idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
12,801 | Why does batch norm have learnable scale and shift? | There is a perfect answer in the Deep Learning Book, Section 8.7.1:
Normalizing the mean and standard deviation of a unit can reduce the expressive power of the neural network containing that unit. To maintain the expressive power of the network, it is common to replace the batch of hidden unit activations H with γH+β... | Why does batch norm have learnable scale and shift? | There is a perfect answer in the Deep Learning Book, Section 8.7.1:
Normalizing the mean and standard deviation of a unit can reduce the expressive power of the neural network containing that unit. T | Why does batch norm have learnable scale and shift?
There is a perfect answer in the Deep Learning Book, Section 8.7.1:
Normalizing the mean and standard deviation of a unit can reduce the expressive power of the neural network containing that unit. To maintain the expressive power of the network, it is common to repl... | Why does batch norm have learnable scale and shift?
There is a perfect answer in the Deep Learning Book, Section 8.7.1:
Normalizing the mean and standard deviation of a unit can reduce the expressive power of the neural network containing that unit. T |
12,802 | Can splines be used for prediction? | From my interpretation of the question, the underlying question you are asking is whether or not you can model time as a spline.
The first question I will attempt to answer is whether or not you can use splines to extrapolate your data. The short answer is it depends, but the majority of the time, splines are not th... | Can splines be used for prediction? | From my interpretation of the question, the underlying question you are asking is whether or not you can model time as a spline.
The first question I will attempt to answer is whether or not you ca | Can splines be used for prediction?
From my interpretation of the question, the underlying question you are asking is whether or not you can model time as a spline.
The first question I will attempt to answer is whether or not you can use splines to extrapolate your data. The short answer is it depends, but the majo... | Can splines be used for prediction?
From my interpretation of the question, the underlying question you are asking is whether or not you can model time as a spline.
The first question I will attempt to answer is whether or not you ca |
12,803 | What to say to a client that thinks confidence intervals are too wide to be useful? | It depends on what the client means by "useful". Your client's suggestion that you arbitrarily narrow the intervals seems to reflect a misunderstanding that, by narrowing the intervals you've somehow magically decreased the margin of error. Assuming the data set has already been collected and is fixed (if this isn't th... | What to say to a client that thinks confidence intervals are too wide to be useful? | It depends on what the client means by "useful". Your client's suggestion that you arbitrarily narrow the intervals seems to reflect a misunderstanding that, by narrowing the intervals you've somehow | What to say to a client that thinks confidence intervals are too wide to be useful?
It depends on what the client means by "useful". Your client's suggestion that you arbitrarily narrow the intervals seems to reflect a misunderstanding that, by narrowing the intervals you've somehow magically decreased the margin of er... | What to say to a client that thinks confidence intervals are too wide to be useful?
It depends on what the client means by "useful". Your client's suggestion that you arbitrarily narrow the intervals seems to reflect a misunderstanding that, by narrowing the intervals you've somehow |
12,804 | What to say to a client that thinks confidence intervals are too wide to be useful? | I would suggest it entirely depends on what your client wants to use the confidence intervals for.
Some sort of report/publication/etc. where 95% CI's are normally reported. I might very well tell him "That's not statistically justified" and leave it there, depending on whether or not the client tends to defer to you... | What to say to a client that thinks confidence intervals are too wide to be useful? | I would suggest it entirely depends on what your client wants to use the confidence intervals for.
Some sort of report/publication/etc. where 95% CI's are normally reported. I might very well tell h | What to say to a client that thinks confidence intervals are too wide to be useful?
I would suggest it entirely depends on what your client wants to use the confidence intervals for.
Some sort of report/publication/etc. where 95% CI's are normally reported. I might very well tell him "That's not statistically justifi... | What to say to a client that thinks confidence intervals are too wide to be useful?
I would suggest it entirely depends on what your client wants to use the confidence intervals for.
Some sort of report/publication/etc. where 95% CI's are normally reported. I might very well tell h |
12,805 | What to say to a client that thinks confidence intervals are too wide to be useful? | Use the Standard Deviation, as most people do. 95% CI can be scary when people are used to the 68%CI. | What to say to a client that thinks confidence intervals are too wide to be useful? | Use the Standard Deviation, as most people do. 95% CI can be scary when people are used to the 68%CI. | What to say to a client that thinks confidence intervals are too wide to be useful?
Use the Standard Deviation, as most people do. 95% CI can be scary when people are used to the 68%CI. | What to say to a client that thinks confidence intervals are too wide to be useful?
Use the Standard Deviation, as most people do. 95% CI can be scary when people are used to the 68%CI. |
12,806 | What to say to a client that thinks confidence intervals are too wide to be useful? | You provide a confidence interval at a certain standard level such as 90% or 95%. The client can judge whether or not the interval is too wide to be useful. But of course that does not mean that you can shorten it to make it useful. You can suggest that increasing the sample size will decrease the width of an interv... | What to say to a client that thinks confidence intervals are too wide to be useful? | You provide a confidence interval at a certain standard level such as 90% or 95%. The client can judge whether or not the interval is too wide to be useful. But of course that does not mean that you | What to say to a client that thinks confidence intervals are too wide to be useful?
You provide a confidence interval at a certain standard level such as 90% or 95%. The client can judge whether or not the interval is too wide to be useful. But of course that does not mean that you can shorten it to make it useful. ... | What to say to a client that thinks confidence intervals are too wide to be useful?
You provide a confidence interval at a certain standard level such as 90% or 95%. The client can judge whether or not the interval is too wide to be useful. But of course that does not mean that you |
12,807 | How to fix the problem in this XKCD comic? | "What is the correct way to analyze this data?"
There have been good answer suggesting analyses already. I'd like to add that there is no unique "correct" analysis of the data. For example, does it make sense to assume linearity given that the grade scale is limited? Obviously a linear model will be wrong, but then "al... | How to fix the problem in this XKCD comic? | "What is the correct way to analyze this data?"
There have been good answer suggesting analyses already. I'd like to add that there is no unique "correct" analysis of the data. For example, does it ma | How to fix the problem in this XKCD comic?
"What is the correct way to analyze this data?"
There have been good answer suggesting analyses already. I'd like to add that there is no unique "correct" analysis of the data. For example, does it make sense to assume linearity given that the grade scale is limited? Obviously... | How to fix the problem in this XKCD comic?
"What is the correct way to analyze this data?"
There have been good answer suggesting analyses already. I'd like to add that there is no unique "correct" analysis of the data. For example, does it ma |
12,808 | How to fix the problem in this XKCD comic? | Your question is composed of multiple questions/issues. I can answer the first one, the second is still unclear to me.
summary(lmer(grade ~ loudness + (1 | student), pane3))
What happened here is that the mixed effects model is effectively fitting three lines that have different (random) intercepts, instead of a sing... | How to fix the problem in this XKCD comic? | Your question is composed of multiple questions/issues. I can answer the first one, the second is still unclear to me.
summary(lmer(grade ~ loudness + (1 | student), pane3))
What happened here is th | How to fix the problem in this XKCD comic?
Your question is composed of multiple questions/issues. I can answer the first one, the second is still unclear to me.
summary(lmer(grade ~ loudness + (1 | student), pane3))
What happened here is that the mixed effects model is effectively fitting three lines that have diffe... | How to fix the problem in this XKCD comic?
Your question is composed of multiple questions/issues. I can answer the first one, the second is still unclear to me.
summary(lmer(grade ~ loudness + (1 | student), pane3))
What happened here is th |
12,809 | How to fix the problem in this XKCD comic? | This can be done with the nlme or lme4 packaes easily, all you have to add is a random effect for the students (and slope).
> library(nlme)
> summary(lme(grade~loudness,random=~1|student/loudness,data=pane3))
...
Random effects:
Formula: ~1 | student
(Intercept)
StdDev: 9.131586
Formula: ~1 | loudness... | How to fix the problem in this XKCD comic? | This can be done with the nlme or lme4 packaes easily, all you have to add is a random effect for the students (and slope).
> library(nlme)
> summary(lme(grade~loudness,random=~1|student/loudness,data | How to fix the problem in this XKCD comic?
This can be done with the nlme or lme4 packaes easily, all you have to add is a random effect for the students (and slope).
> library(nlme)
> summary(lme(grade~loudness,random=~1|student/loudness,data=pane3))
...
Random effects:
Formula: ~1 | student
(Intercept)
S... | How to fix the problem in this XKCD comic?
This can be done with the nlme or lme4 packaes easily, all you have to add is a random effect for the students (and slope).
> library(nlme)
> summary(lme(grade~loudness,random=~1|student/loudness,data |
12,810 | What are the disadvantages of the profile likelihood? | The estimate of $\theta_1$ from the profile likelihood is just the MLE. Maximizing with respect to $\theta_2$ for each possible $\theta_1$ and then maximizing with respect to $\theta_1$ is the same as maximizing with respect to $(\theta_1, \theta_2)$ jointly.
The key weakness is that, if you base your estimate of the ... | What are the disadvantages of the profile likelihood? | The estimate of $\theta_1$ from the profile likelihood is just the MLE. Maximizing with respect to $\theta_2$ for each possible $\theta_1$ and then maximizing with respect to $\theta_1$ is the same a | What are the disadvantages of the profile likelihood?
The estimate of $\theta_1$ from the profile likelihood is just the MLE. Maximizing with respect to $\theta_2$ for each possible $\theta_1$ and then maximizing with respect to $\theta_1$ is the same as maximizing with respect to $(\theta_1, \theta_2)$ jointly.
The k... | What are the disadvantages of the profile likelihood?
The estimate of $\theta_1$ from the profile likelihood is just the MLE. Maximizing with respect to $\theta_2$ for each possible $\theta_1$ and then maximizing with respect to $\theta_1$ is the same a |
12,811 | What are the disadvantages of the profile likelihood? | The major drawback is that the profile likelihood is completely meaningless.
The profile likelihood should be viewed as intermediate quantity that facilitates applications of asymptotic approximations (Wilks etc) for the purpose of constructing a confidence intervals and regions.
By itself, however, it doesn't have any... | What are the disadvantages of the profile likelihood? | The major drawback is that the profile likelihood is completely meaningless.
The profile likelihood should be viewed as intermediate quantity that facilitates applications of asymptotic approximations | What are the disadvantages of the profile likelihood?
The major drawback is that the profile likelihood is completely meaningless.
The profile likelihood should be viewed as intermediate quantity that facilitates applications of asymptotic approximations (Wilks etc) for the purpose of constructing a confidence interval... | What are the disadvantages of the profile likelihood?
The major drawback is that the profile likelihood is completely meaningless.
The profile likelihood should be viewed as intermediate quantity that facilitates applications of asymptotic approximations |
12,812 | When do Markov random fields $\neq$ exponential families? | You are entirely correct -- the argument you presented relates the exponential family to the principle of maximum entropy, but doesn't have anything to do with MRFs.
To address your three initial questions:
Can all members from the Exponential families be represented as an MRF?
Yes. In fact, any density or mass funct... | When do Markov random fields $\neq$ exponential families? | You are entirely correct -- the argument you presented relates the exponential family to the principle of maximum entropy, but doesn't have anything to do with MRFs.
To address your three initial ques | When do Markov random fields $\neq$ exponential families?
You are entirely correct -- the argument you presented relates the exponential family to the principle of maximum entropy, but doesn't have anything to do with MRFs.
To address your three initial questions:
Can all members from the Exponential families be repre... | When do Markov random fields $\neq$ exponential families?
You are entirely correct -- the argument you presented relates the exponential family to the principle of maximum entropy, but doesn't have anything to do with MRFs.
To address your three initial ques |
12,813 | Need for centering and standardizing data in regression | You are correct about zeroing the means of the columns of $A$ and $b$.
However, as for adjusting the norms of the columns of $A$, consider what would happen if you started out with a normed $A$, and all the elements of $x$ were of roughly the same magnitude. Then let us multiply one column by, say, $10^{-6}$. The co... | Need for centering and standardizing data in regression | You are correct about zeroing the means of the columns of $A$ and $b$.
However, as for adjusting the norms of the columns of $A$, consider what would happen if you started out with a normed $A$, and | Need for centering and standardizing data in regression
You are correct about zeroing the means of the columns of $A$ and $b$.
However, as for adjusting the norms of the columns of $A$, consider what would happen if you started out with a normed $A$, and all the elements of $x$ were of roughly the same magnitude. The... | Need for centering and standardizing data in regression
You are correct about zeroing the means of the columns of $A$ and $b$.
However, as for adjusting the norms of the columns of $A$, consider what would happen if you started out with a normed $A$, and |
12,814 | "Semi supervised learning" - is this overfitting? | It doesn't appear to be overfitting. Intuitively, overfitting implies training to the quirks (noise) of the training set and therefore doing worse on a held-out test set which does not share these quirks. If I understand what happened, they did not do unexpectedly-poorly on held-out test data and so that empirically ru... | "Semi supervised learning" - is this overfitting? | It doesn't appear to be overfitting. Intuitively, overfitting implies training to the quirks (noise) of the training set and therefore doing worse on a held-out test set which does not share these qui | "Semi supervised learning" - is this overfitting?
It doesn't appear to be overfitting. Intuitively, overfitting implies training to the quirks (noise) of the training set and therefore doing worse on a held-out test set which does not share these quirks. If I understand what happened, they did not do unexpectedly-poorl... | "Semi supervised learning" - is this overfitting?
It doesn't appear to be overfitting. Intuitively, overfitting implies training to the quirks (noise) of the training set and therefore doing worse on a held-out test set which does not share these qui |
12,815 | "Semi supervised learning" - is this overfitting? | It is not gross over fitting (depending on definition). Target information of test set is preserved. Semi-supervised allow to generate an extra synthetic data set to train the model on. In the described approach, original training data is mixed unweighted with synthetic in ratio 4:3. Thus, if the quality of the synthet... | "Semi supervised learning" - is this overfitting? | It is not gross over fitting (depending on definition). Target information of test set is preserved. Semi-supervised allow to generate an extra synthetic data set to train the model on. In the describ | "Semi supervised learning" - is this overfitting?
It is not gross over fitting (depending on definition). Target information of test set is preserved. Semi-supervised allow to generate an extra synthetic data set to train the model on. In the described approach, original training data is mixed unweighted with synthetic... | "Semi supervised learning" - is this overfitting?
It is not gross over fitting (depending on definition). Target information of test set is preserved. Semi-supervised allow to generate an extra synthetic data set to train the model on. In the describ |
12,816 | "Semi supervised learning" - is this overfitting? | No, it is not overfitting.
I think your worry here is that the model is byhearting the data instead of modeling it. That depends on the complexity of the model (which remained the same) and size of the data. It happens when the model is too complex and/or when the training data is too small, neither of which is the ... | "Semi supervised learning" - is this overfitting? | No, it is not overfitting.
I think your worry here is that the model is byhearting the data instead of modeling it. That depends on the complexity of the model (which remained the same) and size of | "Semi supervised learning" - is this overfitting?
No, it is not overfitting.
I think your worry here is that the model is byhearting the data instead of modeling it. That depends on the complexity of the model (which remained the same) and size of the data. It happens when the model is too complex and/or when the tr... | "Semi supervised learning" - is this overfitting?
No, it is not overfitting.
I think your worry here is that the model is byhearting the data instead of modeling it. That depends on the complexity of the model (which remained the same) and size of |
12,817 | "Semi supervised learning" - is this overfitting? | By this definition: "Overfitting occurs when a statistical model describes random error or noise instead of the underlying relationship."(wikipedia), the solution is not overfitting.
But in this situation:
- Test data is a stream of items and not a fixed set of items.
OR
- Prediction process should not contain learning... | "Semi supervised learning" - is this overfitting? | By this definition: "Overfitting occurs when a statistical model describes random error or noise instead of the underlying relationship."(wikipedia), the solution is not overfitting.
But in this situa | "Semi supervised learning" - is this overfitting?
By this definition: "Overfitting occurs when a statistical model describes random error or noise instead of the underlying relationship."(wikipedia), the solution is not overfitting.
But in this situation:
- Test data is a stream of items and not a fixed set of items.
O... | "Semi supervised learning" - is this overfitting?
By this definition: "Overfitting occurs when a statistical model describes random error or noise instead of the underlying relationship."(wikipedia), the solution is not overfitting.
But in this situa |
12,818 | For which distributions does uncorrelatedness imply independence? | "Nevertheless if the two variables are normally distributed, then uncorrelatedness does imply independence" is a very common fallacy.
That only applies if they are jointly normally distributed.
The counterexample I have seen most often is normal $X \sim N(0,1)$ and independent Rademacher $Y$ (so that it is 1 or -1 with... | For which distributions does uncorrelatedness imply independence? | "Nevertheless if the two variables are normally distributed, then uncorrelatedness does imply independence" is a very common fallacy.
That only applies if they are jointly normally distributed.
The co | For which distributions does uncorrelatedness imply independence?
"Nevertheless if the two variables are normally distributed, then uncorrelatedness does imply independence" is a very common fallacy.
That only applies if they are jointly normally distributed.
The counterexample I have seen most often is normal $X \sim ... | For which distributions does uncorrelatedness imply independence?
"Nevertheless if the two variables are normally distributed, then uncorrelatedness does imply independence" is a very common fallacy.
That only applies if they are jointly normally distributed.
The co |
12,819 | Power analysis for Kruskal-Wallis or Mann-Whitney U test using R? | It's certainly possible to calculate power.
To be more specific - if you make sufficient assumptions to obtain a situation in which you can calculate (in some fashion) the probability of rejection, you can compute power.
In the Wilcoxon-Mann-Whitney, if (for example) you assume the distribution shapes (make an assumpt... | Power analysis for Kruskal-Wallis or Mann-Whitney U test using R? | It's certainly possible to calculate power.
To be more specific - if you make sufficient assumptions to obtain a situation in which you can calculate (in some fashion) the probability of rejection, yo | Power analysis for Kruskal-Wallis or Mann-Whitney U test using R?
It's certainly possible to calculate power.
To be more specific - if you make sufficient assumptions to obtain a situation in which you can calculate (in some fashion) the probability of rejection, you can compute power.
In the Wilcoxon-Mann-Whitney, if... | Power analysis for Kruskal-Wallis or Mann-Whitney U test using R?
It's certainly possible to calculate power.
To be more specific - if you make sufficient assumptions to obtain a situation in which you can calculate (in some fashion) the probability of rejection, yo |
12,820 | Power analysis for Kruskal-Wallis or Mann-Whitney U test using R? | I had exactly the same question as you. After searching a bit I found the MultNonParam package in R (pdf):
kwpower(nreps, shifts, distname=c("normal","logistic"), level=0.05, mc=0, taylor=FALSE)
nreps: The numbers in each group.
shifts: The offsets for the various populations, under the alternative hypothesis.
distna... | Power analysis for Kruskal-Wallis or Mann-Whitney U test using R? | I had exactly the same question as you. After searching a bit I found the MultNonParam package in R (pdf):
kwpower(nreps, shifts, distname=c("normal","logistic"), level=0.05, mc=0, taylor=FALSE)
nre | Power analysis for Kruskal-Wallis or Mann-Whitney U test using R?
I had exactly the same question as you. After searching a bit I found the MultNonParam package in R (pdf):
kwpower(nreps, shifts, distname=c("normal","logistic"), level=0.05, mc=0, taylor=FALSE)
nreps: The numbers in each group.
shifts: The offsets for... | Power analysis for Kruskal-Wallis or Mann-Whitney U test using R?
I had exactly the same question as you. After searching a bit I found the MultNonParam package in R (pdf):
kwpower(nreps, shifts, distname=c("normal","logistic"), level=0.05, mc=0, taylor=FALSE)
nre |
12,821 | Why is there -1 in beta distribution density function? | This is a story about degrees of freedom and statistical parameters and why it is nice that the two have a direct simple connection.
Historically, the "$-1$" terms appeared in Euler's studies of the Beta function. He was using that parameterization by 1763, and so was Adrien-Marie Legendre: their usage established the... | Why is there -1 in beta distribution density function? | This is a story about degrees of freedom and statistical parameters and why it is nice that the two have a direct simple connection.
Historically, the "$-1$" terms appeared in Euler's studies of the B | Why is there -1 in beta distribution density function?
This is a story about degrees of freedom and statistical parameters and why it is nice that the two have a direct simple connection.
Historically, the "$-1$" terms appeared in Euler's studies of the Beta function. He was using that parameterization by 1763, and so... | Why is there -1 in beta distribution density function?
This is a story about degrees of freedom and statistical parameters and why it is nice that the two have a direct simple connection.
Historically, the "$-1$" terms appeared in Euler's studies of the B |
12,822 | Why is there -1 in beta distribution density function? | The notation is misleading you. There is a "hidden $-1$" in your formula $(1)$, because in $(1)$, $\alpha$ and $\beta$ must be bigger than $-1$ (the second link you provided in your question says this explicitly). The $\alpha$'s and $\beta$'s in the two formulas are not the same parameters; they have different ranges: ... | Why is there -1 in beta distribution density function? | The notation is misleading you. There is a "hidden $-1$" in your formula $(1)$, because in $(1)$, $\alpha$ and $\beta$ must be bigger than $-1$ (the second link you provided in your question says this | Why is there -1 in beta distribution density function?
The notation is misleading you. There is a "hidden $-1$" in your formula $(1)$, because in $(1)$, $\alpha$ and $\beta$ must be bigger than $-1$ (the second link you provided in your question says this explicitly). The $\alpha$'s and $\beta$'s in the two formulas ar... | Why is there -1 in beta distribution density function?
The notation is misleading you. There is a "hidden $-1$" in your formula $(1)$, because in $(1)$, $\alpha$ and $\beta$ must be bigger than $-1$ (the second link you provided in your question says this |
12,823 | Why is there -1 in beta distribution density function? | For me, the existence of -1 in the exponent is related with the develpment of the Gamma function. The motivation of the Gamma function is to find a smooth curve to connect the points of a factorial $x!$. Since it is not possible to compute $x!$ directly if $x$ is not integer, the idea was to find a function for any $x ... | Why is there -1 in beta distribution density function? | For me, the existence of -1 in the exponent is related with the develpment of the Gamma function. The motivation of the Gamma function is to find a smooth curve to connect the points of a factorial $x | Why is there -1 in beta distribution density function?
For me, the existence of -1 in the exponent is related with the develpment of the Gamma function. The motivation of the Gamma function is to find a smooth curve to connect the points of a factorial $x!$. Since it is not possible to compute $x!$ directly if $x$ is n... | Why is there -1 in beta distribution density function?
For me, the existence of -1 in the exponent is related with the develpment of the Gamma function. The motivation of the Gamma function is to find a smooth curve to connect the points of a factorial $x |
12,824 | Regularization for ARIMA models | Answering Question 1.
Chen & Chan "Subset ARMA selection via the adaptive Lasso" (2011)* use a workaround to avoid the computationally demanding maximum likelihood estimation. Citing the paper, they
propose to find an optimal subset ARMA model by fitting an adaptive Lasso regression of the time series $y_t$ on its own... | Regularization for ARIMA models | Answering Question 1.
Chen & Chan "Subset ARMA selection via the adaptive Lasso" (2011)* use a workaround to avoid the computationally demanding maximum likelihood estimation. Citing the paper, they
| Regularization for ARIMA models
Answering Question 1.
Chen & Chan "Subset ARMA selection via the adaptive Lasso" (2011)* use a workaround to avoid the computationally demanding maximum likelihood estimation. Citing the paper, they
propose to find an optimal subset ARMA model by fitting an adaptive Lasso regression of ... | Regularization for ARIMA models
Answering Question 1.
Chen & Chan "Subset ARMA selection via the adaptive Lasso" (2011)* use a workaround to avoid the computationally demanding maximum likelihood estimation. Citing the paper, they
|
12,825 | Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions | Let's take care of the routine calculus for you, so you can get to the heart of the problem and enjoy formulating a solution. It comes down to constructing rectangles as unions and differences of triangles.
First, choose values of $a$ and $b$ that make the details as simple as possible. I like $a=0,b=1$: the univaria... | Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions | Let's take care of the routine calculus for you, so you can get to the heart of the problem and enjoy formulating a solution. It comes down to constructing rectangles as unions and differences of tri | Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions
Let's take care of the routine calculus for you, so you can get to the heart of the problem and enjoy formulating a solution. It comes down to constructing rectangles as unions and differences of triangles.
First, choose values of $a$ and $b$ tha... | Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions
Let's take care of the routine calculus for you, so you can get to the heart of the problem and enjoy formulating a solution. It comes down to constructing rectangles as unions and differences of tri |
12,826 | Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions | Following @whuber's answer, we have the joint density of $(Y_{(1)},Y_{(n)})$
$$f(y_1, y_n,a,b)=\frac{n(n-1)}{(b-a)^n}(y_n-y_1)^{n-1},\quad\forall a\leq y_1\leq y_n\leq b\text{ and }a,b\in\mathbb{R}$$
For any function $g(x_1,x_n)$ so that $\mathbb{E}_{a,b}\left[g(y_1,y_n)\right]=0,\forall a,b\in\mathbb{R}\text{ and }a<b... | Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions | Following @whuber's answer, we have the joint density of $(Y_{(1)},Y_{(n)})$
$$f(y_1, y_n,a,b)=\frac{n(n-1)}{(b-a)^n}(y_n-y_1)^{n-1},\quad\forall a\leq y_1\leq y_n\leq b\text{ and }a,b\in\mathbb{R}$$
| Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions
Following @whuber's answer, we have the joint density of $(Y_{(1)},Y_{(n)})$
$$f(y_1, y_n,a,b)=\frac{n(n-1)}{(b-a)^n}(y_n-y_1)^{n-1},\quad\forall a\leq y_1\leq y_n\leq b\text{ and }a,b\in\mathbb{R}$$
For any function $g(x_1,x_n)$ so that $\mathbb{... | Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions
Following @whuber's answer, we have the joint density of $(Y_{(1)},Y_{(n)})$
$$f(y_1, y_n,a,b)=\frac{n(n-1)}{(b-a)^n}(y_n-y_1)^{n-1},\quad\forall a\leq y_1\leq y_n\leq b\text{ and }a,b\in\mathbb{R}$$
|
12,827 | Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions | I think it is worth elaborating a little bit the step of how to reach $g = 0$ a.e. $\lambda$ from the integral equation in @Tan's and @whuber's answer, as it demonstrates some classical measure theory techniques that could be used in other similar completeness proving problems.
Denote $g(x, y)(y - x)^{n - 2}$ by $f(x, ... | Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions | I think it is worth elaborating a little bit the step of how to reach $g = 0$ a.e. $\lambda$ from the integral equation in @Tan's and @whuber's answer, as it demonstrates some classical measure theory | Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions
I think it is worth elaborating a little bit the step of how to reach $g = 0$ a.e. $\lambda$ from the integral equation in @Tan's and @whuber's answer, as it demonstrates some classical measure theory techniques that could be used in other similar... | Jointly Complete Sufficient Statistics for Uniform$(a, b)$ Distributions
I think it is worth elaborating a little bit the step of how to reach $g = 0$ a.e. $\lambda$ from the integral equation in @Tan's and @whuber's answer, as it demonstrates some classical measure theory |
12,828 | Classification with noisy labels? | The right thing to do here is to change the model, not the loss. Your goal is still to correctly classify as many data points as possible (which determines the loss), but your assumptions about the data have changed (which are encoded in a statistical model, the neural network in this case).
Let $\mathbf{p}_t$ be a vec... | Classification with noisy labels? | The right thing to do here is to change the model, not the loss. Your goal is still to correctly classify as many data points as possible (which determines the loss), but your assumptions about the da | Classification with noisy labels?
The right thing to do here is to change the model, not the loss. Your goal is still to correctly classify as many data points as possible (which determines the loss), but your assumptions about the data have changed (which are encoded in a statistical model, the neural network in this ... | Classification with noisy labels?
The right thing to do here is to change the model, not the loss. Your goal is still to correctly classify as many data points as possible (which determines the loss), but your assumptions about the da |
12,829 | Classification with noisy labels? | This approach has been proven to work in many realistic settings with substantive theory for models with error in every predicted probability output for every example.
The approach counts up an unnormalized estimate of the joint distribution of true labels and noisy/given labels. Using that estimate, it finds the labe... | Classification with noisy labels? | This approach has been proven to work in many realistic settings with substantive theory for models with error in every predicted probability output for every example.
The approach counts up an unnor | Classification with noisy labels?
This approach has been proven to work in many realistic settings with substantive theory for models with error in every predicted probability output for every example.
The approach counts up an unnormalized estimate of the joint distribution of true labels and noisy/given labels. Usin... | Classification with noisy labels?
This approach has been proven to work in many realistic settings with substantive theory for models with error in every predicted probability output for every example.
The approach counts up an unnor |
12,830 | Preventing overfitting of LSTM on small dataset | You could try:
Reduce the number of hidden units, I know you said it already seems low, but given that the input layer only has 80 features, it actually can be that 128 is too much. A rule of thumb is to have the number of hidden units be in-between the number of input units (80) and output classes (5);
Alternatively,... | Preventing overfitting of LSTM on small dataset | You could try:
Reduce the number of hidden units, I know you said it already seems low, but given that the input layer only has 80 features, it actually can be that 128 is too much. A rule of thumb i | Preventing overfitting of LSTM on small dataset
You could try:
Reduce the number of hidden units, I know you said it already seems low, but given that the input layer only has 80 features, it actually can be that 128 is too much. A rule of thumb is to have the number of hidden units be in-between the number of input u... | Preventing overfitting of LSTM on small dataset
You could try:
Reduce the number of hidden units, I know you said it already seems low, but given that the input layer only has 80 features, it actually can be that 128 is too much. A rule of thumb i |
12,831 | Combining information from multiple studies to estimate the mean and variance of normally distributed data - Bayesian vs meta-analytic approaches | The two approaches (meta-analysis and Bayesian updating) are not really that distinct. Meta-analytic models are in fact often framed as Bayesian models, since the idea of adding evidence to prior knowledge (possibly quite vague) about the phenomenon at hand lends itself naturally to a meta-analysis. An article that des... | Combining information from multiple studies to estimate the mean and variance of normally distribute | The two approaches (meta-analysis and Bayesian updating) are not really that distinct. Meta-analytic models are in fact often framed as Bayesian models, since the idea of adding evidence to prior know | Combining information from multiple studies to estimate the mean and variance of normally distributed data - Bayesian vs meta-analytic approaches
The two approaches (meta-analysis and Bayesian updating) are not really that distinct. Meta-analytic models are in fact often framed as Bayesian models, since the idea of add... | Combining information from multiple studies to estimate the mean and variance of normally distribute
The two approaches (meta-analysis and Bayesian updating) are not really that distinct. Meta-analytic models are in fact often framed as Bayesian models, since the idea of adding evidence to prior know |
12,832 | Combining information from multiple studies to estimate the mean and variance of normally distributed data - Bayesian vs meta-analytic approaches | If I understand your question correctly, then this differs from the usual meta-analysis setup in that you want to estimate not only a common mean, but also a common variance. So the sampling model for the raw data is $y_{ij} \sim N(\mu, \sigma^2)$ for observation $i = 1,...n_j$ from study $j = 1,...,K$. If that is righ... | Combining information from multiple studies to estimate the mean and variance of normally distribute | If I understand your question correctly, then this differs from the usual meta-analysis setup in that you want to estimate not only a common mean, but also a common variance. So the sampling model for | Combining information from multiple studies to estimate the mean and variance of normally distributed data - Bayesian vs meta-analytic approaches
If I understand your question correctly, then this differs from the usual meta-analysis setup in that you want to estimate not only a common mean, but also a common variance.... | Combining information from multiple studies to estimate the mean and variance of normally distribute
If I understand your question correctly, then this differs from the usual meta-analysis setup in that you want to estimate not only a common mean, but also a common variance. So the sampling model for |
12,833 | Test if multidimensional distributions are the same | I just did a lot of research on multivariate two sample tests when I realized that the Kolmogorov-Smirnov test wasn't multivariate. So I looked at the Chi test, Hotelling's T^2, Anderson-Darling, Cramer-von Mises criterion, Shapiro-Wilk, etc. You have to be careful because some of these tests rely on the vectors being ... | Test if multidimensional distributions are the same | I just did a lot of research on multivariate two sample tests when I realized that the Kolmogorov-Smirnov test wasn't multivariate. So I looked at the Chi test, Hotelling's T^2, Anderson-Darling, Cram | Test if multidimensional distributions are the same
I just did a lot of research on multivariate two sample tests when I realized that the Kolmogorov-Smirnov test wasn't multivariate. So I looked at the Chi test, Hotelling's T^2, Anderson-Darling, Cramer-von Mises criterion, Shapiro-Wilk, etc. You have to be careful be... | Test if multidimensional distributions are the same
I just did a lot of research on multivariate two sample tests when I realized that the Kolmogorov-Smirnov test wasn't multivariate. So I looked at the Chi test, Hotelling's T^2, Anderson-Darling, Cram |
12,834 | Test if multidimensional distributions are the same | Yes, there are nonparametric ways of testing if two multivariate samples are from the same joint distribution. I will mention details excluding the ones mentioned by L Fischman. The basic problem you are asking can be called as a 'Two-Sample-Problem' and a good amount of research is going on currently in journals like ... | Test if multidimensional distributions are the same | Yes, there are nonparametric ways of testing if two multivariate samples are from the same joint distribution. I will mention details excluding the ones mentioned by L Fischman. The basic problem you | Test if multidimensional distributions are the same
Yes, there are nonparametric ways of testing if two multivariate samples are from the same joint distribution. I will mention details excluding the ones mentioned by L Fischman. The basic problem you are asking can be called as a 'Two-Sample-Problem' and a good amount... | Test if multidimensional distributions are the same
Yes, there are nonparametric ways of testing if two multivariate samples are from the same joint distribution. I will mention details excluding the ones mentioned by L Fischman. The basic problem you |
12,835 | Test if multidimensional distributions are the same | R package np (non-parametric) has a test for equality of densities of continous and categorical data using integrated squared density. Li, Maasoumi, and Racine(2009)
As well as np conditional pdf in section 6. | Test if multidimensional distributions are the same | R package np (non-parametric) has a test for equality of densities of continous and categorical data using integrated squared density. Li, Maasoumi, and Racine(2009)
As well as np conditional pdf in s | Test if multidimensional distributions are the same
R package np (non-parametric) has a test for equality of densities of continous and categorical data using integrated squared density. Li, Maasoumi, and Racine(2009)
As well as np conditional pdf in section 6. | Test if multidimensional distributions are the same
R package np (non-parametric) has a test for equality of densities of continous and categorical data using integrated squared density. Li, Maasoumi, and Racine(2009)
As well as np conditional pdf in s |
12,836 | Test if multidimensional distributions are the same | As I am working on the same problem, I can share some of my insights so far (which is far from expertise). You are asking for a test that answers the question whether or not two sample distributions are drawn from the same distribution. A question that is also asked frequently in testing is if two sample distributions ... | Test if multidimensional distributions are the same | As I am working on the same problem, I can share some of my insights so far (which is far from expertise). You are asking for a test that answers the question whether or not two sample distributions a | Test if multidimensional distributions are the same
As I am working on the same problem, I can share some of my insights so far (which is far from expertise). You are asking for a test that answers the question whether or not two sample distributions are drawn from the same distribution. A question that is also asked f... | Test if multidimensional distributions are the same
As I am working on the same problem, I can share some of my insights so far (which is far from expertise). You are asking for a test that answers the question whether or not two sample distributions a |
12,837 | Test if multidimensional distributions are the same | In summary, this is hard!
So it is useful to step back from the abstract question. Why do you want to compare these distributions? Perhaps this goal can be met some other way.
For example, one reason for doing this is when training a GAN. In this situation the training is iterative and stochastic. So it is sufficient t... | Test if multidimensional distributions are the same | In summary, this is hard!
So it is useful to step back from the abstract question. Why do you want to compare these distributions? Perhaps this goal can be met some other way.
For example, one reason | Test if multidimensional distributions are the same
In summary, this is hard!
So it is useful to step back from the abstract question. Why do you want to compare these distributions? Perhaps this goal can be met some other way.
For example, one reason for doing this is when training a GAN. In this situation the trainin... | Test if multidimensional distributions are the same
In summary, this is hard!
So it is useful to step back from the abstract question. Why do you want to compare these distributions? Perhaps this goal can be met some other way.
For example, one reason |
12,838 | How to calculate the confidence interval of the mean of means? | There is a natural exact confidence interval for the grandmean in the balanced random one-way ANOVA model $$(y_{ij} \mid \mu_i) \sim_{\text{iid}} {\cal N}(\mu_i, \sigma^2_w), \quad j=1,\ldots,J,
\qquad
\mu_i \sim_{\text{iid}} {\cal N}(\mu, \sigma^2_b), \quad i=1,\ldots,I.$$
Indeed, it is easy to check that the distri... | How to calculate the confidence interval of the mean of means? | There is a natural exact confidence interval for the grandmean in the balanced random one-way ANOVA model $$(y_{ij} \mid \mu_i) \sim_{\text{iid}} {\cal N}(\mu_i, \sigma^2_w), \quad j=1,\ldots,J,
\qqu | How to calculate the confidence interval of the mean of means?
There is a natural exact confidence interval for the grandmean in the balanced random one-way ANOVA model $$(y_{ij} \mid \mu_i) \sim_{\text{iid}} {\cal N}(\mu_i, \sigma^2_w), \quad j=1,\ldots,J,
\qquad
\mu_i \sim_{\text{iid}} {\cal N}(\mu, \sigma^2_b), \q... | How to calculate the confidence interval of the mean of means?
There is a natural exact confidence interval for the grandmean in the balanced random one-way ANOVA model $$(y_{ij} \mid \mu_i) \sim_{\text{iid}} {\cal N}(\mu_i, \sigma^2_w), \quad j=1,\ldots,J,
\qqu |
12,839 | How to calculate the confidence interval of the mean of means? | This is a question of estimation within a linear mixed effects model. The problem is that the variance of the grand mean is a weighted sum of two variance components which have to be separately estimated (via an ANOVA of the data). The estimates have different degrees of freedom. Therefore, although one can attempt ... | How to calculate the confidence interval of the mean of means? | This is a question of estimation within a linear mixed effects model. The problem is that the variance of the grand mean is a weighted sum of two variance components which have to be separately estim | How to calculate the confidence interval of the mean of means?
This is a question of estimation within a linear mixed effects model. The problem is that the variance of the grand mean is a weighted sum of two variance components which have to be separately estimated (via an ANOVA of the data). The estimates have diff... | How to calculate the confidence interval of the mean of means?
This is a question of estimation within a linear mixed effects model. The problem is that the variance of the grand mean is a weighted sum of two variance components which have to be separately estim |
12,840 | How to calculate the confidence interval of the mean of means? | You can't have one confidence interval that solves both of your problems. You have to pick one. You can either derive one from a mean square error term of within experiment variance that allows you to say something about how accurately you can estimate the values within experiment or you can do it between and it will... | How to calculate the confidence interval of the mean of means? | You can't have one confidence interval that solves both of your problems. You have to pick one. You can either derive one from a mean square error term of within experiment variance that allows you | How to calculate the confidence interval of the mean of means?
You can't have one confidence interval that solves both of your problems. You have to pick one. You can either derive one from a mean square error term of within experiment variance that allows you to say something about how accurately you can estimate th... | How to calculate the confidence interval of the mean of means?
You can't have one confidence interval that solves both of your problems. You have to pick one. You can either derive one from a mean square error term of within experiment variance that allows you |
12,841 | How to calculate the confidence interval of the mean of means? | I think the CI for grand mean is too wide [17,62] even for the range of original data.
This experiments are VERY common in chemistry. For example, in certification of reference materials you have to pick up some bottles from whole lot in a random way, and you have to carry out replicate analysis on each bottles. How do... | How to calculate the confidence interval of the mean of means? | I think the CI for grand mean is too wide [17,62] even for the range of original data.
This experiments are VERY common in chemistry. For example, in certification of reference materials you have to p | How to calculate the confidence interval of the mean of means?
I think the CI for grand mean is too wide [17,62] even for the range of original data.
This experiments are VERY common in chemistry. For example, in certification of reference materials you have to pick up some bottles from whole lot in a random way, and y... | How to calculate the confidence interval of the mean of means?
I think the CI for grand mean is too wide [17,62] even for the range of original data.
This experiments are VERY common in chemistry. For example, in certification of reference materials you have to p |
12,842 | Standardized VS centered variables | Yes
Yes
You standardize variables to compare the importance of independent variables in determining the outcome variables.
You may want to center a variable when you use an interaction term--its effect will be meaningfully interpretable if the minimum value of one of the interacted variables is not zero.
If you are reg... | Standardized VS centered variables | Yes
Yes
You standardize variables to compare the importance of independent variables in determining the outcome variables.
You may want to center a variable when you use an interaction term--its effec | Standardized VS centered variables
Yes
Yes
You standardize variables to compare the importance of independent variables in determining the outcome variables.
You may want to center a variable when you use an interaction term--its effect will be meaningfully interpretable if the minimum value of one of the interacted va... | Standardized VS centered variables
Yes
Yes
You standardize variables to compare the importance of independent variables in determining the outcome variables.
You may want to center a variable when you use an interaction term--its effec |
12,843 | Computing prediction intervals for logistic regression | Prediction intervals predict where the actual response data values are predicted to fall with a given probability. Since the possible values of the response of a logistic model are restricted to 0 and 1, the 100% prediction interval is therefore $ 0 <= y <= 1 $. No other intervals really make sense for prediction wit... | Computing prediction intervals for logistic regression | Prediction intervals predict where the actual response data values are predicted to fall with a given probability. Since the possible values of the response of a logistic model are restricted to 0 an | Computing prediction intervals for logistic regression
Prediction intervals predict where the actual response data values are predicted to fall with a given probability. Since the possible values of the response of a logistic model are restricted to 0 and 1, the 100% prediction interval is therefore $ 0 <= y <= 1 $. ... | Computing prediction intervals for logistic regression
Prediction intervals predict where the actual response data values are predicted to fall with a given probability. Since the possible values of the response of a logistic model are restricted to 0 an |
12,844 | Computing prediction intervals for logistic regression | I agree with @Greg Snow that there should not be a distinction between prediction interval and confidence interval for binary outcome models as in linear models. He noted the difference between a binomial outcome (y successes out of j trials among n groups) and a binary outcome (success or failure of one subject among ... | Computing prediction intervals for logistic regression | I agree with @Greg Snow that there should not be a distinction between prediction interval and confidence interval for binary outcome models as in linear models. He noted the difference between a bino | Computing prediction intervals for logistic regression
I agree with @Greg Snow that there should not be a distinction between prediction interval and confidence interval for binary outcome models as in linear models. He noted the difference between a binomial outcome (y successes out of j trials among n groups) and a b... | Computing prediction intervals for logistic regression
I agree with @Greg Snow that there should not be a distinction between prediction interval and confidence interval for binary outcome models as in linear models. He noted the difference between a bino |
12,845 | Parameters vs latent variables | In the paper, and in general, (random) variables are everything which is drawn from a probability distribution. Latent (random) variables are the ones you don't directly observe ($y$ is observed, $\beta$ is not, but both are r.v). From a latent random variable you can get a posterior distribution, which is its probabil... | Parameters vs latent variables | In the paper, and in general, (random) variables are everything which is drawn from a probability distribution. Latent (random) variables are the ones you don't directly observe ($y$ is observed, $\be | Parameters vs latent variables
In the paper, and in general, (random) variables are everything which is drawn from a probability distribution. Latent (random) variables are the ones you don't directly observe ($y$ is observed, $\beta$ is not, but both are r.v). From a latent random variable you can get a posterior dist... | Parameters vs latent variables
In the paper, and in general, (random) variables are everything which is drawn from a probability distribution. Latent (random) variables are the ones you don't directly observe ($y$ is observed, $\be |
12,846 | Casting a multivariate linear model as a multiple regression | Basically, can you do everything with the equivalent linear univariate
regression model that you could with the multivariate model?
I believe the answer is no.
If your goal is simply either to estimate the effects (parameters in $\mathbf{B}$) or to further make predictions based on the model, then yes it does not ma... | Casting a multivariate linear model as a multiple regression | Basically, can you do everything with the equivalent linear univariate
regression model that you could with the multivariate model?
I believe the answer is no.
If your goal is simply either to esti | Casting a multivariate linear model as a multiple regression
Basically, can you do everything with the equivalent linear univariate
regression model that you could with the multivariate model?
I believe the answer is no.
If your goal is simply either to estimate the effects (parameters in $\mathbf{B}$) or to further... | Casting a multivariate linear model as a multiple regression
Basically, can you do everything with the equivalent linear univariate
regression model that you could with the multivariate model?
I believe the answer is no.
If your goal is simply either to esti |
12,847 | Casting a multivariate linear model as a multiple regression | Both models are equivalent if you fit appropriate variance-covariance structure. In transformed linear model we need to fit variance-covariance matrix of error component with kronecker product which has limited availability in available computing softwares. Linear Model Theory-Univariate, Multivariate, and Mixed Model... | Casting a multivariate linear model as a multiple regression | Both models are equivalent if you fit appropriate variance-covariance structure. In transformed linear model we need to fit variance-covariance matrix of error component with kronecker product which | Casting a multivariate linear model as a multiple regression
Both models are equivalent if you fit appropriate variance-covariance structure. In transformed linear model we need to fit variance-covariance matrix of error component with kronecker product which has limited availability in available computing softwares. ... | Casting a multivariate linear model as a multiple regression
Both models are equivalent if you fit appropriate variance-covariance structure. In transformed linear model we need to fit variance-covariance matrix of error component with kronecker product which |
12,848 | How to interpret negative ACF (autocorrelation function)? | Negative ACF means that a positive oil return for one observation increases the probability of having a negative oil return for another observation (depending on the lag) and vice-versa. Or you can say (for a stationary time series) if one observation is above the average the other one (depending on the lag) is below a... | How to interpret negative ACF (autocorrelation function)? | Negative ACF means that a positive oil return for one observation increases the probability of having a negative oil return for another observation (depending on the lag) and vice-versa. Or you can sa | How to interpret negative ACF (autocorrelation function)?
Negative ACF means that a positive oil return for one observation increases the probability of having a negative oil return for another observation (depending on the lag) and vice-versa. Or you can say (for a stationary time series) if one observation is above t... | How to interpret negative ACF (autocorrelation function)?
Negative ACF means that a positive oil return for one observation increases the probability of having a negative oil return for another observation (depending on the lag) and vice-versa. Or you can sa |
12,849 | Why does the least square solution give poor results in this case? | The particular phenomenon that you see with the least squares solution in Bishops Figure 4.5 is a phenomenon that only occurs when the number of classes is $\geq 3$.
In ESL, Figure 4.2 on page 105, the phenomenon is called masking. See also ESL Figure 4.3. The least squares solution results in a predictor for the midd... | Why does the least square solution give poor results in this case? | The particular phenomenon that you see with the least squares solution in Bishops Figure 4.5 is a phenomenon that only occurs when the number of classes is $\geq 3$.
In ESL, Figure 4.2 on page 105, t | Why does the least square solution give poor results in this case?
The particular phenomenon that you see with the least squares solution in Bishops Figure 4.5 is a phenomenon that only occurs when the number of classes is $\geq 3$.
In ESL, Figure 4.2 on page 105, the phenomenon is called masking. See also ESL Figure ... | Why does the least square solution give poor results in this case?
The particular phenomenon that you see with the least squares solution in Bishops Figure 4.5 is a phenomenon that only occurs when the number of classes is $\geq 3$.
In ESL, Figure 4.2 on page 105, t |
12,850 | Why does the least square solution give poor results in this case? | Based on the link provided below, the reasons why LS discriminant is not performing good in the upper left graph are as follow:
-Lack of robustness to outliers.
- Certain datasets unsuitable for least squares classification.
- Decision boundary corresponds to ML solution under Gaussian conditional distribution. But bi... | Why does the least square solution give poor results in this case? | Based on the link provided below, the reasons why LS discriminant is not performing good in the upper left graph are as follow:
-Lack of robustness to outliers.
- Certain datasets unsuitable for least | Why does the least square solution give poor results in this case?
Based on the link provided below, the reasons why LS discriminant is not performing good in the upper left graph are as follow:
-Lack of robustness to outliers.
- Certain datasets unsuitable for least squares classification.
- Decision boundary correspo... | Why does the least square solution give poor results in this case?
Based on the link provided below, the reasons why LS discriminant is not performing good in the upper left graph are as follow:
-Lack of robustness to outliers.
- Certain datasets unsuitable for least |
12,851 | Why does the least square solution give poor results in this case? | I believe the issue in your first graph is called "masking", and it's mentioned in "The Elements of statistical learning: Data mining, inference, and prediction" (Hastie, Tibshirani, Friedman. Springer 2001), pages 83-84.
Intuitively (which is the best I can do) I believe this is because predictions of an OLS regressio... | Why does the least square solution give poor results in this case? | I believe the issue in your first graph is called "masking", and it's mentioned in "The Elements of statistical learning: Data mining, inference, and prediction" (Hastie, Tibshirani, Friedman. Springe | Why does the least square solution give poor results in this case?
I believe the issue in your first graph is called "masking", and it's mentioned in "The Elements of statistical learning: Data mining, inference, and prediction" (Hastie, Tibshirani, Friedman. Springer 2001), pages 83-84.
Intuitively (which is the best ... | Why does the least square solution give poor results in this case?
I believe the issue in your first graph is called "masking", and it's mentioned in "The Elements of statistical learning: Data mining, inference, and prediction" (Hastie, Tibshirani, Friedman. Springe |
12,852 | Why does the least square solution give poor results in this case? | Least square is sensitive to scale ( because the new data is of different scale, it will skew the decision boundary) , one usually needs either apply weights (means data to enter to the optimization algorithm is of the same scale) or perform a suitable transformation (mean center, log(1+data) ...etc) on data in such ... | Why does the least square solution give poor results in this case? | Least square is sensitive to scale ( because the new data is of different scale, it will skew the decision boundary) , one usually needs either apply weights (means data to enter to the optimization a | Why does the least square solution give poor results in this case?
Least square is sensitive to scale ( because the new data is of different scale, it will skew the decision boundary) , one usually needs either apply weights (means data to enter to the optimization algorithm is of the same scale) or perform a suitable... | Why does the least square solution give poor results in this case?
Least square is sensitive to scale ( because the new data is of different scale, it will skew the decision boundary) , one usually needs either apply weights (means data to enter to the optimization a |
12,853 | How exactly does Chi-square feature selection work? | The chi-square test is a statistical test of independence to determine the dependency of two variables. It shares similarities with coefficient of determination, R². However, chi-square test is only applicable to categorical or nominal data while R² is only applicable to numeric data.
From the definition, of chi-square... | How exactly does Chi-square feature selection work? | The chi-square test is a statistical test of independence to determine the dependency of two variables. It shares similarities with coefficient of determination, R². However, chi-square test is only a | How exactly does Chi-square feature selection work?
The chi-square test is a statistical test of independence to determine the dependency of two variables. It shares similarities with coefficient of determination, R². However, chi-square test is only applicable to categorical or nominal data while R² is only applicable... | How exactly does Chi-square feature selection work?
The chi-square test is a statistical test of independence to determine the dependency of two variables. It shares similarities with coefficient of determination, R². However, chi-square test is only a |
12,854 | Adjusting for covariates in ROC curve analysis | The way that you've envisioned the analysis is really not the way I would suggest you start out thinking about it. First of all it is easy to show that if cutoffs must be used, cutoffs are not applied on individual features but on the overall predicted probability. The optimal cutoff for a single covariate depends on... | Adjusting for covariates in ROC curve analysis | The way that you've envisioned the analysis is really not the way I would suggest you start out thinking about it. First of all it is easy to show that if cutoffs must be used, cutoffs are not applie | Adjusting for covariates in ROC curve analysis
The way that you've envisioned the analysis is really not the way I would suggest you start out thinking about it. First of all it is easy to show that if cutoffs must be used, cutoffs are not applied on individual features but on the overall predicted probability. The o... | Adjusting for covariates in ROC curve analysis
The way that you've envisioned the analysis is really not the way I would suggest you start out thinking about it. First of all it is easy to show that if cutoffs must be used, cutoffs are not applie |
12,855 | Adjusting for covariates in ROC curve analysis | The point of the Janes, Pepe article on covariate adjusted ROC curves is allowing a more flexible interpretation of the estimated ROC curve values. This is a method of stratifying ROC curves among specific groups in the population of interest. The estimated true positive fraction (TPF; eq. sensitivity) and true negativ... | Adjusting for covariates in ROC curve analysis | The point of the Janes, Pepe article on covariate adjusted ROC curves is allowing a more flexible interpretation of the estimated ROC curve values. This is a method of stratifying ROC curves among spe | Adjusting for covariates in ROC curve analysis
The point of the Janes, Pepe article on covariate adjusted ROC curves is allowing a more flexible interpretation of the estimated ROC curve values. This is a method of stratifying ROC curves among specific groups in the population of interest. The estimated true positive f... | Adjusting for covariates in ROC curve analysis
The point of the Janes, Pepe article on covariate adjusted ROC curves is allowing a more flexible interpretation of the estimated ROC curve values. This is a method of stratifying ROC curves among spe |
12,856 | What is the difference between $R^2$ and variance score in Scikit-learn? | $R^2 = 1- \frac{SSE}{TSS}$
$\text{explained variance score} = 1 - \mathrm{Var}[\hat{y} - y]\, /\, \mathrm{Var}[y]$, where the $\mathrm{Var}$ is biased variance, i.e. $\mathrm{Var}[\hat{y} - y] = \frac{1}{n}\sum(error - mean(error))^2$. Compared with $R^2$, the only difference is from the mean(error). if mean(error)=0,... | What is the difference between $R^2$ and variance score in Scikit-learn? | $R^2 = 1- \frac{SSE}{TSS}$
$\text{explained variance score} = 1 - \mathrm{Var}[\hat{y} - y]\, /\, \mathrm{Var}[y]$, where the $\mathrm{Var}$ is biased variance, i.e. $\mathrm{Var}[\hat{y} - y] = \fra | What is the difference between $R^2$ and variance score in Scikit-learn?
$R^2 = 1- \frac{SSE}{TSS}$
$\text{explained variance score} = 1 - \mathrm{Var}[\hat{y} - y]\, /\, \mathrm{Var}[y]$, where the $\mathrm{Var}$ is biased variance, i.e. $\mathrm{Var}[\hat{y} - y] = \frac{1}{n}\sum(error - mean(error))^2$. Compared w... | What is the difference between $R^2$ and variance score in Scikit-learn?
$R^2 = 1- \frac{SSE}{TSS}$
$\text{explained variance score} = 1 - \mathrm{Var}[\hat{y} - y]\, /\, \mathrm{Var}[y]$, where the $\mathrm{Var}$ is biased variance, i.e. $\mathrm{Var}[\hat{y} - y] = \fra |
12,857 | What is the difference between $R^2$ and variance score in Scikit-learn? | Dean's answer is right.
Only I think there is a minor typo here:
$Var[\hat{y}-y]=sum(error^2-mean(error))/n$.
I guess it should be $Var[\hat{y}-y]=sum(error-mean(error))^2/n$.
My reference is the source code of sklearn here:https://github.com/scikit-learn/scikit-learn/blob/bf24c7e3d/sklearn/metrics/_regression.py#L396 | What is the difference between $R^2$ and variance score in Scikit-learn? | Dean's answer is right.
Only I think there is a minor typo here:
$Var[\hat{y}-y]=sum(error^2-mean(error))/n$.
I guess it should be $Var[\hat{y}-y]=sum(error-mean(error))^2/n$.
My reference is the sou | What is the difference between $R^2$ and variance score in Scikit-learn?
Dean's answer is right.
Only I think there is a minor typo here:
$Var[\hat{y}-y]=sum(error^2-mean(error))/n$.
I guess it should be $Var[\hat{y}-y]=sum(error-mean(error))^2/n$.
My reference is the source code of sklearn here:https://github.com/sci... | What is the difference between $R^2$ and variance score in Scikit-learn?
Dean's answer is right.
Only I think there is a minor typo here:
$Var[\hat{y}-y]=sum(error^2-mean(error))/n$.
I guess it should be $Var[\hat{y}-y]=sum(error-mean(error))^2/n$.
My reference is the sou |
12,858 | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function different from Logistic Regression? | Using gradient descent, we optimize (minimize) the cost function
$$J(\mathbf{w}) = \sum_{i} \frac{1}{2}(y_i - \hat{y_i})^2 \quad \quad y_i,\hat{y_i} \in \mathbb{R}$$
If you minimize the mean squared error, then it's different from logistic regression. Logistic regression is normally associated with the cross entropy ... | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function | Using gradient descent, we optimize (minimize) the cost function
$$J(\mathbf{w}) = \sum_{i} \frac{1}{2}(y_i - \hat{y_i})^2 \quad \quad y_i,\hat{y_i} \in \mathbb{R}$$
If you minimize the mean squared | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function different from Logistic Regression?
Using gradient descent, we optimize (minimize) the cost function
$$J(\mathbf{w}) = \sum_{i} \frac{1}{2}(y_i - \hat{y_i})^2 \quad \quad y_i,\hat{y_i} \in \mathbb{R}$$
If you minimize... | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function
Using gradient descent, we optimize (minimize) the cost function
$$J(\mathbf{w}) = \sum_{i} \frac{1}{2}(y_i - \hat{y_i})^2 \quad \quad y_i,\hat{y_i} \in \mathbb{R}$$
If you minimize the mean squared |
12,859 | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function different from Logistic Regression? | Because gradient descent updates each parameter in a way that it reduces output error which must be continues function of all parameters. Threshold based activation is not differentiable that is why sigmoid or tanh activation is used.
Here is a single-layer NN
$\frac{dJ(w,b)}{d\omega_{kj}} =\frac{dJ(w,b)}{dz_k}\cdot \... | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function | Because gradient descent updates each parameter in a way that it reduces output error which must be continues function of all parameters. Threshold based activation is not differentiable that is why s | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function different from Logistic Regression?
Because gradient descent updates each parameter in a way that it reduces output error which must be continues function of all parameters. Threshold based activation is not differentia... | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function
Because gradient descent updates each parameter in a way that it reduces output error which must be continues function of all parameters. Threshold based activation is not differentiable that is why s |
12,860 | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function different from Logistic Regression? | Intuitively, I think of a multilayer perceptron as computing a nonlinear transformation on my input features, and then feeding these transformed variables into a logistic regression.
The multinomial (that is, N > 2 possible labels) case may make this more clear. In traditional logistic regression, for a given data poi... | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function | Intuitively, I think of a multilayer perceptron as computing a nonlinear transformation on my input features, and then feeding these transformed variables into a logistic regression.
The multinomial ( | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function different from Logistic Regression?
Intuitively, I think of a multilayer perceptron as computing a nonlinear transformation on my input features, and then feeding these transformed variables into a logistic regression.
... | From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function
Intuitively, I think of a multilayer perceptron as computing a nonlinear transformation on my input features, and then feeding these transformed variables into a logistic regression.
The multinomial ( |
12,861 | If the LASSO is equivalent to linear regression with a Laplace prior how can there be mass on sets with components at zero? | Like all the comments above, the Bayesian interpretation of LASSO is not taking the expected value of the posterior distribution, which is what you would want to do if you were a purist. If that would be the case, then you would be right that there is very small chance that the posterior would be zero given the data.... | If the LASSO is equivalent to linear regression with a Laplace prior how can there be mass on sets w | Like all the comments above, the Bayesian interpretation of LASSO is not taking the expected value of the posterior distribution, which is what you would want to do if you were a purist. If that wou | If the LASSO is equivalent to linear regression with a Laplace prior how can there be mass on sets with components at zero?
Like all the comments above, the Bayesian interpretation of LASSO is not taking the expected value of the posterior distribution, which is what you would want to do if you were a purist. If that... | If the LASSO is equivalent to linear regression with a Laplace prior how can there be mass on sets w
Like all the comments above, the Bayesian interpretation of LASSO is not taking the expected value of the posterior distribution, which is what you would want to do if you were a purist. If that wou |
12,862 | How can I pool posterior means and credible intervals after multiple imputation? | With particularly well-behaved posteriors that can be adequately described by a parametric description of a distribution, you might be able to simply take the mean and variance that best describes your posterior and go from there. I suspect this may be adequate in many circumstances where you aren't getting genuinely o... | How can I pool posterior means and credible intervals after multiple imputation? | With particularly well-behaved posteriors that can be adequately described by a parametric description of a distribution, you might be able to simply take the mean and variance that best describes you | How can I pool posterior means and credible intervals after multiple imputation?
With particularly well-behaved posteriors that can be adequately described by a parametric description of a distribution, you might be able to simply take the mean and variance that best describes your posterior and go from there. I suspec... | How can I pool posterior means and credible intervals after multiple imputation?
With particularly well-behaved posteriors that can be adequately described by a parametric description of a distribution, you might be able to simply take the mean and variance that best describes you |
12,863 | How can I pool posterior means and credible intervals after multiple imputation? | Yes, based on the paper by Zhou et al , you can simply combine the MCMC draws from each imputed dataset and combine them together to approximate the posterior distribution. However, based on their simulations (as noted in the paper), this approach requires a large number of imputed datasets (e.g., 100). | How can I pool posterior means and credible intervals after multiple imputation? | Yes, based on the paper by Zhou et al , you can simply combine the MCMC draws from each imputed dataset and combine them together to approximate the posterior distribution. However, based on their sim | How can I pool posterior means and credible intervals after multiple imputation?
Yes, based on the paper by Zhou et al , you can simply combine the MCMC draws from each imputed dataset and combine them together to approximate the posterior distribution. However, based on their simulations (as noted in the paper), this ... | How can I pool posterior means and credible intervals after multiple imputation?
Yes, based on the paper by Zhou et al , you can simply combine the MCMC draws from each imputed dataset and combine them together to approximate the posterior distribution. However, based on their sim |
12,864 | How can I pool posterior means and credible intervals after multiple imputation? | If you use stata there is a procedure called "mim" that pooled the data after imputation using for mixed effect models. I don't know if it is available in R. | How can I pool posterior means and credible intervals after multiple imputation? | If you use stata there is a procedure called "mim" that pooled the data after imputation using for mixed effect models. I don't know if it is available in R. | How can I pool posterior means and credible intervals after multiple imputation?
If you use stata there is a procedure called "mim" that pooled the data after imputation using for mixed effect models. I don't know if it is available in R. | How can I pool posterior means and credible intervals after multiple imputation?
If you use stata there is a procedure called "mim" that pooled the data after imputation using for mixed effect models. I don't know if it is available in R. |
12,865 | What does it mean to take the expectation with respect to a probability distribution? | The expression
$$\mathbb E[g(x;y;\theta;h(x,z),...)]$$
always means "the expected value with respect to the joint distribution of all things having a non-degenerate distribution inside the brackets."
Once you start putting subscripts in $\mathbb E$ then you specify perhaps a "narrower" joint distribution for which you ... | What does it mean to take the expectation with respect to a probability distribution? | The expression
$$\mathbb E[g(x;y;\theta;h(x,z),...)]$$
always means "the expected value with respect to the joint distribution of all things having a non-degenerate distribution inside the brackets."
| What does it mean to take the expectation with respect to a probability distribution?
The expression
$$\mathbb E[g(x;y;\theta;h(x,z),...)]$$
always means "the expected value with respect to the joint distribution of all things having a non-degenerate distribution inside the brackets."
Once you start putting subscripts ... | What does it mean to take the expectation with respect to a probability distribution?
The expression
$$\mathbb E[g(x;y;\theta;h(x,z),...)]$$
always means "the expected value with respect to the joint distribution of all things having a non-degenerate distribution inside the brackets."
|
12,866 | Why does XGBoost have a learning rate? | In particular, am I missing something jumping out at me from these two equations?
From what I've looked at in Friedman's paper, the 'learning rate' $\epsilon$ (there, called 'shrinkage' and denoted by $\nu$) is applied after choosing those weights $w_j^*$ which minimise the cost function. That is, we determine the boo... | Why does XGBoost have a learning rate? | In particular, am I missing something jumping out at me from these two equations?
From what I've looked at in Friedman's paper, the 'learning rate' $\epsilon$ (there, called 'shrinkage' and denoted b | Why does XGBoost have a learning rate?
In particular, am I missing something jumping out at me from these two equations?
From what I've looked at in Friedman's paper, the 'learning rate' $\epsilon$ (there, called 'shrinkage' and denoted by $\nu$) is applied after choosing those weights $w_j^*$ which minimise the cost ... | Why does XGBoost have a learning rate?
In particular, am I missing something jumping out at me from these two equations?
From what I've looked at in Friedman's paper, the 'learning rate' $\epsilon$ (there, called 'shrinkage' and denoted b |
12,867 | Why does XGBoost have a learning rate? | In my opinion, classical boosting and XGBoost have almost the same grounds for the learning rate. I personally see two three reasons for this.
A common approach is to view classical boosting as gradient descent (GD) in the function space ([1], p.3). As for the simplest univariate GD, we need to define a learning rate... | Why does XGBoost have a learning rate? | In my opinion, classical boosting and XGBoost have almost the same grounds for the learning rate. I personally see two three reasons for this.
A common approach is to view classical boosting as grad | Why does XGBoost have a learning rate?
In my opinion, classical boosting and XGBoost have almost the same grounds for the learning rate. I personally see two three reasons for this.
A common approach is to view classical boosting as gradient descent (GD) in the function space ([1], p.3). As for the simplest univariat... | Why does XGBoost have a learning rate?
In my opinion, classical boosting and XGBoost have almost the same grounds for the learning rate. I personally see two three reasons for this.
A common approach is to view classical boosting as grad |
12,868 | Why does XGBoost have a learning rate? | Parameters for Tree Booster eta [default=0.3, alias: learning_rate]
step size shrinkage used in update to prevents overfitting. After each
boosting step, we can directly get the weights of new features. and
eta actually shrinks the feature weights to make the boosting process
more conservative. range: [0,1]
Fr... | Why does XGBoost have a learning rate? | Parameters for Tree Booster eta [default=0.3, alias: learning_rate]
step size shrinkage used in update to prevents overfitting. After each
boosting step, we can directly get the weights of new fea | Why does XGBoost have a learning rate?
Parameters for Tree Booster eta [default=0.3, alias: learning_rate]
step size shrinkage used in update to prevents overfitting. After each
boosting step, we can directly get the weights of new features. and
eta actually shrinks the feature weights to make the boosting proces... | Why does XGBoost have a learning rate?
Parameters for Tree Booster eta [default=0.3, alias: learning_rate]
step size shrinkage used in update to prevents overfitting. After each
boosting step, we can directly get the weights of new fea |
12,869 | Why does XGBoost have a learning rate? | Adding to montols answer:
I think he is right on most points, except that, from my understanding, it is the learning rate 𝜖, not 𝜆, that controls for validity of the Taylor expansion(TE). This is because 𝜖 scales the final step size taken towards the TE-minimum and for small 𝜖 TE clearly becomes a better approximat... | Why does XGBoost have a learning rate? | Adding to montols answer:
I think he is right on most points, except that, from my understanding, it is the learning rate 𝜖, not 𝜆, that controls for validity of the Taylor expansion(TE). This is beca | Why does XGBoost have a learning rate?
Adding to montols answer:
I think he is right on most points, except that, from my understanding, it is the learning rate 𝜖, not 𝜆, that controls for validity of the Taylor expansion(TE). This is because 𝜖 scales the final step size taken towards the TE-minimum and for small 𝜖... | Why does XGBoost have a learning rate?
Adding to montols answer:
I think he is right on most points, except that, from my understanding, it is the learning rate 𝜖, not 𝜆, that controls for validity of the Taylor expansion(TE). This is beca |
12,870 | Link between variance and pairwise distances within a variable | Just to provide an "official" answer, to supplement the solutions sketched in the comments, notice
None of $\operatorname{Var} ((X_i))$, $\operatorname{Var} ((Y_i))$, $\sum_{i,j}(X_i-X_j)^2$, or $\sum_{i,j} (Y_i-Y_j)^2$ are changed by shifting all $X_i$ uniformly to $X_i-\mu$ for some constant $\mu$ or shifting all $Y... | Link between variance and pairwise distances within a variable | Just to provide an "official" answer, to supplement the solutions sketched in the comments, notice
None of $\operatorname{Var} ((X_i))$, $\operatorname{Var} ((Y_i))$, $\sum_{i,j}(X_i-X_j)^2$, or $\su | Link between variance and pairwise distances within a variable
Just to provide an "official" answer, to supplement the solutions sketched in the comments, notice
None of $\operatorname{Var} ((X_i))$, $\operatorname{Var} ((Y_i))$, $\sum_{i,j}(X_i-X_j)^2$, or $\sum_{i,j} (Y_i-Y_j)^2$ are changed by shifting all $X_i$ un... | Link between variance and pairwise distances within a variable
Just to provide an "official" answer, to supplement the solutions sketched in the comments, notice
None of $\operatorname{Var} ((X_i))$, $\operatorname{Var} ((Y_i))$, $\sum_{i,j}(X_i-X_j)^2$, or $\su |
12,871 | Marginal distribution of the diagonal of an inverse Wishart distributed matrix | In general one can decompose a any covariance matrix into a variance-correlation decomposition as
$$ \Sigma = \text{diag}(\Sigma) \ Q \ \text{diag}(\Sigma)^\top = D\ Q \ D^\top$$
Here $Q$ is the correlation matrix with unit diagonals $q_{ii} = 1$. Thus, the diagonal entries of $\Sigma$ are now a part of a diagonal m... | Marginal distribution of the diagonal of an inverse Wishart distributed matrix | In general one can decompose a any covariance matrix into a variance-correlation decomposition as
$$ \Sigma = \text{diag}(\Sigma) \ Q \ \text{diag}(\Sigma)^\top = D\ Q \ D^\top$$
Here $Q$ is the co | Marginal distribution of the diagonal of an inverse Wishart distributed matrix
In general one can decompose a any covariance matrix into a variance-correlation decomposition as
$$ \Sigma = \text{diag}(\Sigma) \ Q \ \text{diag}(\Sigma)^\top = D\ Q \ D^\top$$
Here $Q$ is the correlation matrix with unit diagonals $q_{... | Marginal distribution of the diagonal of an inverse Wishart distributed matrix
In general one can decompose a any covariance matrix into a variance-correlation decomposition as
$$ \Sigma = \text{diag}(\Sigma) \ Q \ \text{diag}(\Sigma)^\top = D\ Q \ D^\top$$
Here $Q$ is the co |
12,872 | Is there such a thing as an adjusted $R^2$ for a quantile regression model? | I think what the reviewers are asking is to take the pseudo-$R^2$-values and "unbias" them for number of samples in the quantile range, $n_Q$, and number of parameters in the model, $p$. In other words, adjusted-$R^2$ in its usual context. That is that the corrected unexplained fraction is larger than the gross unexpla... | Is there such a thing as an adjusted $R^2$ for a quantile regression model? | I think what the reviewers are asking is to take the pseudo-$R^2$-values and "unbias" them for number of samples in the quantile range, $n_Q$, and number of parameters in the model, $p$. In other word | Is there such a thing as an adjusted $R^2$ for a quantile regression model?
I think what the reviewers are asking is to take the pseudo-$R^2$-values and "unbias" them for number of samples in the quantile range, $n_Q$, and number of parameters in the model, $p$. In other words, adjusted-$R^2$ in its usual context. That... | Is there such a thing as an adjusted $R^2$ for a quantile regression model?
I think what the reviewers are asking is to take the pseudo-$R^2$-values and "unbias" them for number of samples in the quantile range, $n_Q$, and number of parameters in the model, $p$. In other word |
12,873 | Is there such a thing as an adjusted $R^2$ for a quantile regression model? | You had better not use $R^2$ to compare two quantile regression models, because the quantile regression model's loss function is not based on MSE.
You can try AIC or BIC. | Is there such a thing as an adjusted $R^2$ for a quantile regression model? | You had better not use $R^2$ to compare two quantile regression models, because the quantile regression model's loss function is not based on MSE.
You can try AIC or BIC. | Is there such a thing as an adjusted $R^2$ for a quantile regression model?
You had better not use $R^2$ to compare two quantile regression models, because the quantile regression model's loss function is not based on MSE.
You can try AIC or BIC. | Is there such a thing as an adjusted $R^2$ for a quantile regression model?
You had better not use $R^2$ to compare two quantile regression models, because the quantile regression model's loss function is not based on MSE.
You can try AIC or BIC. |
12,874 | Multiple mediation analysis in R | The lavaan package is an R package for SEM. You can use it to test for multiple mediation hypothesis, and there is boostrap. | Multiple mediation analysis in R | The lavaan package is an R package for SEM. You can use it to test for multiple mediation hypothesis, and there is boostrap. | Multiple mediation analysis in R
The lavaan package is an R package for SEM. You can use it to test for multiple mediation hypothesis, and there is boostrap. | Multiple mediation analysis in R
The lavaan package is an R package for SEM. You can use it to test for multiple mediation hypothesis, and there is boostrap. |
12,875 | First step for big data ($N = 10^{10}$, $p = 2000$) | You should check out online methods for regression and classification for datasets of this size. These approaches would let you use the whole dataset without having to load it into memory.
You might also check out Vowpal Wabbit (VW):
https://github.com/JohnLangford/vowpal_wabbit/wiki
It uses an out of core online metho... | First step for big data ($N = 10^{10}$, $p = 2000$) | You should check out online methods for regression and classification for datasets of this size. These approaches would let you use the whole dataset without having to load it into memory.
You might a | First step for big data ($N = 10^{10}$, $p = 2000$)
You should check out online methods for regression and classification for datasets of this size. These approaches would let you use the whole dataset without having to load it into memory.
You might also check out Vowpal Wabbit (VW):
https://github.com/JohnLangford/vo... | First step for big data ($N = 10^{10}$, $p = 2000$)
You should check out online methods for regression and classification for datasets of this size. These approaches would let you use the whole dataset without having to load it into memory.
You might a |
12,876 | First step for big data ($N = 10^{10}$, $p = 2000$) | I would suggest using Hadoop and RMR (a specific package for Map Reduce in R).
With this strategy you can run large datasets on comodity computers with an affordable configuration (probably in two hours you come up with both Hadoop and RMR (RHadoop) installed and running).
In fact, if you have more than one computer yo... | First step for big data ($N = 10^{10}$, $p = 2000$) | I would suggest using Hadoop and RMR (a specific package for Map Reduce in R).
With this strategy you can run large datasets on comodity computers with an affordable configuration (probably in two hou | First step for big data ($N = 10^{10}$, $p = 2000$)
I would suggest using Hadoop and RMR (a specific package for Map Reduce in R).
With this strategy you can run large datasets on comodity computers with an affordable configuration (probably in two hours you come up with both Hadoop and RMR (RHadoop) installed and runn... | First step for big data ($N = 10^{10}$, $p = 2000$)
I would suggest using Hadoop and RMR (a specific package for Map Reduce in R).
With this strategy you can run large datasets on comodity computers with an affordable configuration (probably in two hou |
12,877 | First step for big data ($N = 10^{10}$, $p = 2000$) | This is more a comment than an answer, but I can't post it as a comment (requires 50 rep)..
Have you tried to use PCA on your dataset? It can help you to reduce the variable space and find a possible direction on which variable exclude from you regression model. Doing so, the model will be easier to compute.
Here you c... | First step for big data ($N = 10^{10}$, $p = 2000$) | This is more a comment than an answer, but I can't post it as a comment (requires 50 rep)..
Have you tried to use PCA on your dataset? It can help you to reduce the variable space and find a possible | First step for big data ($N = 10^{10}$, $p = 2000$)
This is more a comment than an answer, but I can't post it as a comment (requires 50 rep)..
Have you tried to use PCA on your dataset? It can help you to reduce the variable space and find a possible direction on which variable exclude from you regression model. Doing... | First step for big data ($N = 10^{10}$, $p = 2000$)
This is more a comment than an answer, but I can't post it as a comment (requires 50 rep)..
Have you tried to use PCA on your dataset? It can help you to reduce the variable space and find a possible |
12,878 | "Interestingness" function for StackExchange questions | One might define an interesting question as one that has received comparatively many votes given the number of views. To this end, you can create a baseline curve that reflects the expected number of votes given the views. Curves that attracted a lot more votes than the baseline were considered particularly interesting... | "Interestingness" function for StackExchange questions | One might define an interesting question as one that has received comparatively many votes given the number of views. To this end, you can create a baseline curve that reflects the expected number of | "Interestingness" function for StackExchange questions
One might define an interesting question as one that has received comparatively many votes given the number of views. To this end, you can create a baseline curve that reflects the expected number of votes given the views. Curves that attracted a lot more votes tha... | "Interestingness" function for StackExchange questions
One might define an interesting question as one that has received comparatively many votes given the number of views. To this end, you can create a baseline curve that reflects the expected number of |
12,879 | "Interestingness" function for StackExchange questions | This is my theory. I think there are two kinds of questions: those that remain mostly within SE (which usually have fewer views), and those that are viewed by outsiders because it was linked from somewhere else (usually have more views).
For the questions that remain mostly within SE, votes are a good measure of inter... | "Interestingness" function for StackExchange questions | This is my theory. I think there are two kinds of questions: those that remain mostly within SE (which usually have fewer views), and those that are viewed by outsiders because it was linked from some | "Interestingness" function for StackExchange questions
This is my theory. I think there are two kinds of questions: those that remain mostly within SE (which usually have fewer views), and those that are viewed by outsiders because it was linked from somewhere else (usually have more views).
For the questions that rem... | "Interestingness" function for StackExchange questions
This is my theory. I think there are two kinds of questions: those that remain mostly within SE (which usually have fewer views), and those that are viewed by outsiders because it was linked from some |
12,880 | Model selection with Firth logistic regression | If you want to justify the use of BIC: you can replace the maximum likelihood with the maximum a posteriori (MAP) estimate and the resulting 'BIC'-type criterion remains asymptotically valid (in the limit as the sample size $n \to \infty$). As mentioned by @probabilityislogic, Firth's logistic regression is equivalent ... | Model selection with Firth logistic regression | If you want to justify the use of BIC: you can replace the maximum likelihood with the maximum a posteriori (MAP) estimate and the resulting 'BIC'-type criterion remains asymptotically valid (in the l | Model selection with Firth logistic regression
If you want to justify the use of BIC: you can replace the maximum likelihood with the maximum a posteriori (MAP) estimate and the resulting 'BIC'-type criterion remains asymptotically valid (in the limit as the sample size $n \to \infty$). As mentioned by @probabilityislo... | Model selection with Firth logistic regression
If you want to justify the use of BIC: you can replace the maximum likelihood with the maximum a posteriori (MAP) estimate and the resulting 'BIC'-type criterion remains asymptotically valid (in the l |
12,881 | Latent variable interpretation of generalized linear models (GLMs) | For models with more than one discrete outcome, there are several versions of logit models (e.g. conditional logit, multinomial logit, mixed logit, nested logit, ...). See Kenneth Train's book on the subject:
For example, in conditional logit, the outcome, $y$, is the car chosen by an individual, and there may be, say ... | Latent variable interpretation of generalized linear models (GLMs) | For models with more than one discrete outcome, there are several versions of logit models (e.g. conditional logit, multinomial logit, mixed logit, nested logit, ...). See Kenneth Train's book on the | Latent variable interpretation of generalized linear models (GLMs)
For models with more than one discrete outcome, there are several versions of logit models (e.g. conditional logit, multinomial logit, mixed logit, nested logit, ...). See Kenneth Train's book on the subject:
For example, in conditional logit, the outco... | Latent variable interpretation of generalized linear models (GLMs)
For models with more than one discrete outcome, there are several versions of logit models (e.g. conditional logit, multinomial logit, mixed logit, nested logit, ...). See Kenneth Train's book on the |
12,882 | Is there an example where MLE produces a biased estimate of the mean? | Christoph Hanck has not posted the details of his proposed example. I take it he means the uniform distribution on the interval $[0,\theta],$ based on an i.i.d. sample $X_1,\ldots,X_n$ of size more than $n=1.$
The mean is $\theta/2$.
The MLE of the mean is $\max\{X_1,\ldots,X_n\}/2.$
That is biased since $\Pr(\max < \t... | Is there an example where MLE produces a biased estimate of the mean? | Christoph Hanck has not posted the details of his proposed example. I take it he means the uniform distribution on the interval $[0,\theta],$ based on an i.i.d. sample $X_1,\ldots,X_n$ of size more th | Is there an example where MLE produces a biased estimate of the mean?
Christoph Hanck has not posted the details of his proposed example. I take it he means the uniform distribution on the interval $[0,\theta],$ based on an i.i.d. sample $X_1,\ldots,X_n$ of size more than $n=1.$
The mean is $\theta/2$.
The MLE of the m... | Is there an example where MLE produces a biased estimate of the mean?
Christoph Hanck has not posted the details of his proposed example. I take it he means the uniform distribution on the interval $[0,\theta],$ based on an i.i.d. sample $X_1,\ldots,X_n$ of size more th |
12,883 | Is there an example where MLE produces a biased estimate of the mean? | Here's an example that I think some may find surprising:
In logistic regression, for any finite sample size with non-deterministic outcomes (i.e. $0 < p_{i} < 1$), any estimated regression coefficient is not only biased, the mean of the regression coefficient is actually undefined.
This is because for any finite samp... | Is there an example where MLE produces a biased estimate of the mean? | Here's an example that I think some may find surprising:
In logistic regression, for any finite sample size with non-deterministic outcomes (i.e. $0 < p_{i} < 1$), any estimated regression coefficien | Is there an example where MLE produces a biased estimate of the mean?
Here's an example that I think some may find surprising:
In logistic regression, for any finite sample size with non-deterministic outcomes (i.e. $0 < p_{i} < 1$), any estimated regression coefficient is not only biased, the mean of the regression c... | Is there an example where MLE produces a biased estimate of the mean?
Here's an example that I think some may find surprising:
In logistic regression, for any finite sample size with non-deterministic outcomes (i.e. $0 < p_{i} < 1$), any estimated regression coefficien |
12,884 | Is there an example where MLE produces a biased estimate of the mean? | Although @MichaelHardy has made the point, here is a more detailed argument as to why the MLE of the maximum (and hence, that of the mean $\theta/2$, by invariance) is not unbiased, although it is in a different model (see the edit below).
We estimate the upper bound of the uniform distribution $U[0,\theta]$. Here, $y... | Is there an example where MLE produces a biased estimate of the mean? | Although @MichaelHardy has made the point, here is a more detailed argument as to why the MLE of the maximum (and hence, that of the mean $\theta/2$, by invariance) is not unbiased, although it is in | Is there an example where MLE produces a biased estimate of the mean?
Although @MichaelHardy has made the point, here is a more detailed argument as to why the MLE of the maximum (and hence, that of the mean $\theta/2$, by invariance) is not unbiased, although it is in a different model (see the edit below).
We estimat... | Is there an example where MLE produces a biased estimate of the mean?
Although @MichaelHardy has made the point, here is a more detailed argument as to why the MLE of the maximum (and hence, that of the mean $\theta/2$, by invariance) is not unbiased, although it is in |
12,885 | Is there an example where MLE produces a biased estimate of the mean? | Completing here the omission in my answer over at math.se referenced by the OP,
assume that we have an i.i.d. sample of size $n$ of random variables following the Half Normal distribution. The density and moments of this distribution are
$$f_H(x) = \sqrt{2/\pi}\cdot \frac 1{v^{1/2}}\cdot \exp\big\{-\frac {x^2}{2v} \... | Is there an example where MLE produces a biased estimate of the mean? | Completing here the omission in my answer over at math.se referenced by the OP,
assume that we have an i.i.d. sample of size $n$ of random variables following the Half Normal distribution. The dens | Is there an example where MLE produces a biased estimate of the mean?
Completing here the omission in my answer over at math.se referenced by the OP,
assume that we have an i.i.d. sample of size $n$ of random variables following the Half Normal distribution. The density and moments of this distribution are
$$f_H(x) ... | Is there an example where MLE produces a biased estimate of the mean?
Completing here the omission in my answer over at math.se referenced by the OP,
assume that we have an i.i.d. sample of size $n$ of random variables following the Half Normal distribution. The dens |
12,886 | Is there an example where MLE produces a biased estimate of the mean? | The famous Neyman Scott problem has an inconsistent MLE in that it never even converges to the right thing. Motivates the use of conditional likelihood.
Take $(X_i, Y_i) \sim \mathcal{N}\left(\mu_i, \sigma^2 \right)$. The MLE of $\mu_i$ is $(X_i + Y_i)/2$ and of $\sigma^2$ is $\hat{\sigma}^2 = \sum_{i=1}^n \frac{1}{n} ... | Is there an example where MLE produces a biased estimate of the mean? | The famous Neyman Scott problem has an inconsistent MLE in that it never even converges to the right thing. Motivates the use of conditional likelihood.
Take $(X_i, Y_i) \sim \mathcal{N}\left(\mu_i, \ | Is there an example where MLE produces a biased estimate of the mean?
The famous Neyman Scott problem has an inconsistent MLE in that it never even converges to the right thing. Motivates the use of conditional likelihood.
Take $(X_i, Y_i) \sim \mathcal{N}\left(\mu_i, \sigma^2 \right)$. The MLE of $\mu_i$ is $(X_i + Y_... | Is there an example where MLE produces a biased estimate of the mean?
The famous Neyman Scott problem has an inconsistent MLE in that it never even converges to the right thing. Motivates the use of conditional likelihood.
Take $(X_i, Y_i) \sim \mathcal{N}\left(\mu_i, \ |
12,887 | Is there an example where MLE produces a biased estimate of the mean? | There is an infinite range of examples for this phenomenon since
the maximum likelihood estimator of a bijective transform $\Psi(\theta)$ of a parameter $\theta$ is the bijective transform of the maximum likelihood estimator of $\theta$, $\Psi(\hat{\theta}_\text{MLE})$;
the expectation of the bijective transform of th... | Is there an example where MLE produces a biased estimate of the mean? | There is an infinite range of examples for this phenomenon since
the maximum likelihood estimator of a bijective transform $\Psi(\theta)$ of a parameter $\theta$ is the bijective transform of the max | Is there an example where MLE produces a biased estimate of the mean?
There is an infinite range of examples for this phenomenon since
the maximum likelihood estimator of a bijective transform $\Psi(\theta)$ of a parameter $\theta$ is the bijective transform of the maximum likelihood estimator of $\theta$, $\Psi(\hat{... | Is there an example where MLE produces a biased estimate of the mean?
There is an infinite range of examples for this phenomenon since
the maximum likelihood estimator of a bijective transform $\Psi(\theta)$ of a parameter $\theta$ is the bijective transform of the max |
12,888 | Example of strong correlation coefficient with a high p value | The Bottom Line
The sample correlation coefficient needed to reject the hypothesis that the true (Pearson) correlation coefficient is zero becomes small quite fast as the sample size increases. So, in general, no, you cannot simultaneously have a large (in magnitude) correlation coefficient and a simultaneously large $... | Example of strong correlation coefficient with a high p value | The Bottom Line
The sample correlation coefficient needed to reject the hypothesis that the true (Pearson) correlation coefficient is zero becomes small quite fast as the sample size increases. So, in | Example of strong correlation coefficient with a high p value
The Bottom Line
The sample correlation coefficient needed to reject the hypothesis that the true (Pearson) correlation coefficient is zero becomes small quite fast as the sample size increases. So, in general, no, you cannot simultaneously have a large (in m... | Example of strong correlation coefficient with a high p value
The Bottom Line
The sample correlation coefficient needed to reject the hypothesis that the true (Pearson) correlation coefficient is zero becomes small quite fast as the sample size increases. So, in |
12,889 | Example of strong correlation coefficient with a high p value | cor.test(c(1,2,3),c(1,2,2))
cor = 0.866, p = 0.333 | Example of strong correlation coefficient with a high p value | cor.test(c(1,2,3),c(1,2,2))
cor = 0.866, p = 0.333 | Example of strong correlation coefficient with a high p value
cor.test(c(1,2,3),c(1,2,2))
cor = 0.866, p = 0.333 | Example of strong correlation coefficient with a high p value
cor.test(c(1,2,3),c(1,2,2))
cor = 0.866, p = 0.333 |
12,890 | Example of strong correlation coefficient with a high p value | A high estimate of the correlation coefficient with a high p-value could only occur with a very small sample size. I was about to provide an illustration, but Aaron has just done that! | Example of strong correlation coefficient with a high p value | A high estimate of the correlation coefficient with a high p-value could only occur with a very small sample size. I was about to provide an illustration, but Aaron has just done that! | Example of strong correlation coefficient with a high p value
A high estimate of the correlation coefficient with a high p-value could only occur with a very small sample size. I was about to provide an illustration, but Aaron has just done that! | Example of strong correlation coefficient with a high p value
A high estimate of the correlation coefficient with a high p-value could only occur with a very small sample size. I was about to provide an illustration, but Aaron has just done that! |
12,891 | Example of strong correlation coefficient with a high p value | I believe by the Fisher R-Z transform, the hyperbolic arctan of the sample correlation, under the null, is approximately normal with mean zero and standard error $1 / \sqrt{n-3}$. So to get, for example, a sample correlation $\hat{\rho} > 0$ with a fixed p-value, $p$, you would need
$$p = 2 - 2 \Phi\left(\operatorname{... | Example of strong correlation coefficient with a high p value | I believe by the Fisher R-Z transform, the hyperbolic arctan of the sample correlation, under the null, is approximately normal with mean zero and standard error $1 / \sqrt{n-3}$. So to get, for examp | Example of strong correlation coefficient with a high p value
I believe by the Fisher R-Z transform, the hyperbolic arctan of the sample correlation, under the null, is approximately normal with mean zero and standard error $1 / \sqrt{n-3}$. So to get, for example, a sample correlation $\hat{\rho} > 0$ with a fixed p-v... | Example of strong correlation coefficient with a high p value
I believe by the Fisher R-Z transform, the hyperbolic arctan of the sample correlation, under the null, is approximately normal with mean zero and standard error $1 / \sqrt{n-3}$. So to get, for examp |
12,892 | Example of strong correlation coefficient with a high p value | Yes. A p-value depends on the sample size, so a small sample can give this.
Say the true effect size was very small, and you draw a small sample. By luck, you get a few data points with very high correlation. The p-value will be high, as it should be. The correlation is high but it's not a very dependable result.
T... | Example of strong correlation coefficient with a high p value | Yes. A p-value depends on the sample size, so a small sample can give this.
Say the true effect size was very small, and you draw a small sample. By luck, you get a few data points with very high co | Example of strong correlation coefficient with a high p value
Yes. A p-value depends on the sample size, so a small sample can give this.
Say the true effect size was very small, and you draw a small sample. By luck, you get a few data points with very high correlation. The p-value will be high, as it should be. Th... | Example of strong correlation coefficient with a high p value
Yes. A p-value depends on the sample size, so a small sample can give this.
Say the true effect size was very small, and you draw a small sample. By luck, you get a few data points with very high co |
12,893 | Finding a way to simulate random numbers for this distribution | There is a straightforward (and if I may add, elegant) solution to this exercise: since $1-F(x)$ appears like a product of two survival distributions:
$$(1-F(x))=\exp\left\{-ax-\frac{b}{p+1}x^{p+1}\right\}=\underbrace{\exp\left\{-ax\right\}}_{1-F_1(x)}\underbrace{\exp\left\{-\frac{b}{p+1}x^{p+1}\right\}}_{1-F_2(x)}$$
t... | Finding a way to simulate random numbers for this distribution | There is a straightforward (and if I may add, elegant) solution to this exercise: since $1-F(x)$ appears like a product of two survival distributions:
$$(1-F(x))=\exp\left\{-ax-\frac{b}{p+1}x^{p+1}\ri | Finding a way to simulate random numbers for this distribution
There is a straightforward (and if I may add, elegant) solution to this exercise: since $1-F(x)$ appears like a product of two survival distributions:
$$(1-F(x))=\exp\left\{-ax-\frac{b}{p+1}x^{p+1}\right\}=\underbrace{\exp\left\{-ax\right\}}_{1-F_1(x)}\unde... | Finding a way to simulate random numbers for this distribution
There is a straightforward (and if I may add, elegant) solution to this exercise: since $1-F(x)$ appears like a product of two survival distributions:
$$(1-F(x))=\exp\left\{-ax-\frac{b}{p+1}x^{p+1}\ri |
12,894 | Finding a way to simulate random numbers for this distribution | You can always numerically solve the inverse transformation.
Below, I do a very simple bisection search. For a given input probability $q$ (I use $q$ since you already have a $p$ in your formula), I start with $x_L=0$ and $x_R=1$. Then I double $x_R$ until $F(x_R)>q$. Finally, I iteratively bisect the interval $[x_L,x_... | Finding a way to simulate random numbers for this distribution | You can always numerically solve the inverse transformation.
Below, I do a very simple bisection search. For a given input probability $q$ (I use $q$ since you already have a $p$ in your formula), I s | Finding a way to simulate random numbers for this distribution
You can always numerically solve the inverse transformation.
Below, I do a very simple bisection search. For a given input probability $q$ (I use $q$ since you already have a $p$ in your formula), I start with $x_L=0$ and $x_R=1$. Then I double $x_R$ until ... | Finding a way to simulate random numbers for this distribution
You can always numerically solve the inverse transformation.
Below, I do a very simple bisection search. For a given input probability $q$ (I use $q$ since you already have a $p$ in your formula), I s |
12,895 | Finding a way to simulate random numbers for this distribution | There is a somewhat convoluted if direct resolution by accept-reject. First, a simple differentiation shows that the pdf of the distribution is
$$f(x)=(a+bx^p)\exp\left\{-ax-\frac{b}{p+1}x^{p+1}\right\}$$
Second, since
$$f(x)=ae^{-ax}\underbrace{e^{-bx^{p+1}/(p+1)}}_{\le 1}+bx^pe^{-bx^{p+1}/(p+1)}\underbrace{e^{-ax}}_{... | Finding a way to simulate random numbers for this distribution | There is a somewhat convoluted if direct resolution by accept-reject. First, a simple differentiation shows that the pdf of the distribution is
$$f(x)=(a+bx^p)\exp\left\{-ax-\frac{b}{p+1}x^{p+1}\right | Finding a way to simulate random numbers for this distribution
There is a somewhat convoluted if direct resolution by accept-reject. First, a simple differentiation shows that the pdf of the distribution is
$$f(x)=(a+bx^p)\exp\left\{-ax-\frac{b}{p+1}x^{p+1}\right\}$$
Second, since
$$f(x)=ae^{-ax}\underbrace{e^{-bx^{p+1... | Finding a way to simulate random numbers for this distribution
There is a somewhat convoluted if direct resolution by accept-reject. First, a simple differentiation shows that the pdf of the distribution is
$$f(x)=(a+bx^p)\exp\left\{-ax-\frac{b}{p+1}x^{p+1}\right |
12,896 | Is median fairer than mean? | The problem is that you haven't really defined what it means to have a good or fair rating. You suggest in a comment on @Kevin's answer that you don't like it if one bad review takes down an item. But comparing two items where one has a "perfect record" and the other has one bad review, maybe that difference should be ... | Is median fairer than mean? | The problem is that you haven't really defined what it means to have a good or fair rating. You suggest in a comment on @Kevin's answer that you don't like it if one bad review takes down an item. But | Is median fairer than mean?
The problem is that you haven't really defined what it means to have a good or fair rating. You suggest in a comment on @Kevin's answer that you don't like it if one bad review takes down an item. But comparing two items where one has a "perfect record" and the other has one bad review, mayb... | Is median fairer than mean?
The problem is that you haven't really defined what it means to have a good or fair rating. You suggest in a comment on @Kevin's answer that you don't like it if one bad review takes down an item. But |
12,897 | Is median fairer than mean? | The answer you get depends on the question you ask.
Mean and median answer different questions. So they give different answers. It's not that one is "fairer" than another. Medians are often used with highly skewed data (such as income). But, even there, sometimes the mean is best. And sometimes you don't want ANY ... | Is median fairer than mean? | The answer you get depends on the question you ask.
Mean and median answer different questions. So they give different answers. It's not that one is "fairer" than another. Medians are often used wi | Is median fairer than mean?
The answer you get depends on the question you ask.
Mean and median answer different questions. So they give different answers. It's not that one is "fairer" than another. Medians are often used with highly skewed data (such as income). But, even there, sometimes the mean is best. And s... | Is median fairer than mean?
The answer you get depends on the question you ask.
Mean and median answer different questions. So they give different answers. It's not that one is "fairer" than another. Medians are often used wi |
12,898 | Is median fairer than mean? | If the only choices are integers in the range 1 to 5, can any really be considered an outlier?
I'm sure that with small sample sizes, popular outlier tests will fail, but that just points out the problems inherent in small samples. Indeed, given a sample of 5, 5, 5, 5, 5, 1, Grubbs' test reports 1 as an outlier at $\a... | Is median fairer than mean? | If the only choices are integers in the range 1 to 5, can any really be considered an outlier?
I'm sure that with small sample sizes, popular outlier tests will fail, but that just points out the pro | Is median fairer than mean?
If the only choices are integers in the range 1 to 5, can any really be considered an outlier?
I'm sure that with small sample sizes, popular outlier tests will fail, but that just points out the problems inherent in small samples. Indeed, given a sample of 5, 5, 5, 5, 5, 1, Grubbs' test re... | Is median fairer than mean?
If the only choices are integers in the range 1 to 5, can any really be considered an outlier?
I'm sure that with small sample sizes, popular outlier tests will fail, but that just points out the pro |
12,899 | Is median fairer than mean? | An experiment shows that median's error is always bigger than mean.
It depends on cost function you use.
MSE is minimized by mean. Therefore if you use MSE median will be always worse than mean.
BUT, if you would use absolute error, than the mean would be worse!
A nice explanation on this can be found here:
http://w... | Is median fairer than mean? | An experiment shows that median's error is always bigger than mean.
It depends on cost function you use.
MSE is minimized by mean. Therefore if you use MSE median will be always worse than mean.
BUT | Is median fairer than mean?
An experiment shows that median's error is always bigger than mean.
It depends on cost function you use.
MSE is minimized by mean. Therefore if you use MSE median will be always worse than mean.
BUT, if you would use absolute error, than the mean would be worse!
A nice explanation on this ... | Is median fairer than mean?
An experiment shows that median's error is always bigger than mean.
It depends on cost function you use.
MSE is minimized by mean. Therefore if you use MSE median will be always worse than mean.
BUT |
12,900 | Is median fairer than mean? | Just a quick thought:
If you assume that each rating is drawn from a latent continuous variable, then you could define the median of this underlying continuous variable of interest as your value of interest, rather than the mean of this underlying distribution. Where the distribution is symmetric, then the mean and the... | Is median fairer than mean? | Just a quick thought:
If you assume that each rating is drawn from a latent continuous variable, then you could define the median of this underlying continuous variable of interest as your value of in | Is median fairer than mean?
Just a quick thought:
If you assume that each rating is drawn from a latent continuous variable, then you could define the median of this underlying continuous variable of interest as your value of interest, rather than the mean of this underlying distribution. Where the distribution is symm... | Is median fairer than mean?
Just a quick thought:
If you assume that each rating is drawn from a latent continuous variable, then you could define the median of this underlying continuous variable of interest as your value of in |
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