ON RELATING 'WHY?' AND 'WHY NOT?' EXPLANATIONS

Abstract

Explanations of Machine Learning (ML) models often address a 'Why?' question. Such explanations can be related with selecting feature-value pairs which are sufficient for the prediction. Recent work has investigated explanations that address a 'Why Not?' question, i.e. finding a change of feature values that guarantee a change of prediction. Given their goals, these two forms of explaining predictions of ML models appear to be mostly unrelated. However, this paper demonstrates otherwise, and establishes a rigorous formal relationship between 'Why?' and 'Why Not?' explanations. Concretely, the paper proves that, for any given instance, 'Why?' explanations are minimal hitting sets of 'Why Not?' explanations and vice-versa. Furthermore, the paper devises novel algorithms for extracting and enumerating both forms of explanations.

1. INTRODUCTION

The importance of devising mechanisms for computing explanations of Machine Learning (ML) models cannot be overstated, as illustrated by the fast-growing body of work in this area. A glimpse of the importance of explainable AI (XAI) is offered by a growing number of recent surveys and overviews Hoffman & Klein ( 2017 & Lee (2017) . Most other work seeks to find a (often minimal) set of feature value pairs which is sufficient for the prediction, i.e. as long as those features take the specified values, the prediction does not change. For rigorous approaches, the answer to a 'Why prediction π?' question has been referred to as PI-explanations Shih et al. (2018; 2019 ), abductive explanations Ignatiev et al. (2019a)) , but also as (minimal) sufficient reasons Darwiche & Hirth (2020); Darwiche (2020). (Hereinafter, we use the term abductive explanation because of the other forms of explanations studied in the paper.)



A taxonomy of ML model explanations used in this paper is included in Appendix A. There is also a recent XAI service offered by Google: https://cloud.google.com/ explainable-ai/, inspired on similar ideas Google (2019).



); Hoffman et al. (2017); Biran & Cotton (2017); Montavon et al. (2018); Klein (2018); Hoffman et al. (2018a); Adadi & Berrada (2018); Alonso et al. (2018); Dosilovic et al. (2018); Hoffman et al. (2018b); Guidotti et al. (2019); Samek et al. (2019); Samek & Müller (2019); Miller (2019b;a); Anjomshoae et al. (2019); Mittelstadt et al. (2019); Xu et al. (2019). Past work on computing explanations has mostly addressed local (or instance-dependent) explanations Ribeiro et al. (2016); Lundberg & Lee (2017); Ribeiro et al. (2018); Shih et al. (2018; 2019); Ignatiev et al. (2019a); Darwiche & Hirth (2020); Darwiche (2020). Exceptions include for example approaches that distill ML models, e.g. the case of NNs Frosst & Hinton (2017) among many others Ribeiro et al. (2016), or recent work on relating explanations with adversarial examples Ignatiev et al. (2019b), both of which can be seen as seeking global (or instance-independent) explanations. Prior research has also mostly considered model-agnostic explanations Ribeiro et al. (2016); Lundberg & Lee (2017); Ribeiro et al. (2018). Recent work on model-based explanations, e.g. Shih et al. (2018); Ignatiev et al. (2019a), refers to local (or global) model-agnostic explanations as heuristic, given that these approaches offer no formal guarantees with respect to the underlying ML model 1 . Examples of heuristic approaches include Ribeiro et al. (2016); Lundberg & Lee (2017); Ribeiro et al. (2018), among many others 2 . In contrast, local (or global) model-based explanations are referred to as rigorous, since these offer the strongest formal guarantees with respect to the underlying ML model. Concrete examples of such rigorous approaches include Shih et al. (2018); Tran & d'Avila Garcez (2018); Shih et al. (2019); Ignatiev et al. (2019a;b); Darwiche & Hirth (2020); Jha et al. (2019). Most work on computing explanations aims to answer a 'Why prediction π?' question. Some work proposes approximating the ML model's behavior with a linear model Ribeiro et al. (2016); Lundberg

