are announced online: e.g. UK national lottery. You just need to construct an appropriate function which maps this outpu | Is there a verifiable way to generate discrete random variables on the basis of an external event?
Many countries have state lottery which is regularly audited, and whose results are announced online: e.g. UK national lottery. You just need to construct an appropriate function which maps this output space to your desir... | Is there a verifiable way to generate discrete random variables on the basis of an external event?
Many countries have state lottery which is regularly audited, and whose results are announced online: e.g. UK national lottery. You just need to construct an appropriate function which maps this outpu |
44,328 | Is there a verifiable way to generate discrete random variables on the basis of an external event? | This reminds me of a question from Algorithms class a long time ago. Let the external event be a (preferrably continuous) random variable $Y$. To generate a value of $X$, take two independent observations of $Y$ and let $X$ be $1$ if the first observation of $Y$ is greater than the second, let it be $0$ if the second i... | Is there a verifiable way to generate discrete random variables on the basis of an external event? | This reminds me of a question from Algorithms class a long time ago. Let the external event be a (preferrably continuous) random variable $Y$. To generate a value of $X$, take two independent observat | Is there a verifiable way to generate discrete random variables on the basis of an external event?
This reminds me of a question from Algorithms class a long time ago. Let the external event be a (preferrably continuous) random variable $Y$. To generate a value of $X$, take two independent observations of $Y$ and let $... | Is there a verifiable way to generate discrete random variables on the basis of an external event?
This reminds me of a question from Algorithms class a long time ago. Let the external event be a (preferrably continuous) random variable $Y$. To generate a value of $X$, take two independent observat |
44,329 | Is there a verifiable way to generate discrete random variables on the basis of an external event? | I didn't quite understand what you meant by "on the basis of an external event." But you can certainly flip a fair coin in a manner that a remote user can cryptographically verify.
Consider this algorithm:
Bob picks a uniformly random boolean value, TRUE or FALSE. He also chooses a large random number. He sends Alice ... | Is there a verifiable way to generate discrete random variables on the basis of an external event? | I didn't quite understand what you meant by "on the basis of an external event." But you can certainly flip a fair coin in a manner that a remote user can cryptographically verify.
Consider this algor | Is there a verifiable way to generate discrete random variables on the basis of an external event?
I didn't quite understand what you meant by "on the basis of an external event." But you can certainly flip a fair coin in a manner that a remote user can cryptographically verify.
Consider this algorithm:
Bob picks a un... | Is there a verifiable way to generate discrete random variables on the basis of an external event?
I didn't quite understand what you meant by "on the basis of an external event." But you can certainly flip a fair coin in a manner that a remote user can cryptographically verify.
Consider this algor |
44,330 | Is there a verifiable way to generate discrete random variables on the basis of an external event? | an easy way to generate symmetric bernoulli trials is to flip a coin twice. if the first toss is H and the second is T, say X = 1. if it's the other way round, say X = 0. if the two tosses match [2H or 2T], discard the outcome and continue. no matter what the bias of the coin, X will be symmetric bernoulli. | Is there a verifiable way to generate discrete random variables on the basis of an external event? | an easy way to generate symmetric bernoulli trials is to flip a coin twice. if the first toss is H and the second is T, say X = 1. if it's the other way round, say X = 0. if the two tosses match [2H o | Is there a verifiable way to generate discrete random variables on the basis of an external event?
an easy way to generate symmetric bernoulli trials is to flip a coin twice. if the first toss is H and the second is T, say X = 1. if it's the other way round, say X = 0. if the two tosses match [2H or 2T], discard the ou... | Is there a verifiable way to generate discrete random variables on the basis of an external event?
an easy way to generate symmetric bernoulli trials is to flip a coin twice. if the first toss is H and the second is T, say X = 1. if it's the other way round, say X = 0. if the two tosses match [2H o |
44,331 | Incorporating boolean data into analysis | You are decribing "categorical variables" (represented in R a factors). These can be incorporated into almost any statistical model by being assigned levels. You would need to give more detail about your particular problem in order to be advised on a particular method.
Edit
If the response variable has two possible ... | Incorporating boolean data into analysis | You are decribing "categorical variables" (represented in R a factors). These can be incorporated into almost any statistical model by being assigned levels. You would need to give more detail about | Incorporating boolean data into analysis
You are decribing "categorical variables" (represented in R a factors). These can be incorporated into almost any statistical model by being assigned levels. You would need to give more detail about your particular problem in order to be advised on a particular method.
Edit
I... | Incorporating boolean data into analysis
You are decribing "categorical variables" (represented in R a factors). These can be incorporated into almost any statistical model by being assigned levels. You would need to give more detail about |
44,332 | Incorporating boolean data into analysis | It sounds like you are trying to predict your boolean response, yes?
This is called classification.
Logistic Regression is the obvious choice here, but there are other methods too. You can't do traditional regression, because the response is not a real number.
The lookup variables are called nominals, and can be dealt ... | Incorporating boolean data into analysis | It sounds like you are trying to predict your boolean response, yes?
This is called classification.
Logistic Regression is the obvious choice here, but there are other methods too. You can't do tradit | Incorporating boolean data into analysis
It sounds like you are trying to predict your boolean response, yes?
This is called classification.
Logistic Regression is the obvious choice here, but there are other methods too. You can't do traditional regression, because the response is not a real number.
The lookup variabl... | Incorporating boolean data into analysis
It sounds like you are trying to predict your boolean response, yes?
This is called classification.
Logistic Regression is the obvious choice here, but there are other methods too. You can't do tradit |
44,333 | Incorporating boolean data into analysis | Ingo Ruczinski has contributed to promote the use of Logic regression for data set consisting of binary variables, with an emphasis on higher-order interaction terms. The main advantage compared to usual or penalized GLMs is that it is more parcimonious in terms of degrees of freedom. The outcome may be continuous or c... | Incorporating boolean data into analysis | Ingo Ruczinski has contributed to promote the use of Logic regression for data set consisting of binary variables, with an emphasis on higher-order interaction terms. The main advantage compared to us | Incorporating boolean data into analysis
Ingo Ruczinski has contributed to promote the use of Logic regression for data set consisting of binary variables, with an emphasis on higher-order interaction terms. The main advantage compared to usual or penalized GLMs is that it is more parcimonious in terms of degrees of fr... | Incorporating boolean data into analysis
Ingo Ruczinski has contributed to promote the use of Logic regression for data set consisting of binary variables, with an emphasis on higher-order interaction terms. The main advantage compared to us |
44,334 | Incorporating boolean data into analysis | Try Random Forest; from my experience it may perform well on such kind of data, and gives you a some additional interesting information, like variable importance and object similarity measure. | Incorporating boolean data into analysis | Try Random Forest; from my experience it may perform well on such kind of data, and gives you a some additional interesting information, like variable importance and object similarity measure. | Incorporating boolean data into analysis
Try Random Forest; from my experience it may perform well on such kind of data, and gives you a some additional interesting information, like variable importance and object similarity measure. | Incorporating boolean data into analysis
Try Random Forest; from my experience it may perform well on such kind of data, and gives you a some additional interesting information, like variable importance and object similarity measure. |
44,335 | Is Kendall's tau uniquely determined by Pearson rho? | Can two different data sets have the same Pearson's ρ, but different Kendall's τ?
Anscombe's quartet gives you four two-dimensional datasets with (almost) identical Pearson correlations, but their Kendall correlations are quite different. In R:
> with(anscombe,cor(x1,y1,method="pearson"))
[1] 0.8164205
> with(anscombe... | Is Kendall's tau uniquely determined by Pearson rho? | Can two different data sets have the same Pearson's ρ, but different Kendall's τ?
Anscombe's quartet gives you four two-dimensional datasets with (almost) identical Pearson correlations, but their Ke | Is Kendall's tau uniquely determined by Pearson rho?
Can two different data sets have the same Pearson's ρ, but different Kendall's τ?
Anscombe's quartet gives you four two-dimensional datasets with (almost) identical Pearson correlations, but their Kendall correlations are quite different. In R:
> with(anscombe,cor(x... | Is Kendall's tau uniquely determined by Pearson rho?
Can two different data sets have the same Pearson's ρ, but different Kendall's τ?
Anscombe's quartet gives you four two-dimensional datasets with (almost) identical Pearson correlations, but their Ke |
44,336 | Is Kendall's tau uniquely determined by Pearson rho? | An indirect approach:
If two $\rho_1 > \rho_2$ can relate to the same $\tau$, then imagine adjusting the dataset a little such that we increase all these three values.
We should be able to arrive to some values $\rho^\prime_1 > \rho_1$, $\rho^\prime_2 > \rho_2$ and $\tau^\prime > \tau$. This should be possible in a con... | Is Kendall's tau uniquely determined by Pearson rho? | An indirect approach:
If two $\rho_1 > \rho_2$ can relate to the same $\tau$, then imagine adjusting the dataset a little such that we increase all these three values.
We should be able to arrive to s | Is Kendall's tau uniquely determined by Pearson rho?
An indirect approach:
If two $\rho_1 > \rho_2$ can relate to the same $\tau$, then imagine adjusting the dataset a little such that we increase all these three values.
We should be able to arrive to some values $\rho^\prime_1 > \rho_1$, $\rho^\prime_2 > \rho_2$ and $... | Is Kendall's tau uniquely determined by Pearson rho?
An indirect approach:
If two $\rho_1 > \rho_2$ can relate to the same $\tau$, then imagine adjusting the dataset a little such that we increase all these three values.
We should be able to arrive to s |
44,337 | Question about running Spearman's correlation instead of Pearson's | Pearson's correlation coefficient ($\boldsymbol{r}$) provides a measure of linear association between paired variables.
Spearman's correlation coefficient ($\boldsymbol{r_{\bf{S}}}$) provides a measure of monotonic association between paired variables.
The latter is different than the former. A linear relationship is j... | Question about running Spearman's correlation instead of Pearson's | Pearson's correlation coefficient ($\boldsymbol{r}$) provides a measure of linear association between paired variables.
Spearman's correlation coefficient ($\boldsymbol{r_{\bf{S}}}$) provides a measur | Question about running Spearman's correlation instead of Pearson's
Pearson's correlation coefficient ($\boldsymbol{r}$) provides a measure of linear association between paired variables.
Spearman's correlation coefficient ($\boldsymbol{r_{\bf{S}}}$) provides a measure of monotonic association between paired variables.
... | Question about running Spearman's correlation instead of Pearson's
Pearson's correlation coefficient ($\boldsymbol{r}$) provides a measure of linear association between paired variables.
Spearman's correlation coefficient ($\boldsymbol{r_{\bf{S}}}$) provides a measur |
44,338 | Question about running Spearman's correlation instead of Pearson's | I think a couple valuable journal articles on this subject are de Winter et al., 2016 and Bishara & Hittner, 2015. I highlight the main points of both below, focusing primarily on Pearson and Spearman coefficients since that is what your question asks.
Bishara & Hittner, 2015
In this simulation study, the authors mainl... | Question about running Spearman's correlation instead of Pearson's | I think a couple valuable journal articles on this subject are de Winter et al., 2016 and Bishara & Hittner, 2015. I highlight the main points of both below, focusing primarily on Pearson and Spearman | Question about running Spearman's correlation instead of Pearson's
I think a couple valuable journal articles on this subject are de Winter et al., 2016 and Bishara & Hittner, 2015. I highlight the main points of both below, focusing primarily on Pearson and Spearman coefficients since that is what your question asks.
... | Question about running Spearman's correlation instead of Pearson's
I think a couple valuable journal articles on this subject are de Winter et al., 2016 and Bishara & Hittner, 2015. I highlight the main points of both below, focusing primarily on Pearson and Spearman |
44,339 | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed] | The TLDR
The short answer to your question is no. You can engage in both null hypothesis significance testing (NHST) as well as exploratory data analysis (EDA) without engaging in morally corrupt research practices. The longer answer to that question can be summarized with "it also depends."
A Practical Example
If we r... | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed] | The TLDR
The short answer to your question is no. You can engage in both null hypothesis significance testing (NHST) as well as exploratory data analysis (EDA) without engaging in morally corrupt rese | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed]
The TLDR
The short answer to your question is no. You can engage in both null hypothesis significance testing (NHST) as well as exploratory data analysis (EDA) without engaging in morally corrupt research practices. The longer answer to tha... | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed]
The TLDR
The short answer to your question is no. You can engage in both null hypothesis significance testing (NHST) as well as exploratory data analysis (EDA) without engaging in morally corrupt rese |
44,340 | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed] | The problem with p-hacking in my view is not the hacking itself, but rather the interpretation of the outcome. Your professor is right saying that if you test and test and test, you will at some point find significance even if nothing is going on. This means that significances that you found in this way cannot be relia... | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed] | The problem with p-hacking in my view is not the hacking itself, but rather the interpretation of the outcome. Your professor is right saying that if you test and test and test, you will at some point | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed]
The problem with p-hacking in my view is not the hacking itself, but rather the interpretation of the outcome. Your professor is right saying that if you test and test and test, you will at some point find significance even if nothing is go... | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed]
The problem with p-hacking in my view is not the hacking itself, but rather the interpretation of the outcome. Your professor is right saying that if you test and test and test, you will at some point |
44,341 | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed] | Here is my take at the answer.
The problem with exploratory analysis
Your professor is correct - exploratory analysis, if done for long enough, will always find some trend that will seem interesting. You can easily check this yourself - just fill the data you had in class with random numbers (or shuffle it between part... | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed] | Here is my take at the answer.
The problem with exploratory analysis
Your professor is correct - exploratory analysis, if done for long enough, will always find some trend that will seem interesting. | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed]
Here is my take at the answer.
The problem with exploratory analysis
Your professor is correct - exploratory analysis, if done for long enough, will always find some trend that will seem interesting. You can easily check this yourself - jus... | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed]
Here is my take at the answer.
The problem with exploratory analysis
Your professor is correct - exploratory analysis, if done for long enough, will always find some trend that will seem interesting. |
44,342 | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed] | couldn't procedures like Cross Validation be used
Yes, p-hacking, can certainly be reduced by tests like these that represent the significance correctly.
But that's the whole point about p-hacking, it is the case when such techniques as cross validation are not used and when the expression of the statistical significa... | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed] | couldn't procedures like Cross Validation be used
Yes, p-hacking, can certainly be reduced by tests like these that represent the significance correctly.
But that's the whole point about p-hacking, i | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed]
couldn't procedures like Cross Validation be used
Yes, p-hacking, can certainly be reduced by tests like these that represent the significance correctly.
But that's the whole point about p-hacking, it is the case when such techniques as cr... | Is "Exploratory Data Analysis" Fundamentally At Odds With "P-Hacking"? [closed]
couldn't procedures like Cross Validation be used
Yes, p-hacking, can certainly be reduced by tests like these that represent the significance correctly.
But that's the whole point about p-hacking, i |
44,343 | Is more data really always better in machine learning? | You are right, it is not only about the size of the dataset. As two other answers pointed out, having more data (vs very little) is desired, as even in a noiseless scenario it may help you to get a more precise estimate. On another hand, as you argue, it is also about the quality of the data.
There's a great lecture by... | Is more data really always better in machine learning? | You are right, it is not only about the size of the dataset. As two other answers pointed out, having more data (vs very little) is desired, as even in a noiseless scenario it may help you to get a mo | Is more data really always better in machine learning?
You are right, it is not only about the size of the dataset. As two other answers pointed out, having more data (vs very little) is desired, as even in a noiseless scenario it may help you to get a more precise estimate. On another hand, as you argue, it is also ab... | Is more data really always better in machine learning?
You are right, it is not only about the size of the dataset. As two other answers pointed out, having more data (vs very little) is desired, as even in a noiseless scenario it may help you to get a mo |
44,344 | Is more data really always better in machine learning? | Intuitively, having more data will tell the neural network where to turn, by how much, and in what direction (up/down, left/right, combinations, extensions in high-dimension spaces, etc).
Imagine your true function to be a parabola. However, you only have two data points. You have no way to capture the curvature. You c... | Is more data really always better in machine learning? | Intuitively, having more data will tell the neural network where to turn, by how much, and in what direction (up/down, left/right, combinations, extensions in high-dimension spaces, etc).
Imagine your | Is more data really always better in machine learning?
Intuitively, having more data will tell the neural network where to turn, by how much, and in what direction (up/down, left/right, combinations, extensions in high-dimension spaces, etc).
Imagine your true function to be a parabola. However, you only have two data ... | Is more data really always better in machine learning?
Intuitively, having more data will tell the neural network where to turn, by how much, and in what direction (up/down, left/right, combinations, extensions in high-dimension spaces, etc).
Imagine your |
44,345 | Is more data really always better in machine learning? | My intuition is that, given $(x_{i},y_{i})_{i=1}^n$ and $(x_{i},y_{i})_{i=1}^N$ have the same "information" (I know this is a fuzzy term), using $(x_{i},y_{i})_{i=1}^N$ should not better the fit. It should even make generalisation worse since we overfit.
At first I was skeptical, thinking 'how can you overfit if there... | Is more data really always better in machine learning? | My intuition is that, given $(x_{i},y_{i})_{i=1}^n$ and $(x_{i},y_{i})_{i=1}^N$ have the same "information" (I know this is a fuzzy term), using $(x_{i},y_{i})_{i=1}^N$ should not better the fit. It s | Is more data really always better in machine learning?
My intuition is that, given $(x_{i},y_{i})_{i=1}^n$ and $(x_{i},y_{i})_{i=1}^N$ have the same "information" (I know this is a fuzzy term), using $(x_{i},y_{i})_{i=1}^N$ should not better the fit. It should even make generalisation worse since we overfit.
At first ... | Is more data really always better in machine learning?
My intuition is that, given $(x_{i},y_{i})_{i=1}^n$ and $(x_{i},y_{i})_{i=1}^N$ have the same "information" (I know this is a fuzzy term), using $(x_{i},y_{i})_{i=1}^N$ should not better the fit. It s |
44,346 | Misuse of mixed effects model | The misunderstanding here is in how random intercepts are modeled. They aren't confounded with the diagnosis predictor in the way that you fear. The random intercepts are modeled as a Gaussian distribution with a mean of 0. They are not modeled individually in the same way as the fixed effects diagnosis and sequencing_... | Misuse of mixed effects model | The misunderstanding here is in how random intercepts are modeled. They aren't confounded with the diagnosis predictor in the way that you fear. The random intercepts are modeled as a Gaussian distrib | Misuse of mixed effects model
The misunderstanding here is in how random intercepts are modeled. They aren't confounded with the diagnosis predictor in the way that you fear. The random intercepts are modeled as a Gaussian distribution with a mean of 0. They are not modeled individually in the same way as the fixed eff... | Misuse of mixed effects model
The misunderstanding here is in how random intercepts are modeled. They aren't confounded with the diagnosis predictor in the way that you fear. The random intercepts are modeled as a Gaussian distrib |
44,347 | Misuse of mixed effects model | You are missing something fundamental about mixed models; the model does not look erroneous to me: adding diagnosis to the model gives you the effect of the diagnosis, adding the random intercept just gives you random variation around that effect.
eg if effect of diagnosis is +5 then all individuals with the diagnosis ... | Misuse of mixed effects model | You are missing something fundamental about mixed models; the model does not look erroneous to me: adding diagnosis to the model gives you the effect of the diagnosis, adding the random intercept just | Misuse of mixed effects model
You are missing something fundamental about mixed models; the model does not look erroneous to me: adding diagnosis to the model gives you the effect of the diagnosis, adding the random intercept just gives you random variation around that effect.
eg if effect of diagnosis is +5 then all i... | Misuse of mixed effects model
You are missing something fundamental about mixed models; the model does not look erroneous to me: adding diagnosis to the model gives you the effect of the diagnosis, adding the random intercept just |
44,348 | Simple linear regressions among three pairs of variables | First, it is possible for these conditions simultaneously to hold, as I will show.
Second, the regression of $Y$ on $X+Z$ must lie in the open interval $(10/9,2)$ and can attain any value in that interval.
Vector notation is particularly convenient here.
The given information tells us (in the order given in the questi... | Simple linear regressions among three pairs of variables | First, it is possible for these conditions simultaneously to hold, as I will show.
Second, the regression of $Y$ on $X+Z$ must lie in the open interval $(10/9,2)$ and can attain any value in that inte | Simple linear regressions among three pairs of variables
First, it is possible for these conditions simultaneously to hold, as I will show.
Second, the regression of $Y$ on $X+Z$ must lie in the open interval $(10/9,2)$ and can attain any value in that interval.
Vector notation is particularly convenient here.
The giv... | Simple linear regressions among three pairs of variables
First, it is possible for these conditions simultaneously to hold, as I will show.
Second, the regression of $Y$ on $X+Z$ must lie in the open interval $(10/9,2)$ and can attain any value in that inte |
44,349 | Simple linear regressions among three pairs of variables | Note: OP states there is likely an error in the original question. My answer assumes everything OP states is correct thus the following answer may be incorrect
Let's focus on the denominator of the final expression. Let
$$A = \sum_{i = 1}^n x_i^2 + 2x_i z_i + z_i^2$$
If we can show that $A > 2$ then we know that $\hat{... | Simple linear regressions among three pairs of variables | Note: OP states there is likely an error in the original question. My answer assumes everything OP states is correct thus the following answer may be incorrect
Let's focus on the denominator of the fi | Simple linear regressions among three pairs of variables
Note: OP states there is likely an error in the original question. My answer assumes everything OP states is correct thus the following answer may be incorrect
Let's focus on the denominator of the final expression. Let
$$A = \sum_{i = 1}^n x_i^2 + 2x_i z_i + z_i... | Simple linear regressions among three pairs of variables
Note: OP states there is likely an error in the original question. My answer assumes everything OP states is correct thus the following answer may be incorrect
Let's focus on the denominator of the fi |
44,350 | What is the probability of having all wealth concentrated into one single pocket after n trades? | it's a rigged game :) you have an absorbing state: one guy got all money. if somehow at any given moment one guy got all the money, then nobody has anything left to trade, and the game stops. it's pretty much certainty that if you play long enough this is bound to happen eventually, i.e. at some point you'll observe th... | What is the probability of having all wealth concentrated into one single pocket after n trades? | it's a rigged game :) you have an absorbing state: one guy got all money. if somehow at any given moment one guy got all the money, then nobody has anything left to trade, and the game stops. it's pre | What is the probability of having all wealth concentrated into one single pocket after n trades?
it's a rigged game :) you have an absorbing state: one guy got all money. if somehow at any given moment one guy got all the money, then nobody has anything left to trade, and the game stops. it's pretty much certainty that... | What is the probability of having all wealth concentrated into one single pocket after n trades?
it's a rigged game :) you have an absorbing state: one guy got all money. if somehow at any given moment one guy got all the money, then nobody has anything left to trade, and the game stops. it's pre |
44,351 | What is the probability of having all wealth concentrated into one single pocket after n trades? | Here is an order-of-magnitude calculation of how long it takes to have only one player remaining.
For any player, let $p$ be the probability that they have exited the game after $n$ turns. So the probability that $8$ players have exited and $2$ remain is $45p^8(1-p)^2$. The probability that $9$ players have exited and ... | What is the probability of having all wealth concentrated into one single pocket after n trades? | Here is an order-of-magnitude calculation of how long it takes to have only one player remaining.
For any player, let $p$ be the probability that they have exited the game after $n$ turns. So the prob | What is the probability of having all wealth concentrated into one single pocket after n trades?
Here is an order-of-magnitude calculation of how long it takes to have only one player remaining.
For any player, let $p$ be the probability that they have exited the game after $n$ turns. So the probability that $8$ player... | What is the probability of having all wealth concentrated into one single pocket after n trades?
Here is an order-of-magnitude calculation of how long it takes to have only one player remaining.
For any player, let $p$ be the probability that they have exited the game after $n$ turns. So the prob |
44,352 | What is the probability of having all wealth concentrated into one single pocket after n trades? | The answer by Aksakal already explains it enough why the wealth is ending up into one single pocket. In this answer we elaborate a bit further on the quantitative approach by Matt F.
One could compute the probability in terms of the probability of a specific player remaining in the game and consider the position of the... | What is the probability of having all wealth concentrated into one single pocket after n trades? | The answer by Aksakal already explains it enough why the wealth is ending up into one single pocket. In this answer we elaborate a bit further on the quantitative approach by Matt F.
One could compute | What is the probability of having all wealth concentrated into one single pocket after n trades?
The answer by Aksakal already explains it enough why the wealth is ending up into one single pocket. In this answer we elaborate a bit further on the quantitative approach by Matt F.
One could compute the probability in ter... | What is the probability of having all wealth concentrated into one single pocket after n trades?
The answer by Aksakal already explains it enough why the wealth is ending up into one single pocket. In this answer we elaborate a bit further on the quantitative approach by Matt F.
One could compute |
44,353 | What should it mean when someone says: "There's a $70$% chance of something happening | It's not an elementary or trivial question. It's a philosophical one. It touches the deepest foundations of statistics. It's almost a religious question if Bayesians overhear it. There are many ways to answer it. For instance, it could mean that if our Universe forked this moment and we observed infinite number of evol... | What should it mean when someone says: "There's a $70$% chance of something happening | It's not an elementary or trivial question. It's a philosophical one. It touches the deepest foundations of statistics. It's almost a religious question if Bayesians overhear it. There are many ways t | What should it mean when someone says: "There's a $70$% chance of something happening
It's not an elementary or trivial question. It's a philosophical one. It touches the deepest foundations of statistics. It's almost a religious question if Bayesians overhear it. There are many ways to answer it. For instance, it coul... | What should it mean when someone says: "There's a $70$% chance of something happening
It's not an elementary or trivial question. It's a philosophical one. It touches the deepest foundations of statistics. It's almost a religious question if Bayesians overhear it. There are many ways t |
44,354 | What should it mean when someone says: "There's a $70$% chance of something happening | When you're talking about a repeatable event, the interpretation is pretty easy. A probability of 70% means that when you observe the event, the prediction should be borne out (in the long run) 7 times out of 10.
When you're talking about a non-repeatable event, then the best interpretation is as a level of confidence... | What should it mean when someone says: "There's a $70$% chance of something happening | When you're talking about a repeatable event, the interpretation is pretty easy. A probability of 70% means that when you observe the event, the prediction should be borne out (in the long run) 7 tim | What should it mean when someone says: "There's a $70$% chance of something happening
When you're talking about a repeatable event, the interpretation is pretty easy. A probability of 70% means that when you observe the event, the prediction should be borne out (in the long run) 7 times out of 10.
When you're talking ... | What should it mean when someone says: "There's a $70$% chance of something happening
When you're talking about a repeatable event, the interpretation is pretty easy. A probability of 70% means that when you observe the event, the prediction should be borne out (in the long run) 7 tim |
44,355 | What should it mean when someone says: "There's a $70$% chance of something happening | First of all, without any kind of demonstration (transparency) this value means nothing.
On the other hand, my guess about this specific statement should mean this:
Prediction Guy: Me and my team are using a model that fits and predicts the stock market (Specifically the Dow Jones, for example). Now, we made the mode... | What should it mean when someone says: "There's a $70$% chance of something happening | First of all, without any kind of demonstration (transparency) this value means nothing.
On the other hand, my guess about this specific statement should mean this:
Prediction Guy: Me and my team ar | What should it mean when someone says: "There's a $70$% chance of something happening
First of all, without any kind of demonstration (transparency) this value means nothing.
On the other hand, my guess about this specific statement should mean this:
Prediction Guy: Me and my team are using a model that fits and pred... | What should it mean when someone says: "There's a $70$% chance of something happening
First of all, without any kind of demonstration (transparency) this value means nothing.
On the other hand, my guess about this specific statement should mean this:
Prediction Guy: Me and my team ar |
44,356 | Limitations of Shapiro test | The Shapiro-Wilk test is not especially sensitive to outliers. There are normality tests that focus on outliers, by looking at a combination of skewness and kurtosis, but they are different.
Patrick Royston says about the Shapiro-Wilk test
Its power characteristics are well known and may be summarized by
saying th... | Limitations of Shapiro test | The Shapiro-Wilk test is not especially sensitive to outliers. There are normality tests that focus on outliers, by looking at a combination of skewness and kurtosis, but they are different.
Patrick | Limitations of Shapiro test
The Shapiro-Wilk test is not especially sensitive to outliers. There are normality tests that focus on outliers, by looking at a combination of skewness and kurtosis, but they are different.
Patrick Royston says about the Shapiro-Wilk test
Its power characteristics are well known and may ... | Limitations of Shapiro test
The Shapiro-Wilk test is not especially sensitive to outliers. There are normality tests that focus on outliers, by looking at a combination of skewness and kurtosis, but they are different.
Patrick |
44,357 | Limitations of Shapiro test | Certainly that can happen.
Assume your original data was normal. Really normal. Then remove "outliers". E.g., everything more than 3 standard deviations away from the mean. What are we left with? A truncated normal distribution. Which is, by definition, not a normal distribution any more.
So the Shapiro-Wilk test shoul... | Limitations of Shapiro test | Certainly that can happen.
Assume your original data was normal. Really normal. Then remove "outliers". E.g., everything more than 3 standard deviations away from the mean. What are we left with? A tr | Limitations of Shapiro test
Certainly that can happen.
Assume your original data was normal. Really normal. Then remove "outliers". E.g., everything more than 3 standard deviations away from the mean. What are we left with? A truncated normal distribution. Which is, by definition, not a normal distribution any more.
So... | Limitations of Shapiro test
Certainly that can happen.
Assume your original data was normal. Really normal. Then remove "outliers". E.g., everything more than 3 standard deviations away from the mean. What are we left with? A tr |
44,358 | Activation function between LSTM layers | The purpose of the Rectified Linear Activation Function (or ReLU for short) is to allow the neural network to learn nonlinear dependencies.
Specifically, the way this works is that ReLU will return input directly if the value is greater than 0. If less than 0, then 0.0 is simply returned. The idea is to allow the netwo... | Activation function between LSTM layers | The purpose of the Rectified Linear Activation Function (or ReLU for short) is to allow the neural network to learn nonlinear dependencies.
Specifically, the way this works is that ReLU will return in | Activation function between LSTM layers
The purpose of the Rectified Linear Activation Function (or ReLU for short) is to allow the neural network to learn nonlinear dependencies.
Specifically, the way this works is that ReLU will return input directly if the value is greater than 0. If less than 0, then 0.0 is simply ... | Activation function between LSTM layers
The purpose of the Rectified Linear Activation Function (or ReLU for short) is to allow the neural network to learn nonlinear dependencies.
Specifically, the way this works is that ReLU will return in |
44,359 | Is A truly better than B, given that 56% of 131 respondednts said so? | Let's say you have $X = 73$ out of $n = 131$ favoring A over B. Then a 95%
Agresti-Coull CI for the population proportion $p$ favoring A is of the form
$$\check p \pm 1.96\sqrt{\frac{\check p(1-\check p)}{\check n}},$$
where $\check n = n+ 4$ and $\check p = \frac{X+2}{n+4}.$
This computes to $(.472, .639),$ which incl... | Is A truly better than B, given that 56% of 131 respondednts said so? | Let's say you have $X = 73$ out of $n = 131$ favoring A over B. Then a 95%
Agresti-Coull CI for the population proportion $p$ favoring A is of the form
$$\check p \pm 1.96\sqrt{\frac{\check p(1-\check | Is A truly better than B, given that 56% of 131 respondednts said so?
Let's say you have $X = 73$ out of $n = 131$ favoring A over B. Then a 95%
Agresti-Coull CI for the population proportion $p$ favoring A is of the form
$$\check p \pm 1.96\sqrt{\frac{\check p(1-\check p)}{\check n}},$$
where $\check n = n+ 4$ and $\c... | Is A truly better than B, given that 56% of 131 respondednts said so?
Let's say you have $X = 73$ out of $n = 131$ favoring A over B. Then a 95%
Agresti-Coull CI for the population proportion $p$ favoring A is of the form
$$\check p \pm 1.96\sqrt{\frac{\check p(1-\check |
44,360 | Is A truly better than B, given that 56% of 131 respondednts said so? | First, @NuclearWang is correct. If your survey is as stated, you're learning about what procedure people prefer, not what is better (for some unspecified purpose). I don't think it's a pedantic point, its important to measure what we intend to measure.
The statistics here is pretty simple. You want to know if your d... | Is A truly better than B, given that 56% of 131 respondednts said so? | First, @NuclearWang is correct. If your survey is as stated, you're learning about what procedure people prefer, not what is better (for some unspecified purpose). I don't think it's a pedantic poin | Is A truly better than B, given that 56% of 131 respondednts said so?
First, @NuclearWang is correct. If your survey is as stated, you're learning about what procedure people prefer, not what is better (for some unspecified purpose). I don't think it's a pedantic point, its important to measure what we intend to meas... | Is A truly better than B, given that 56% of 131 respondednts said so?
First, @NuclearWang is correct. If your survey is as stated, you're learning about what procedure people prefer, not what is better (for some unspecified purpose). I don't think it's a pedantic poin |
44,361 | What type of data are dates? | This is a tricky question, and personally I feel this question is more about semantics and conventions.
Let's go to basics. What is Date? It's just a name we give to 86,400 seconds period. Date by definition, is counted from a reference point (year 1 AD).
You could simply treat dates as natural numbers, if your proble... | What type of data are dates? | This is a tricky question, and personally I feel this question is more about semantics and conventions.
Let's go to basics. What is Date? It's just a name we give to 86,400 seconds period. Date by def | What type of data are dates?
This is a tricky question, and personally I feel this question is more about semantics and conventions.
Let's go to basics. What is Date? It's just a name we give to 86,400 seconds period. Date by definition, is counted from a reference point (year 1 AD).
You could simply treat dates as na... | What type of data are dates?
This is a tricky question, and personally I feel this question is more about semantics and conventions.
Let's go to basics. What is Date? It's just a name we give to 86,400 seconds period. Date by def |
44,362 | What type of data are dates? | It is correct that dates do not fit nicely into the Stevens typology https://en.wikipedia.org/wiki/Level_of_measurement#Ordinal_scale of different levels of measurement. Dates are certainly ordered, so we could say that dates are ordinal type, but they are certainly more than that. When talking specifically about days... | What type of data are dates? | It is correct that dates do not fit nicely into the Stevens typology https://en.wikipedia.org/wiki/Level_of_measurement#Ordinal_scale of different levels of measurement. Dates are certainly ordered, | What type of data are dates?
It is correct that dates do not fit nicely into the Stevens typology https://en.wikipedia.org/wiki/Level_of_measurement#Ordinal_scale of different levels of measurement. Dates are certainly ordered, so we could say that dates are ordinal type, but they are certainly more than that. When ta... | What type of data are dates?
It is correct that dates do not fit nicely into the Stevens typology https://en.wikipedia.org/wiki/Level_of_measurement#Ordinal_scale of different levels of measurement. Dates are certainly ordered, |
44,363 | What type of data are dates? | Dates can be ordinal, categorical or both. It really depends on what these dates represent and what you are trying to answer with them.
If the data your dates represent can be described as elapsed time then I would use ordinal.
Examples:
If you are looking at how your process affects the growth of a population over de... | What type of data are dates? | Dates can be ordinal, categorical or both. It really depends on what these dates represent and what you are trying to answer with them.
If the data your dates represent can be described as elapsed tim | What type of data are dates?
Dates can be ordinal, categorical or both. It really depends on what these dates represent and what you are trying to answer with them.
If the data your dates represent can be described as elapsed time then I would use ordinal.
Examples:
If you are looking at how your process affects the g... | What type of data are dates?
Dates can be ordinal, categorical or both. It really depends on what these dates represent and what you are trying to answer with them.
If the data your dates represent can be described as elapsed tim |
44,364 | How does statistical control work in logistic regression? | Is it fair to say that each log-odds associated with a predictor
assumes that the others are held constant at 0?
The logit model is
$\begin{align*}
E(Y_t\vert x_t) &= p_t \\
\log \left( \frac{p_t}{1-p_t}\right) &= \vec{\beta}^\top \vec{x}_t
\end{align*}$
So $\beta_j$ describes a unit move on the log-odds scale ... | How does statistical control work in logistic regression? | Is it fair to say that each log-odds associated with a predictor
assumes that the others are held constant at 0?
The logit model is
$\begin{align*}
E(Y_t\vert x_t) &= p_t \\
\log \left( \frac{ | How does statistical control work in logistic regression?
Is it fair to say that each log-odds associated with a predictor
assumes that the others are held constant at 0?
The logit model is
$\begin{align*}
E(Y_t\vert x_t) &= p_t \\
\log \left( \frac{p_t}{1-p_t}\right) &= \vec{\beta}^\top \vec{x}_t
\end{align*}$... | How does statistical control work in logistic regression?
Is it fair to say that each log-odds associated with a predictor
assumes that the others are held constant at 0?
The logit model is
$\begin{align*}
E(Y_t\vert x_t) &= p_t \\
\log \left( \frac{ |
44,365 | How does statistical control work in logistic regression? | Even in standard linear regression, the coefficient for a predictor represents the association of the outcome variable with that particular predictor when all other predictors are held constant. There is no requirement that they be held constant at values of 0; so long as the others are held constant, under the assumpt... | How does statistical control work in logistic regression? | Even in standard linear regression, the coefficient for a predictor represents the association of the outcome variable with that particular predictor when all other predictors are held constant. There | How does statistical control work in logistic regression?
Even in standard linear regression, the coefficient for a predictor represents the association of the outcome variable with that particular predictor when all other predictors are held constant. There is no requirement that they be held constant at values of 0; ... | How does statistical control work in logistic regression?
Even in standard linear regression, the coefficient for a predictor represents the association of the outcome variable with that particular predictor when all other predictors are held constant. There |
44,366 | Expected Value of $X \sin(X)$ with $X$ normally distributed | Like many exercises involving trigonometric functions, the trick is to use complex numbers, i.e., $\int(\sin(x))\mathrm{d}x = \int Im(e^{ix})\mathrm{d}x = Im(\int e^{ix} \mathrm{d}x)$ here.
Knowing, the sum becomes
\begin{align}
I \triangleq \mathbb{E}[X\sin(X)] = Im \left( \int_{\mathbb{R}} x e^{ix} e^{-\frac{1}{2\si... | Expected Value of $X \sin(X)$ with $X$ normally distributed | Like many exercises involving trigonometric functions, the trick is to use complex numbers, i.e., $\int(\sin(x))\mathrm{d}x = \int Im(e^{ix})\mathrm{d}x = Im(\int e^{ix} \mathrm{d}x)$ here.
Knowing, t | Expected Value of $X \sin(X)$ with $X$ normally distributed
Like many exercises involving trigonometric functions, the trick is to use complex numbers, i.e., $\int(\sin(x))\mathrm{d}x = \int Im(e^{ix})\mathrm{d}x = Im(\int e^{ix} \mathrm{d}x)$ here.
Knowing, the sum becomes
\begin{align}
I \triangleq \mathbb{E}[X\sin(... | Expected Value of $X \sin(X)$ with $X$ normally distributed
Like many exercises involving trigonometric functions, the trick is to use complex numbers, i.e., $\int(\sin(x))\mathrm{d}x = \int Im(e^{ix})\mathrm{d}x = Im(\int e^{ix} \mathrm{d}x)$ here.
Knowing, t |
44,367 | Expected Value of $X \sin(X)$ with $X$ normally distributed | Have you tried a computer algebra system? Here $X \sim N(\mu, \sigma^2)$ with pdf $f(x)$:
Here is the output from mathStatica / Mathematica: | Expected Value of $X \sin(X)$ with $X$ normally distributed | Have you tried a computer algebra system? Here $X \sim N(\mu, \sigma^2)$ with pdf $f(x)$:
Here is the output from mathStatica / Mathematica: | Expected Value of $X \sin(X)$ with $X$ normally distributed
Have you tried a computer algebra system? Here $X \sim N(\mu, \sigma^2)$ with pdf $f(x)$:
Here is the output from mathStatica / Mathematica: | Expected Value of $X \sin(X)$ with $X$ normally distributed
Have you tried a computer algebra system? Here $X \sim N(\mu, \sigma^2)$ with pdf $f(x)$:
Here is the output from mathStatica / Mathematica: |
44,368 | What is the jacobian for a neural network | A Jacobian is quite a general term indeed. Lets take this simple, single-hidden-layer network
$$\hat{\boldsymbol{y}} = g(\mathbf{W}^{(1)} \cdot f(\mathbf{W}^{(0)} \cdot \boldsymbol{x} + \boldsymbol{b}^{(0)}) + \boldsymbol{b}^{(1)})$$
as an example.
When looking around online, I found most people (e.g. here or here) to... | What is the jacobian for a neural network | A Jacobian is quite a general term indeed. Lets take this simple, single-hidden-layer network
$$\hat{\boldsymbol{y}} = g(\mathbf{W}^{(1)} \cdot f(\mathbf{W}^{(0)} \cdot \boldsymbol{x} + \boldsymbol{b | What is the jacobian for a neural network
A Jacobian is quite a general term indeed. Lets take this simple, single-hidden-layer network
$$\hat{\boldsymbol{y}} = g(\mathbf{W}^{(1)} \cdot f(\mathbf{W}^{(0)} \cdot \boldsymbol{x} + \boldsymbol{b}^{(0)}) + \boldsymbol{b}^{(1)})$$
as an example.
When looking around online, ... | What is the jacobian for a neural network
A Jacobian is quite a general term indeed. Lets take this simple, single-hidden-layer network
$$\hat{\boldsymbol{y}} = g(\mathbf{W}^{(1)} \cdot f(\mathbf{W}^{(0)} \cdot \boldsymbol{x} + \boldsymbol{b |
44,369 | What is the jacobian for a neural network | Classical approach for neural network is to take a batch of samples and calculate average gradient over these samples. For the Jacobian instead of calculating average gradient - you calculate gradient per each sample separately. At the end you end up with matrix that has N rows and M columns, where N is a number of sam... | What is the jacobian for a neural network | Classical approach for neural network is to take a batch of samples and calculate average gradient over these samples. For the Jacobian instead of calculating average gradient - you calculate gradient | What is the jacobian for a neural network
Classical approach for neural network is to take a batch of samples and calculate average gradient over these samples. For the Jacobian instead of calculating average gradient - you calculate gradient per each sample separately. At the end you end up with matrix that has N rows... | What is the jacobian for a neural network
Classical approach for neural network is to take a batch of samples and calculate average gradient over these samples. For the Jacobian instead of calculating average gradient - you calculate gradient |
44,370 | What is the jacobian for a neural network | Just a graphical representation of what @Mr Tsjolder has said:
The Input for the network is $\mathbf{X}$
and
Let's take the network $\mathbf{O}$=$\mathbf{W}$*$\mathbf{X}$ (We can any other relationship also!! This is just an example!!)
The Jacobian of this network would then simply be $\mathbf{J} = \frac{\partial {\mat... | What is the jacobian for a neural network | Just a graphical representation of what @Mr Tsjolder has said:
The Input for the network is $\mathbf{X}$
and
Let's take the network $\mathbf{O}$=$\mathbf{W}$*$\mathbf{X}$ (We can any other relationshi | What is the jacobian for a neural network
Just a graphical representation of what @Mr Tsjolder has said:
The Input for the network is $\mathbf{X}$
and
Let's take the network $\mathbf{O}$=$\mathbf{W}$*$\mathbf{X}$ (We can any other relationship also!! This is just an example!!)
The Jacobian of this network would then si... | What is the jacobian for a neural network
Just a graphical representation of what @Mr Tsjolder has said:
The Input for the network is $\mathbf{X}$
and
Let's take the network $\mathbf{O}$=$\mathbf{W}$*$\mathbf{X}$ (We can any other relationshi |
44,371 | Use of prior and posterior predictive distributions? | Some uses of the posterior predictive:
Simulating future data based on your model assumptions and data observed to this point. This is useful for predictions, forecasting, etc.
Model checking via posterior predictive checking. Some comments have directed you to Bayesian Data Analysis, and its author has made a relevan... | Use of prior and posterior predictive distributions? | Some uses of the posterior predictive:
Simulating future data based on your model assumptions and data observed to this point. This is useful for predictions, forecasting, etc.
Model checking via pos | Use of prior and posterior predictive distributions?
Some uses of the posterior predictive:
Simulating future data based on your model assumptions and data observed to this point. This is useful for predictions, forecasting, etc.
Model checking via posterior predictive checking. Some comments have directed you to Baye... | Use of prior and posterior predictive distributions?
Some uses of the posterior predictive:
Simulating future data based on your model assumptions and data observed to this point. This is useful for predictions, forecasting, etc.
Model checking via pos |
44,372 | Use of prior and posterior predictive distributions? | Let's you denote your data as $X$ and imagine that you have some probabilistic model that describes your data in terms of the likelihood of observing your data given some parameter $\theta$. The parameter $\theta$ is unknown and is to be estimated from your data. To estimate your parameter you could use many different ... | Use of prior and posterior predictive distributions? | Let's you denote your data as $X$ and imagine that you have some probabilistic model that describes your data in terms of the likelihood of observing your data given some parameter $\theta$. The param | Use of prior and posterior predictive distributions?
Let's you denote your data as $X$ and imagine that you have some probabilistic model that describes your data in terms of the likelihood of observing your data given some parameter $\theta$. The parameter $\theta$ is unknown and is to be estimated from your data. To ... | Use of prior and posterior predictive distributions?
Let's you denote your data as $X$ and imagine that you have some probabilistic model that describes your data in terms of the likelihood of observing your data given some parameter $\theta$. The param |
44,373 | Analysis strategy for rare outcome with matching | Removing good data from an analysis is scientifically suspect in my humble opinion, and naive matching methods are inefficient. It may be very easy to adjust for patient characteristics using ordinary regression models, paying attention to linearity assumptions etc. Of course it is a good idea to look at overlap in c... | Analysis strategy for rare outcome with matching | Removing good data from an analysis is scientifically suspect in my humble opinion, and naive matching methods are inefficient. It may be very easy to adjust for patient characteristics using ordinar | Analysis strategy for rare outcome with matching
Removing good data from an analysis is scientifically suspect in my humble opinion, and naive matching methods are inefficient. It may be very easy to adjust for patient characteristics using ordinary regression models, paying attention to linearity assumptions etc. Of... | Analysis strategy for rare outcome with matching
Removing good data from an analysis is scientifically suspect in my humble opinion, and naive matching methods are inefficient. It may be very easy to adjust for patient characteristics using ordinar |
44,374 | Analysis strategy for rare outcome with matching | Based on the comments and the availability of such a large control group, I would probably advise to do in a step first exact matching on age groups and sex, and perhaps common disease groups. Hereby, you built different strata. In a second step, you can apply propensity score matching to ensure that treatment and cont... | Analysis strategy for rare outcome with matching | Based on the comments and the availability of such a large control group, I would probably advise to do in a step first exact matching on age groups and sex, and perhaps common disease groups. Hereby, | Analysis strategy for rare outcome with matching
Based on the comments and the availability of such a large control group, I would probably advise to do in a step first exact matching on age groups and sex, and perhaps common disease groups. Hereby, you built different strata. In a second step, you can apply propensity... | Analysis strategy for rare outcome with matching
Based on the comments and the availability of such a large control group, I would probably advise to do in a step first exact matching on age groups and sex, and perhaps common disease groups. Hereby, |
44,375 | Analysis strategy for rare outcome with matching | The propensity score (PS) is a balancing score indicating the probability of treatment assignment conditional on observed baseline characteristics. In a randomized controlled Trial (RCT) the PS is known. Estimation and application of PS therefore, mimic some of the particular characteristics
of an RCT and therefore ar... | Analysis strategy for rare outcome with matching | The propensity score (PS) is a balancing score indicating the probability of treatment assignment conditional on observed baseline characteristics. In a randomized controlled Trial (RCT) the PS is kn | Analysis strategy for rare outcome with matching
The propensity score (PS) is a balancing score indicating the probability of treatment assignment conditional on observed baseline characteristics. In a randomized controlled Trial (RCT) the PS is known. Estimation and application of PS therefore, mimic some of the part... | Analysis strategy for rare outcome with matching
The propensity score (PS) is a balancing score indicating the probability of treatment assignment conditional on observed baseline characteristics. In a randomized controlled Trial (RCT) the PS is kn |
44,376 | Unbiased estimator of variance for a sample drawn from a finite population without replacement | When sampling from a finite population without replacement, the observations are negatively correlated with each other, and the sample variance $s^2 = \frac{1}{n-1} \sum_i \left( x_i - \bar{x} \right)^2$ is a slightly biased estimate of the population variance $\sigma^2$.
The derivation in this link from Robert Serflin... | Unbiased estimator of variance for a sample drawn from a finite population without replacement | When sampling from a finite population without replacement, the observations are negatively correlated with each other, and the sample variance $s^2 = \frac{1}{n-1} \sum_i \left( x_i - \bar{x} \right) | Unbiased estimator of variance for a sample drawn from a finite population without replacement
When sampling from a finite population without replacement, the observations are negatively correlated with each other, and the sample variance $s^2 = \frac{1}{n-1} \sum_i \left( x_i - \bar{x} \right)^2$ is a slightly biased ... | Unbiased estimator of variance for a sample drawn from a finite population without replacement
When sampling from a finite population without replacement, the observations are negatively correlated with each other, and the sample variance $s^2 = \frac{1}{n-1} \sum_i \left( x_i - \bar{x} \right) |
44,377 | Unbiased estimator of variance for a sample drawn from a finite population without replacement | The sample variance is indeed biased for a finite population with simple random sampling without replacement. And the solution to get an unbiased result is to multiply the sample variance by $\frac{N-1}{N}$, where $N$ is the population size.
I’m an engineer, not a mathematician. So my proof was to build a complete samp... | Unbiased estimator of variance for a sample drawn from a finite population without replacement | The sample variance is indeed biased for a finite population with simple random sampling without replacement. And the solution to get an unbiased result is to multiply the sample variance by $\frac{N- | Unbiased estimator of variance for a sample drawn from a finite population without replacement
The sample variance is indeed biased for a finite population with simple random sampling without replacement. And the solution to get an unbiased result is to multiply the sample variance by $\frac{N-1}{N}$, where $N$ is the ... | Unbiased estimator of variance for a sample drawn from a finite population without replacement
The sample variance is indeed biased for a finite population with simple random sampling without replacement. And the solution to get an unbiased result is to multiply the sample variance by $\frac{N- |
44,378 | Unbiased estimator of variance for a sample drawn from a finite population without replacement | I don't know where your statements come from, but it the way you present them they are false. Taking directly the variance of the sample (that is, dividing by $n$) we get a biased estimator, but using sample variance (dividing by $n-1$) we get an unbiased estimator.
I think your statement comes from different conflicti... | Unbiased estimator of variance for a sample drawn from a finite population without replacement | I don't know where your statements come from, but it the way you present them they are false. Taking directly the variance of the sample (that is, dividing by $n$) we get a biased estimator, but using | Unbiased estimator of variance for a sample drawn from a finite population without replacement
I don't know where your statements come from, but it the way you present them they are false. Taking directly the variance of the sample (that is, dividing by $n$) we get a biased estimator, but using sample variance (dividin... | Unbiased estimator of variance for a sample drawn from a finite population without replacement
I don't know where your statements come from, but it the way you present them they are false. Taking directly the variance of the sample (that is, dividing by $n$) we get a biased estimator, but using |
44,379 | Can the coefficients of dummy variables be more than 1 or less than 0? | Yes, coefficients of dummy variables can be more than one or less than zero.
Remember that you can interpret that coefficient as the mean change in your response (dependent) variable when the dummy changes from 0 to 1, holding all other variables constant (i.e. ceteris paribus).
The mean height of people in the United ... | Can the coefficients of dummy variables be more than 1 or less than 0? | Yes, coefficients of dummy variables can be more than one or less than zero.
Remember that you can interpret that coefficient as the mean change in your response (dependent) variable when the dummy ch | Can the coefficients of dummy variables be more than 1 or less than 0?
Yes, coefficients of dummy variables can be more than one or less than zero.
Remember that you can interpret that coefficient as the mean change in your response (dependent) variable when the dummy changes from 0 to 1, holding all other variables co... | Can the coefficients of dummy variables be more than 1 or less than 0?
Yes, coefficients of dummy variables can be more than one or less than zero.
Remember that you can interpret that coefficient as the mean change in your response (dependent) variable when the dummy ch |
44,380 | R - lmer vs glmer | lmer is used to fit linear mixed-effect models, so it assumes that the residual error has a Gaussian distribution. If your dependent variable A is a binary outcome (e.g. a yes/no response), then the error distribution is binomial and not Gaussian.
In this case you have to use glmer, which allow to fit a generalized li... | R - lmer vs glmer | lmer is used to fit linear mixed-effect models, so it assumes that the residual error has a Gaussian distribution. If your dependent variable A is a binary outcome (e.g. a yes/no response), then the e | R - lmer vs glmer
lmer is used to fit linear mixed-effect models, so it assumes that the residual error has a Gaussian distribution. If your dependent variable A is a binary outcome (e.g. a yes/no response), then the error distribution is binomial and not Gaussian.
In this case you have to use glmer, which allow to fi... | R - lmer vs glmer
lmer is used to fit linear mixed-effect models, so it assumes that the residual error has a Gaussian distribution. If your dependent variable A is a binary outcome (e.g. a yes/no response), then the e |
44,381 | difference between Nash-Sutcliffe efficiency and coefficient of determination | The Nash-Sutcliffe model efficiency coefficient is nearly identical to the coefficient of determination. The primary difference is how it is used.
The coefficient of determination ($R^2$) is a measure of the goodness of fit of a statistical model.
\begin{equation}
\begin{aligned}
R^2 = 1 - \frac{\sum (y_i - \hat{y_i})... | difference between Nash-Sutcliffe efficiency and coefficient of determination | The Nash-Sutcliffe model efficiency coefficient is nearly identical to the coefficient of determination. The primary difference is how it is used.
The coefficient of determination ($R^2$) is a measure | difference between Nash-Sutcliffe efficiency and coefficient of determination
The Nash-Sutcliffe model efficiency coefficient is nearly identical to the coefficient of determination. The primary difference is how it is used.
The coefficient of determination ($R^2$) is a measure of the goodness of fit of a statistical m... | difference between Nash-Sutcliffe efficiency and coefficient of determination
The Nash-Sutcliffe model efficiency coefficient is nearly identical to the coefficient of determination. The primary difference is how it is used.
The coefficient of determination ($R^2$) is a measure |
44,382 | difference between Nash-Sutcliffe efficiency and coefficient of determination | This answer is directly copied from Krause et al., (2005)
Krause P, Boyle DP, Bäse F. 2005. Comparison of different efficiency criteria for hydrological model assessment. Advances in Geosciences 5 (5): 89–97 DOI: 10.5194/adgeo-5-89-2005
The coefficient of determination r2 is defined as the squared value of the coeffici... | difference between Nash-Sutcliffe efficiency and coefficient of determination | This answer is directly copied from Krause et al., (2005)
Krause P, Boyle DP, Bäse F. 2005. Comparison of different efficiency criteria for hydrological model assessment. Advances in Geosciences 5 (5) | difference between Nash-Sutcliffe efficiency and coefficient of determination
This answer is directly copied from Krause et al., (2005)
Krause P, Boyle DP, Bäse F. 2005. Comparison of different efficiency criteria for hydrological model assessment. Advances in Geosciences 5 (5): 89–97 DOI: 10.5194/adgeo-5-89-2005
The c... | difference between Nash-Sutcliffe efficiency and coefficient of determination
This answer is directly copied from Krause et al., (2005)
Krause P, Boyle DP, Bäse F. 2005. Comparison of different efficiency criteria for hydrological model assessment. Advances in Geosciences 5 (5) |
44,383 | what is the meaning of 'tail' of kurtosis? | There are two parts to address here -- 1. what does it mean for something to be heavy-tailed? and 2. does higher kurtosis mean a heavier tail and vice-versa?
What's heavy-tailed mean?
a. What heavier tail means in a "handwavy" sense -- most people picture it this way:
but because the tail is quite small, it's better ... | what is the meaning of 'tail' of kurtosis? | There are two parts to address here -- 1. what does it mean for something to be heavy-tailed? and 2. does higher kurtosis mean a heavier tail and vice-versa?
What's heavy-tailed mean?
a. What heavier | what is the meaning of 'tail' of kurtosis?
There are two parts to address here -- 1. what does it mean for something to be heavy-tailed? and 2. does higher kurtosis mean a heavier tail and vice-versa?
What's heavy-tailed mean?
a. What heavier tail means in a "handwavy" sense -- most people picture it this way:
but be... | what is the meaning of 'tail' of kurtosis?
There are two parts to address here -- 1. what does it mean for something to be heavy-tailed? and 2. does higher kurtosis mean a heavier tail and vice-versa?
What's heavy-tailed mean?
a. What heavier |
44,384 | what is the meaning of 'tail' of kurtosis? | Comments from probably deleted duplicate question that are useful:
In fact, higher kurtosis is associated with both increased peakedness and heavier extreme tails, but there's no necessary relationship in either case (you can find counterexamples to higher peak or heavier extreme tails, even though both are typical wit... | what is the meaning of 'tail' of kurtosis? | Comments from probably deleted duplicate question that are useful:
In fact, higher kurtosis is associated with both increased peakedness and heavier extreme tails, but there's no necessary relationshi | what is the meaning of 'tail' of kurtosis?
Comments from probably deleted duplicate question that are useful:
In fact, higher kurtosis is associated with both increased peakedness and heavier extreme tails, but there's no necessary relationship in either case (you can find counterexamples to higher peak or heavier extr... | what is the meaning of 'tail' of kurtosis?
Comments from probably deleted duplicate question that are useful:
In fact, higher kurtosis is associated with both increased peakedness and heavier extreme tails, but there's no necessary relationshi |
44,385 | what is the meaning of 'tail' of kurtosis? | There is most definitely a direct relationship connection between kurtosis and the tails of distribution. One simple connection is as follows: Let $X$ be any random variable with finite fourth moment, let $Z = (X - \mu)/\sigma$, and let $U = Z^4$. Then the kurtosis of $X$ is $E(U)$.
A common way of teaching and underst... | what is the meaning of 'tail' of kurtosis? | There is most definitely a direct relationship connection between kurtosis and the tails of distribution. One simple connection is as follows: Let $X$ be any random variable with finite fourth moment, | what is the meaning of 'tail' of kurtosis?
There is most definitely a direct relationship connection between kurtosis and the tails of distribution. One simple connection is as follows: Let $X$ be any random variable with finite fourth moment, let $Z = (X - \mu)/\sigma$, and let $U = Z^4$. Then the kurtosis of $X$ is $... | what is the meaning of 'tail' of kurtosis?
There is most definitely a direct relationship connection between kurtosis and the tails of distribution. One simple connection is as follows: Let $X$ be any random variable with finite fourth moment, |
44,386 | What is the difference between a $\log_{10}$ and logit transformation? | The function $f(x)=\log_{10}(x)$ is the inverse of exponentiation with base 10. It is a monotonic injective function mapping positive numbers to $\mathbb{R}$. Positive numbers less than 1 are mapped to negative numbers. Positive numbers greater than one are mapped to positive numbers. In regression analysis, logarithm ... | What is the difference between a $\log_{10}$ and logit transformation? | The function $f(x)=\log_{10}(x)$ is the inverse of exponentiation with base 10. It is a monotonic injective function mapping positive numbers to $\mathbb{R}$. Positive numbers less than 1 are mapped t | What is the difference between a $\log_{10}$ and logit transformation?
The function $f(x)=\log_{10}(x)$ is the inverse of exponentiation with base 10. It is a monotonic injective function mapping positive numbers to $\mathbb{R}$. Positive numbers less than 1 are mapped to negative numbers. Positive numbers greater than... | What is the difference between a $\log_{10}$ and logit transformation?
The function $f(x)=\log_{10}(x)$ is the inverse of exponentiation with base 10. It is a monotonic injective function mapping positive numbers to $\mathbb{R}$. Positive numbers less than 1 are mapped t |
44,387 | How does the GLM handle collinear predictors? | Let's predict income with two highly positively correlated variables: Years of work experience and number of carrots eaten in one's lifetime. Let's ignore omitted variable bias issues. Also, let's say years of work experience has a much greater impact on income than carrots eaten.
Your beta parameter estimates would be... | How does the GLM handle collinear predictors? | Let's predict income with two highly positively correlated variables: Years of work experience and number of carrots eaten in one's lifetime. Let's ignore omitted variable bias issues. Also, let's say | How does the GLM handle collinear predictors?
Let's predict income with two highly positively correlated variables: Years of work experience and number of carrots eaten in one's lifetime. Let's ignore omitted variable bias issues. Also, let's say years of work experience has a much greater impact on income than carrots... | How does the GLM handle collinear predictors?
Let's predict income with two highly positively correlated variables: Years of work experience and number of carrots eaten in one's lifetime. Let's ignore omitted variable bias issues. Also, let's say |
44,388 | How does the GLM handle collinear predictors? | This is one of those situations where what is theoretically true, and what is true in practice can be quite different. I'll try to give an example.
Let's suppose we have centered ant standardized both $X$ and $y$ so that:
The predictor covariance is $\Sigma = X^{t} X$.
The intercept estimate is $\beta_0 = 0$.
I'll f... | How does the GLM handle collinear predictors? | This is one of those situations where what is theoretically true, and what is true in practice can be quite different. I'll try to give an example.
Let's suppose we have centered ant standardized bot | How does the GLM handle collinear predictors?
This is one of those situations where what is theoretically true, and what is true in practice can be quite different. I'll try to give an example.
Let's suppose we have centered ant standardized both $X$ and $y$ so that:
The predictor covariance is $\Sigma = X^{t} X$.
Th... | How does the GLM handle collinear predictors?
This is one of those situations where what is theoretically true, and what is true in practice can be quite different. I'll try to give an example.
Let's suppose we have centered ant standardized bot |
44,389 | How does the GLM handle collinear predictors? | @Jason Sanchez has provided a good answer. Let me add some complementary information.
The beta estimates from OLS estimation are each conditional on the other variables included in the model. No variable is given precedence, or used first, etc. For example, it is not the case that the slope for $x_1$ is the slope y... | How does the GLM handle collinear predictors? | @Jason Sanchez has provided a good answer. Let me add some complementary information.
The beta estimates from OLS estimation are each conditional on the other variables included in the model. No va | How does the GLM handle collinear predictors?
@Jason Sanchez has provided a good answer. Let me add some complementary information.
The beta estimates from OLS estimation are each conditional on the other variables included in the model. No variable is given precedence, or used first, etc. For example, it is not th... | How does the GLM handle collinear predictors?
@Jason Sanchez has provided a good answer. Let me add some complementary information.
The beta estimates from OLS estimation are each conditional on the other variables included in the model. No va |
44,390 | How to implement GLM computationally in C++ (or other languages)? [closed] | While there is definitely some educational value of re-implementing GLM framework (or any other statistical framework, for that matter), I question the feasibility of this approach due to complexity and, consequently, time and efforts involved. Having said that, if you indeed want to go this route and review existing o... | How to implement GLM computationally in C++ (or other languages)? [closed] | While there is definitely some educational value of re-implementing GLM framework (or any other statistical framework, for that matter), I question the feasibility of this approach due to complexity a | How to implement GLM computationally in C++ (or other languages)? [closed]
While there is definitely some educational value of re-implementing GLM framework (or any other statistical framework, for that matter), I question the feasibility of this approach due to complexity and, consequently, time and efforts involved. ... | How to implement GLM computationally in C++ (or other languages)? [closed]
While there is definitely some educational value of re-implementing GLM framework (or any other statistical framework, for that matter), I question the feasibility of this approach due to complexity a |
44,391 | Aperiodicity in markov chain | Definition
Let $p_{ii}^{(n)}$ denote the probability of returning to state $i$ at step $n$ and let $t\in\{2, 3\dots\}$.
State $i$ is said to be periodic with period $t$ iff
$ p_{ii}^{(n)} = 0 $ for $n \neq t, 2t, \dots$
$ p_{ii}^{(n)} \neq 0 $ for $n = t, 2t, \dots$
If we can not find a $t$ such that this holds, the ... | Aperiodicity in markov chain | Definition
Let $p_{ii}^{(n)}$ denote the probability of returning to state $i$ at step $n$ and let $t\in\{2, 3\dots\}$.
State $i$ is said to be periodic with period $t$ iff
$ p_{ii}^{(n)} = 0 $ for $ | Aperiodicity in markov chain
Definition
Let $p_{ii}^{(n)}$ denote the probability of returning to state $i$ at step $n$ and let $t\in\{2, 3\dots\}$.
State $i$ is said to be periodic with period $t$ iff
$ p_{ii}^{(n)} = 0 $ for $n \neq t, 2t, \dots$
$ p_{ii}^{(n)} \neq 0 $ for $n = t, 2t, \dots$
If we can not find a $... | Aperiodicity in markov chain
Definition
Let $p_{ii}^{(n)}$ denote the probability of returning to state $i$ at step $n$ and let $t\in\{2, 3\dots\}$.
State $i$ is said to be periodic with period $t$ iff
$ p_{ii}^{(n)} = 0 $ for $ |
44,392 | Aperiodicity in markov chain | In an irreducible chain all states belong to a single communicating class. Periodicity is a class property. This means that, if one of the states in an irreducible Markov Chain is aperiodic, say, then all the remaining states are also aperiodic. Since, $p_{aa}^{(1)}>0$, by the definition of periodicity, state a is aper... | Aperiodicity in markov chain | In an irreducible chain all states belong to a single communicating class. Periodicity is a class property. This means that, if one of the states in an irreducible Markov Chain is aperiodic, say, then | Aperiodicity in markov chain
In an irreducible chain all states belong to a single communicating class. Periodicity is a class property. This means that, if one of the states in an irreducible Markov Chain is aperiodic, say, then all the remaining states are also aperiodic. Since, $p_{aa}^{(1)}>0$, by the definition of... | Aperiodicity in markov chain
In an irreducible chain all states belong to a single communicating class. Periodicity is a class property. This means that, if one of the states in an irreducible Markov Chain is aperiodic, say, then |
44,393 | Aperiodicity in markov chain | For an irreducible markov chain,
Aperiodic: When starting from some state i, we don't know when we will return to the same state i after some transition. We may see the state i after 1,2,3,4,5.. etc number of transition.
Periodic: When we can say that we can return to the state i after some transition with certainty. ... | Aperiodicity in markov chain | For an irreducible markov chain,
Aperiodic: When starting from some state i, we don't know when we will return to the same state i after some transition. We may see the state i after 1,2,3,4,5.. etc n | Aperiodicity in markov chain
For an irreducible markov chain,
Aperiodic: When starting from some state i, we don't know when we will return to the same state i after some transition. We may see the state i after 1,2,3,4,5.. etc number of transition.
Periodic: When we can say that we can return to the state i after som... | Aperiodicity in markov chain
For an irreducible markov chain,
Aperiodic: When starting from some state i, we don't know when we will return to the same state i after some transition. We may see the state i after 1,2,3,4,5.. etc n |
44,394 | Aperiodicity in markov chain | For any state we find the possible no. Of steps in which we can return to the same state.
If gcd of these nos. =1 then state is aperiodic.
If gcd not equals 1 (say 'd'), then period equals 'd'.
For a self loop state it is possible to return to the state in
1,2,3,4........ steps. Gcd = 1.
So the state is certainly aperi... | Aperiodicity in markov chain | For any state we find the possible no. Of steps in which we can return to the same state.
If gcd of these nos. =1 then state is aperiodic.
If gcd not equals 1 (say 'd'), then period equals 'd'.
For a | Aperiodicity in markov chain
For any state we find the possible no. Of steps in which we can return to the same state.
If gcd of these nos. =1 then state is aperiodic.
If gcd not equals 1 (say 'd'), then period equals 'd'.
For a self loop state it is possible to return to the state in
1,2,3,4........ steps. Gcd = 1.
So... | Aperiodicity in markov chain
For any state we find the possible no. Of steps in which we can return to the same state.
If gcd of these nos. =1 then state is aperiodic.
If gcd not equals 1 (say 'd'), then period equals 'd'.
For a |
44,395 | How to prove linearity assumption in regression analysis for a continuous dependent and nominal independent variable? | Let me explain what linearity means with nominal/dummy variables. In essence, it means there is no interaction term between your independent variables that you have left out.†
Suppose we have two nominal variables $x_0$ and $x_1$, each taking values 0 or 1, and a response variable $y$. (The general case is similar.)
If... | How to prove linearity assumption in regression analysis for a continuous dependent and nominal inde | Let me explain what linearity means with nominal/dummy variables. In essence, it means there is no interaction term between your independent variables that you have left out.†
Suppose we have two nomi | How to prove linearity assumption in regression analysis for a continuous dependent and nominal independent variable?
Let me explain what linearity means with nominal/dummy variables. In essence, it means there is no interaction term between your independent variables that you have left out.†
Suppose we have two nomina... | How to prove linearity assumption in regression analysis for a continuous dependent and nominal inde
Let me explain what linearity means with nominal/dummy variables. In essence, it means there is no interaction term between your independent variables that you have left out.†
Suppose we have two nomi |
44,396 | How to prove linearity assumption in regression analysis for a continuous dependent and nominal independent variable? | Consider the model for regression of $y$ on $x$:
$$\operatorname{E}Y=\beta_0 + \beta_1 x$$
If $x$ is a dummy variable representing a level of a categorical variable then it can take only the values 0 & 1:
$$\operatorname{E}Y=\beta_0 \qquad \text{when } x=0$$
$$\operatorname{E}Y=\beta_0 + \beta_1 \qquad \text{when } x=1... | How to prove linearity assumption in regression analysis for a continuous dependent and nominal inde | Consider the model for regression of $y$ on $x$:
$$\operatorname{E}Y=\beta_0 + \beta_1 x$$
If $x$ is a dummy variable representing a level of a categorical variable then it can take only the values 0 | How to prove linearity assumption in regression analysis for a continuous dependent and nominal independent variable?
Consider the model for regression of $y$ on $x$:
$$\operatorname{E}Y=\beta_0 + \beta_1 x$$
If $x$ is a dummy variable representing a level of a categorical variable then it can take only the values 0 & ... | How to prove linearity assumption in regression analysis for a continuous dependent and nominal inde
Consider the model for regression of $y$ on $x$:
$$\operatorname{E}Y=\beta_0 + \beta_1 x$$
If $x$ is a dummy variable representing a level of a categorical variable then it can take only the values 0 |
44,397 | What does "shift invariant" mean in convolutional neural network? | For CNNs, I think it means the invariance to small* displacements of the input image. For example in the character recognition task, if you train the system by shifting (i.e. sliding the images to left/right and up/down) a little bit, you learn a more generalizable detector, that works under difficult conditions, i.e. ... | What does "shift invariant" mean in convolutional neural network? | For CNNs, I think it means the invariance to small* displacements of the input image. For example in the character recognition task, if you train the system by shifting (i.e. sliding the images to lef | What does "shift invariant" mean in convolutional neural network?
For CNNs, I think it means the invariance to small* displacements of the input image. For example in the character recognition task, if you train the system by shifting (i.e. sliding the images to left/right and up/down) a little bit, you learn a more ge... | What does "shift invariant" mean in convolutional neural network?
For CNNs, I think it means the invariance to small* displacements of the input image. For example in the character recognition task, if you train the system by shifting (i.e. sliding the images to lef |
44,398 | What does "shift invariant" mean in convolutional neural network? | Shift-invariance: this means that if we shift the input in time (or shift the entries in a vector) then the output is shifted by the same amount
http://pillowlab.princeton.edu/teaching/mathtools16/slides/lec22_LSIsystems.pdf | What does "shift invariant" mean in convolutional neural network? | Shift-invariance: this means that if we shift the input in time (or shift the entries in a vector) then the output is shifted by the same amount
http://pillowlab.princeton.edu/teaching/mathtools16/sl | What does "shift invariant" mean in convolutional neural network?
Shift-invariance: this means that if we shift the input in time (or shift the entries in a vector) then the output is shifted by the same amount
http://pillowlab.princeton.edu/teaching/mathtools16/slides/lec22_LSIsystems.pdf | What does "shift invariant" mean in convolutional neural network?
Shift-invariance: this means that if we shift the input in time (or shift the entries in a vector) then the output is shifted by the same amount
http://pillowlab.princeton.edu/teaching/mathtools16/sl |
44,399 | What does "shift invariant" mean in convolutional neural network? | Adding to the previous answers, in math terms:
$$f(x)\implies Transform\ T\implies g(x)$$
If the transform is shift invariant, then:
$$f(x+a)\implies Transform\ T\implies g(x+a)$$
I.e. the $a$ shift is carried through the transform "untouched"
Source: This excellent ETH lecture by Prof. Buhmann | What does "shift invariant" mean in convolutional neural network? | Adding to the previous answers, in math terms:
$$f(x)\implies Transform\ T\implies g(x)$$
If the transform is shift invariant, then:
$$f(x+a)\implies Transform\ T\implies g(x+a)$$
I.e. the $a$ shift i | What does "shift invariant" mean in convolutional neural network?
Adding to the previous answers, in math terms:
$$f(x)\implies Transform\ T\implies g(x)$$
If the transform is shift invariant, then:
$$f(x+a)\implies Transform\ T\implies g(x+a)$$
I.e. the $a$ shift is carried through the transform "untouched"
Source: Th... | What does "shift invariant" mean in convolutional neural network?
Adding to the previous answers, in math terms:
$$f(x)\implies Transform\ T\implies g(x)$$
If the transform is shift invariant, then:
$$f(x+a)\implies Transform\ T\implies g(x+a)$$
I.e. the $a$ shift i |
44,400 | What does "shift invariant" mean in convolutional neural network? | Shift-Invariance arises from Computer Vision tasks such as Image Classification.
At a high level it means that the classifier should not be affected by the position of the object (e.g. cat) in the image.
[From Bronstein et. al. Geometric DL]
A little more:
MLPs do not have this property. The claim that CNNs are shift-i... | What does "shift invariant" mean in convolutional neural network? | Shift-Invariance arises from Computer Vision tasks such as Image Classification.
At a high level it means that the classifier should not be affected by the position of the object (e.g. cat) in the ima | What does "shift invariant" mean in convolutional neural network?
Shift-Invariance arises from Computer Vision tasks such as Image Classification.
At a high level it means that the classifier should not be affected by the position of the object (e.g. cat) in the image.
[From Bronstein et. al. Geometric DL]
A little mor... | What does "shift invariant" mean in convolutional neural network?
Shift-Invariance arises from Computer Vision tasks such as Image Classification.
At a high level it means that the classifier should not be affected by the position of the object (e.g. cat) in the ima |
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