CausalSHAP (Causal SHApley Additive imPacts) is a game theoretic approach to explain the causal impact of any variable in a machine learning model. It follows directly from the ideas in shap (https://github.com/slundberg/shap) from Lundberg et al.

Modification to SHAP (CausalSHAP™) that could give us member-level impact scores:

Basically, as opposed to averaging the change in model score of adding a feature F to the model with the value it has in the data, instead average the difference in adding as 1 as opposed to adding as 0 (assuming a binary treatment variable).

More detail:

Assuming binary feature $i$:

Current SHAP (simplified) with current impact methodology For each member $j$:

• For each ordered subset of features $S$ excluding feature $i$, calculate the change in model score $m_{ijS}$ by adding feature $j$ with data value $v_{ij}$ to $S$

• Take weighted average of $m_{ijS}$ over all $S$ (weighting based on some kernel, in practice this is sampled etc) ==> result is $Shap_{ij}$ (value of feature $i$ to member $j$)

• Average $m_{ij}$ over all $j$ to get $m_i$, which is average shap value of feature $i$ over members, $Shap_i$

CausalSHAP™ For each member $j$:

• For each ordered subset of features $S$ excluding feature $i$, calculate the change in model score $m_{ijS,0}$ by adding feature $i$ with data value $0$ to $S$

• calculate the change in model score $m_{ijS,1}$ by adding feature $i$ with data value $1$ to $S$

• calculate the impact value $m_{ijS} == m_{ijS,1} - m_{ijS,0}$

• Take weighted average of $m_{ijS}$ over all $S$ (weighting based on some kernel, in practice this is sampled etc) ==> result is $CausalShapImpact_{ij}$ (impact of toggling feature $i$ to member $j$)

• Impact Score: Average $CausalShapImpact_{ij}$ over all members $j$ to get $CausalShapImpact_i$

So basically instead of just finding the average impact of adding feature as it exists in the data, find the average impact of it being 1 vs it being 0.