Regression on bimodal target variable

Question

I'm working on a problem where I need to fit a regression on solubility data from a collection of molecules. The response variable (solubility) displays a bimodal distribution, suggesting there are different populations in my data:

After training a baseline random forest model, I plotted the regression line and the bimodal nature of the target variable is pretty visible:

However, when I inspected the residuals I noticed the were centered around 0 but still showing the bimodal distribution

I'm not sure what would be a sound approach here (its my first time seeing this kind of distribution in this particular type of data).

1. I read in here that regressions don't make assumptions about the distribution of the target variable. Does that apply for all algorithms (e.g. PLS, random forest etc)?

2. I was following this kernel and it seems the author was trying to separate the populations. Is this a possible solution if a regression is required? My intuition is that we could use the classifier to predict from which population a sample comes from and then use the equivalent regression model to make predictions.

3. Is the bimodal pattern in my residual plot worrying or I should only be concerned if they are centered around zero?

Answer 1

Your residuals, as I judge from the histogram, have a normal-looking distribution. You’re noticing that the predictions have bimodality, which is a different claim.

I don’t want to claim that there is no regression method that cares about the distribution of the predictions, rather than the residuals, but I can’t think of one.

What concerns me is that your residual-actual plot seems to have a decreasing trend. For instance, the residuals in the $0-50$ $x$-axis range are a bit higher than those in the $200-250$ range, as histograms of those subsets are likely to reflect. You want the residuals to be pretty consistently centered around zero, not indicating overestimates in one region and underestimates in another.