[Paper Review] L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Data

Jianbo Chen, Le Song+2 more|arXiv (Cornell University)|Aug 7, 2018

Bayesian Modeling and Causal Inference55 citations

TL;DR

This paper introduces L-Shapley (local) and C-Shapley (connected) scores to efficiently compute instancewise feature importance for graph-structured data, achieving linear-time complexity and relating to Shapley and Myerson values.

ABSTRACT

We study instancewise feature importance scoring as a method for model interpretation. Any such method yields, for each predicted instance, a vector of importance scores associated with the feature vector. Methods based on the Shapley score have been proposed as a fair way of computing feature attributions of this kind, but incur an exponential complexity in the number of features. This combinatorial explosion arises from the definition of the Shapley value and prevents these methods from being scalable to large data sets and complex models. We focus on settings in which the data have a graph structure, and the contribution of features to the target variable is well-approximated by a graph-structured factorization. In such settings, we develop two algorithms with linear complexity for instancewise feature importance scoring. We establish the relationship of our methods to the Shapley value and another closely related concept known as the Myerson value from cooperative game theory. We demonstrate on both language and image data that our algorithms compare favorably with other methods for model interpretation.

Motivation & Objective

• Motivate the use of instancewise feature importance scoring for interpreting black-box models.
• Develop scalable, graph-structured approximations to the Shapley value that leverage local and connected neighborhoods.
• Establish theoretical connections to Shapley and Myerson values under graph-based locality assumptions.
• Demonstrate empirical performance of the proposed methods on language and image data.
• Provide practical guidance on computation and relations to existing interpretation frameworks.

Proposed method

• Define vx(S) as the expected negative log probability conditioned on subset S of features.
• Introduce L-Shapley: average marginal contributions restricted to the k-neighborhood Nk(i) to approximate Shapley.
• Introduce C-Shapley: use connected subsets within Nk(i) and Myerson-style coefficients to approximate Shapley.
• Relate C-Shapley to the Myerson value for graph-restricted coalitional games with decomposability v(S)=sum of v over connected components.
• Provide complexity analyses: L-Shapley costs exponential in k but linear in d for line/grid graphs; C-Shapley costs O(k^2 d) on line graphs.
• Discuss potential to combine with sampling-based or regression-based approximations (KernelSHAP, etc.).

Experimental results

Research questions

• RQ1 Can graph-structured modifications of Shapley values (L-Shapley and C-Shapley) provide accurate instancewise feature attributions with reduced computation?
• RQ2 How do L-Shapley and C-Shapley relate to Myerson values under local additivity, and under what conditions are they close to the true Shapley values?
• RQ3 What is the empirical performance of L-Shapley and C-Shapley on text and image classification tasks compared to existing interpretation methods?
• RQ4 What are practical guidance and complexity considerations for applying these methods to real-world models?

Key findings

• L-Shapley and C-Shapley achieve linear-complexity approximations to Shapley values by exploiting graph structure.
• The methods yield provable error bounds relative to Shapley under specified mutual-information-type conditions.
• C-Shapley corresponds to the Myerson value on graphs under decomposability and local additivity.
• Empirical results show competitive or superior performance to KernelSHAP, SampleShapley, LIME, and Saliency on text and image tasks.
• The approach scales to language and image data with modest computational budgets and enables interaction-aware attributions within neighborhoods.