Additive Models Explained: A Computational Complexity Approach

TL;DR

This paper investigates the computational complexity of generating explanations for Generalized Additive Models (GAMs), revealing diverse complexity outcomes influenced by model structure, input domain, and explanation type, challenging assumptions of their interpretability.

Contribution

It provides a comprehensive complexity analysis of explaining GAMs, highlighting conditions that make explanation computationally feasible or hard, which was previously underexplored.

Findings

Explanation complexity varies with input space structure.

Differences in explanation difficulty depend on component models and input domains.

Neural additive models can be easier to explain under certain conditions.

Abstract

Generalized Additive Models (GAMs) are commonly considered *interpretable* within the ML community, as their structure makes the relationship between inputs and outputs relatively understandable. Therefore, it may seem natural to hypothesize that obtaining meaningful explanations for GAMs could be performed efficiently and would not be computationally infeasible. In this work, we challenge this hypothesis by analyzing the *computational complexity* of generating different explanations for various forms of GAMs across multiple contexts. Our analysis reveals a surprisingly diverse landscape of both positive and negative complexity outcomes. Particularly, under standard complexity assumptions such as P!=NP, we establish several key findings: (1) in stark contrast to many other common ML models, the complexity of generating explanations for GAMs is heavily influenced by the structure of the input space; (2) the complexity of explaining GAMs varies significantly with the types of component models used - but interestingly, these differences only emerge under specific input domain settings; (3) significant complexity distinctions appear for obtaining explanations in regression tasks versus classification tasks in GAMs; and (4) expressing complex models like neural networks additively (e.g., as neural additive models) can make them easier to explain, though interestingly, this benefit appears only for certain explanation methods and input domains. Collectively, these results shed light on the feasibility of computing diverse explanations for GAMs, offering a rigorous theoretical picture of the conditions under which such computations are possible or provably hard.