Re:The Central Limit Theorem and Its Misuse
by eanzenberg on Monday December 30, 2019 @11:45AM
(#21914614)
For example, there were times where features were excluded because their "p-value was too large to be significant", regardless that the underlying distribution was not Gaussian. p-value from a t-test, like in lots of regression software, requires Gaussian distributions.
Re:The Central Limit Theorem and Its Misuse
by QuesnayJr on Monday December 30, 2019 @03:43PM
(#21916533)
If the data set is large, then the coefficient is approximately Gaussian, because of the CLT. This is one appropriate setting to use the CLT (unless you think you are in a setting where the CLT doesn't hold, such as infinite variance).
Re:The Central Limit Theorem and Its Misuse
by eanzenberg on Wednesday January 01, 2020 @09:56PM
(#21932620)
For example, lets say height is a feature in your model. No matter how big the size of data, it will never be Gaussian, it is bi-modal. So the t-test in regression won’t be valid. Most ml is done on raw data.
Re:The Central Limit Theorem and Its Misuse
by QuesnayJr on Thursday January 02, 2020 @01:05PM
(#21937907)
If the t test is on a regression coefficient, then the sampling distribution is approximately Gaussian (for big enough data). It doesn't matter how many modes that the original data feature has. This is standard asymptotics in hypothesis testing.
Re:The Central Limit Theorem and Its Misuse
by eanzenberg on Thursday January 02, 2020 @03:12PM
(#21939299)
No, a t-test makes no assumptions that the underlying data is Gaussian. Again, most ml is done on raw data. If the raw feature is bimodal then the raw data is bimodal.
Re:The Central Limit Theorem and Its Misuse
by QuesnayJr on Friday January 03, 2020 @06:33AM
(#21945022)
I can't figure out if you are agreeing or disagreeing with me. If you do non-penalized regression on raw data, then the t statstic will be approximately Gaussian, even if the raw data is bimodal. This follows from the CLT.
Re:The Central Limit Theorem and Its Misuse
by eanzenberg on Saturday January 04, 2020 @08:29PM
(#21958966)
What is the standard deviation of a bimodal distribution with modes at 0 and inf? Is that a meaningful stat?
Re:The Central Limit Theorem and Its Misuse
by throwlaplace on Monday December 30, 2019 @11:17AM
(#21914341)
>which accounts for the distribution used
what does this mean? are you trying to say the code uses the empirical distribution as a proxy for the true distribution?
To your specific examples - the coefficient of a linear regression is distributed normally (?). Similarly, we know the expected distribution of most maximum likelihood estimators (logistic regression, etc.), and programs will give you the right p-value.
Of course, omitted variable bias is still a problem and it is possible to mis-specify your model. However, I think most data scientists are presenting aggregate statistics (means, regression coefficients) like you said, and that we have a pretty good handle on the underlying distributions.