I have a target variable that has the following distribution. I have tried the typical regression models such as logistic regression, ridge regression, catboost regression etc. but I'm thinking that I could use a model that takes into account the features but also some kind of prior knowledge of the distribution of the target variable. Im trying to predict duration in minutes and I’m trying to use machine learning to predict that. Some of my features might have normal or other distributions but do not really know how to use even that. Any suggestions? enter image description here

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    $\begingroup$ This does not make sense to me, because the regression is modeling conditional distributions, not the marginal (pooled) distribution, of $y$. Do you have some knowledge of the conditional distribution? $\endgroup$
    – Dave
    Sep 22 at 14:04
  • $\begingroup$ I'm confused. You say you're using logistic regression but your target value looks continuous? $\endgroup$
    – Adrià Luz
    Sep 22 at 15:41
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    $\begingroup$ @AdriàLuz Logistic regression could make sense for positive integer values (and zero) if we allow the $n$ of the conditional $Binom(n, p)$ distribution to exceed $1$, though that is not the typical way logistic regression is used in a machine learning setting (as a "classifier"). Given the mention of ridge regression and catboost, it seems safe to assume a machine learning context. // Azal, what kind of data are you trying to predict, categorical or numerical? That will help identify the correct model (though my previous remarks about conditional vs marginal still apply). $\endgroup$
    – Dave
    Sep 22 at 15:55
  • $\begingroup$ Thanks @Dave. That's interesting - do you have any resources on this version of logistic regression? $\endgroup$
    – Adrià Luz
    Sep 22 at 16:23
  • $\begingroup$ Im trying to predict duration. My y is duration of events in minutes $\endgroup$
    – azal
    Sep 22 at 18:03

You're looking at the marginal, not the conditional, and regression makes assumptions about the conditional.

It seems like your outcome is bounded below by 0, so you may want to choose a likelihood which supports this (e.g. exponential or gamma). It also seems like the outcome is bounded above by 40. Is that true? If so, rescale so the outcome is on [0,1] and consider beta regression.


if for any theoretical reasons your values can only range between a known minimum (0 in your case) and a known maximum (40 in your case or another value, say 100) you can rescale them to be between 0 and 1 and use fractional logistic regression. If there is no mass at 0 and 1 the beta function (beta regression) could also be a choice.

I hope it helps



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