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Popular feature importance techniques compute additive approximations to nonlinear models by first defining a cooperative game describing the value of different subsets of the model’s features, then calculating the resulting game’s Shapley values to attribute credit additively between the features. However, the specific modeling settings in which the Shapley values are a poor approximation for the true game have not been well-described. In this paper we utilize an interpretation of Shapley values as the result of an orthogonal projection between vector spaces to calculate a residual representing the kernel component of that projection. We provide an algorithm for computing these residuals, characterize different modeling settings based on the value of the residuals, and demonstrate that they capture information about model predictions that Shapley values cannot. 

The increasing adoption of machine learning tools has led to calls for accountability via model interpretability. But what does it mean for a machine learning model to be interpretable by humans, and how can this be assessed? We focus on two definitions of interpretability that have been introduced in the machine learning literature: simulatability (a user's ability to run a model on a given input) and "what if" local explainability (a user's ability to correctly determine a model's prediction under local changes to the input, given knowledge of the model's original prediction). Through a user study with 1,000 participants, we test whether humans perform well on tasks that mimic the definitions of simulatability and "what if" local explainability on models that are typically considered locally interpretable. To track the relative interpretability of models, we employ a simple metric, the runtime operation count on the simulatability task. We find evidence that as the number of operations increases, participant accuracy on the local interpretability tasks decreases. In addition, this evidence is consistent with the common intuition that decision trees and logistic regression models are interpretable and are more interpretable than neural networks. 

Motivated by the need to audit complex and black box models, there has been extensive research on quantifying how data features influence model predictions. Feature influence can be direct (a direct influence on model outcomes) and indirect (model outcomes are influenced via proxy features). Feature influence can also be expressed in aggregate over the training or test data or locally with respect to a single point. Current research has typically focused on one of each of these dimensions. In this paper, we develop disentangled influence audits, a procedure to audit the indirect influence of features. Specifically, we show that disentangled representations provide a mechanism to identify proxy features in the dataset, while allowing an explicit computation of feature influence on either individual outcomes or aggregate-level outcomes. We show through both theory and experiments that disentangled influence audits can both detect proxy features and show, for each individual or in aggregate, which of these proxy features affects the classifier being audited the most. In this respect, our method is more powerful than existing methods for ascertaining feature influence.