Shapley values for the individual data sets

[bernddude]

I really like the approach of using Shapley values to estimate the contribution of individual nodes from the DAG.
However from earlier work with the Shap package i know that in many cases the average over Shapley coefficients provides limited insight into the true dependencies.
I wonder is there a way to get access to the individual Shapley coefficients the gcm package calculates ?

I had a quick look at the code however didn't see an easy way to extract them ?

many thanks in advance for your help, Bernd

[bloebp]

Hey,

To which coefficients are you referring to? Generally, the results are the estimated Shapley values for each "player" (meaning depends on the value function). Do you have an example to clarify?

[bernddude]

I was referring to the values calculated for example by the intrinsic_causal_influece routine. It seem to me that the Shapley values are only used internally. If it would be possible to get the values for each Player that's exactly what i was looking for ?
A typical example why i am asking is that in many of the scenarios or data i am working with the typical cases won't have much dependency by design. We set the system up to be robust against small changes. However the problem cases feature significant dependencies and are dominated by individual nodes. To be able to investigate those cases would be very helpful.
Obviously with enough effort one could partition the data sets to only analyze those boundary cases, however that introduces human intervention and judgement calls which i typically like to avoid .
does that help ?

[bloebp]

Ok so the values that you get from the methods are already the "raw" Shapley values, only in a few methods there is a post-processing like averaging.
If you want to dive deeper into what is going on, you can either take a look at the Shapley estimation directly. For example, if you use early stopping (default by more than 5 features), then you can insert a print statement of evaluated_subsets e.g. after line https://github.com/py-why/dowhy/blob/main/dowhy/gcm/shapley.py#L363.

Otherwise, what is probably easier to interpret and analyze, you can add some print statements (or directly debug (you should then set the n_jobs to 1 then)) to the value function. For instance for ICC in https://github.com/py-why/dowhy/blob/main/dowhy/gcm/influence.py#L408
You can check what the predictions return when certain noise columns are randomized (depending on the given subset/coalition) or what attribution_func(shape_into_2d(predictions), target_values) actually computes for a specific subset of players. Otherwise, as you see, the Shapley values are directly returned (and only extended with the node names): https://github.com/py-why/dowhy/blob/main/dowhy/gcm/influence.py#L431

Just to avoid another confusion, these are not the 'classical feature relevance' Shapley values. Here, we only use the concept of having a fair attribution by symmetrizing over the coalitions, but the underlying value/characteristic/set function is special.

[bernddude]

Thx a lot for the help and the explanation . I found the evaluate_shapley function yesterday evening and will have a look whether i can use it and maybe write some of my own wrapper to calculate what i had in mind.
Also thx for the head up about the detail regarding the potential difference between the traditional Shapely coefficients. I will definitely check that out, since i did indeed overlooked that detail so far.
Maybe what i will do is to run a side by side comparison using the Shap package which i have been using. My main thought was that especially with anything but very simple models the results for Shapley coefficients can become quite sensitive to minor details in the data. Hence not very representative. I was very much interested whether this situation can be improved by the use of a Causal Model with a better representation of the underlying interactions ?
I should emphasize, that i really do mean this as a question. I might be quite wrong, however the question seem to me worth exploring ?

[bloebp]

Ok got it. In that case, keep in mind that there is a difference between the feature relevance of a prediction model and the "intrinsic" influence of the noise terms. Generally, you can represent your target in a graph as a function based on the upstream noise, i.e., Y = f(N_0,...,N_n) and see this as a model you want to explain with SHAP (this is also then very close to the idea of ICC) or you just model your target as Y = f(X_0,...,X_n), i.e. just the upstream nodes. This is probably closer to a typical prediction problem. However, in that case, most features would probably get small or no relevance. For instance in case of X->Y->Z, if you want to predict Z, then only Y is really relevant and X would get 0 relevance (assuming there is no confounder or other direct effects from X to Z).