# How to model probabilistic inputs with continuous output using regression

I have trained a multi-output classifier that takes an image as input and returns softmax logits as output. To be specific, the multi-output classifier takes an image and says the probability that various objects are in the image.

I have trained a single-output classifier that takes an image as input and returns softmax logits as output. To be specific, the single-output classifier takes images and describes how the image was taken.

In other words, the multi-output classifier describes what is in the image whereas the single-output classifier describes the entire image.

I am now trying to explain the results of the single-output classifier. I would like to use the results from the multi-output classifier to better understand the single-output classifier. To do this, I am considering creating a regression of the image loss (from the single-output classifier) on the object logits (of the multi-output classifier).

Should I transform the logits, transform the output, or consider a different specification when creating this regression of a continuous output on probabilistic inputs? What is the distributional motivation behind your suggestion?

• I thintk you need to provide more context. What is it you are trying to predict? Assuming you are starting from a linear model, then it seems odd to have probability as an input to predict a continuous quantity. – seanv507 Jul 4 '19 at 6:26
• Adding logit inputs to logistic regression seemed counterintuitive to me. The problem is that the coefficient then changes the steepness of the logistic function rather than absolute probability, so values corresponding to less than 50 % are squashed down and values higher than 50% squashed high – seanv507 Jul 4 '19 at 6:34
• @seanv507, thanks for your help. I've included examples of what types of circumstances I am thinking of for clarification. – Joseph Konan Jul 4 '19 at 22:05
• I think it is better if you give the exact problem you are trying to solve than your understanding of the abstract general problem ( as in examples 1,2,3). That way the experienced statisticians on this forum can point you to the right approach. – seanv507 Jul 5 '19 at 17:46
• I still do not see much context there. Be specific, and state the ultimate goals of the analysis. – Frank Harrell Jul 9 '19 at 11:52