# How to estimate the marginal distribution of a class with respect to one predictor in a classification task?

I have a dataset with a binary dependent variable $$y \in \{0,1\}$$ and a set of predictors $$x1,x2,..,t$$. Here, $$t$$ is the time in minutes (in 24 hrs, that is $$t \in (0,1440)$$). I want to estimate the marginal probability distribution of $$y$$ with respect to $$t$$. I am approaching this problem as a binary classification task and creating a classifier with all $$x1,x2,..,t$$ predictors, then, am planning to vary $$t$$ between 0 to 1440 and try to estimate the probabilities. Will this work? Is there any efficient method to do this? Also, please suggest some machine learning/deep learning algorithms for this task? I am betting on RF, Xgboost, Deep Neural networks. I have 84k records. (Note that I want to estimate $$P(y=1|\{x1..t_i\}$$, probability of y=1 as time increases over the day)

• This looks like a time series problem, in which case it might make sense to take into account observations across time in the instances. Do you have sequences of observations with all your variables (including y) at regular intervals for t? – Erwan Dec 7 '19 at 13:37