How to show probabilities instead of logits in local explanations

[francescopisu]

@paulbkoch I'm looking for a way to go about showing probabilities in local explanations.

At the moment, this is what we have:

1. feature contributions in terms of logits (positive and negative)
2. an intercept

To obtain the predicted score for the positive class (in a binary setting), interpretml does the following:

1. start a sum using the intercept value as the initial value
2. iterate over each feature (including interactions)
   2.1) get the corresponding logit indexing the model.term_scores_ attribute (which has to do with bins and such, I need to dig deeper in this regard)
   2.2) add that logit to the current sum value (which started from the intercept)
3. add a 0 to the final sum of logits and obtain an array with two columns an N rows depending on the number of samples that we are predicting: [0, sum_of_logits]
4. apply softmax to get predicted "probabilities" for negative and positive class

What I want to know is the following:
is there a way, starting from the predicted probability of the positive class (let's say 0.85), to know the individual contribution of each feature in terms of probability ?
e.g.
feat1: +0.12
feat2: -0.13
feat3: +0.4
...
so that the sum of each individual contribution (ideally a "partial" probability) add up to the predicted probability of positive class (i.e., 0.85) ?
Additional question: How should we treat the intercept in such a case ?

---

I tried passing each contribution in terms of logits to the logistic function but obviously it makes little sense

Thank you very much. You did an outstanding work with this library!

[paulbkoch]

Hi @francescopisu -- Traditionally, you cannot do this since the relationship between changes in probability and logits is nonlinear (softmax). There is however a very interesting paper that came out a few months ago where they were able to do this by using an approximation of the sigmoid function (https://arxiv.org/pdf/2211.06360.pdf). I was thinking someday we might implement this as an option because it would be pretty neat to be able to offer additive probabilities. To do it justice though I think you would want to modify the loss function to better match their sigmoid approximation.