Luke Merrick

Luke Merrick

Given a model $f$ that predicts a target $y$ from a vector of input features $\pmb{x} = x_1, x_2, \ldots, x_M$, we seek to measure the importance of each feature with respect to the model's ability to make a good prediction. To this end, we consider how (on average) some measure of goodness or badness of prediction (which we term "loss" $\ell$), changes when we hide or ablate each feature from the model. To ablate a feature, we replace its value with another possible value randomly. By averaging over many points and many possible replacements, we measure the importance of a feature on the model's ability to make good predictions. Furthermore, we present statistical measures of uncertainty that quantify how confident we are that the feature importance we measure from our finite dataset and finite number of ablations is close to the theoretical true importance value.

Luke Merrick, Ankur Taly

A number of techniques have been proposed to explain a machine learning model's prediction by attributing it to the corresponding input features. Popular among these are techniques that apply the Shapley value method from cooperative game theory. While existing papers focus on the axiomatic motivation of Shapley values, and efficient techniques for computing them, they offer little justification for the game formulations used, and do not address the uncertainty implicit in their methods' outputs. For instance, the popular SHAP algorithm's formulation may give substantial attributions to features that play no role in the model. In this work, we illustrate how subtle differences in the underlying game formulations of existing methods can cause large differences in the attributions for a prediction. We then present a general game formulation that unifies existing methods, and enables straightforward confidence intervals on their attributions. Furthermore, it allows us to interpret the attributions as contrastive explanations of an input relative to a distribution of reference inputs. We tie this idea to classic research in cognitive psychology on contrastive explanations, and propose a conceptual framework for generating and interpreting explanations for ML models, called formulate, approximate, explain (FAE). We apply this framework to explain black-box models trained on two UCI datasets and a Lending Club dataset.