Logic-Based Explainability in Machine Learning

Abstract

The last decade witnessed an ever-increasing stream of successes in Machine Learning (ML). These successes offer clear evidence that ML is bound to become pervasive in a wide range of practical uses, including many that directly affect humans. Unfortunately, the operation of the most successful ML models is incomprehensible for human decision makers. As a result, the use of ML models, especially in highrisk and safety-critical settings is not without concern. In recent years, there have been efforts on devising approaches for explaining ML models. Most of these efforts have focused on so-called model-agnostic approaches. However, all model-agnostic and related approaches offer no guarantees of rigor, hence being referred to as non-formal. For example, such non-formal explanations can be consistent with different predictions, which renders them useless in practice. This paper overviews the ongoing research efforts on computing rigorous model-based explanations of ML models; these being referred to as formal explanations. These efforts encompass a variety of topics, that include the actual definitions of explanations, the characterization of the complexity of computing explanations, the currently best logical encodings for reasoning about different ML models, and also how to make explanations interpretable for human decision makers, among others.

No silver bullet: interpretable ML models must be explained

“… Decision tree, adapted from (Hu et al, 2019 , Figure 5b), for the dataset. This DT is also studied more recently in Izza et al ( 2022a ) and Marques-Silva ( 2022 ). Each feature tests a possible play for the player.…”

“…The rest of this section offers a brief overview of logic-based explainability. More detailed overviews can be found elsewhere (Marques-Silva, 2022 ; Marques-Silva and Ignatiev, 2022 ).…”

“…There has been steady progress in the efficient computation of explanations (Marques-Silva, 2022 ; Marques-Silva and Ignatiev, 2022 ) (and references therein). Moreover, a number of related research topics have been investigated, including enumeration of explanations (Ignatiev et al, 2020a ), explainability queries (Audemard et al, 2020 , 2021 ; Huang et al, 2021b ), probabilistic explanations (Wäldchen et al, 2021 ; Arenas et al, 2022 ; Izza et al, 2022b ), or taking into account constraints in feature space (Gorji and Rubin, 2022 ; Yu et al, 2022 ).…”

Delivering Trustworthy AI through Formal XAI

“…This section offers a brief perspective of the emerging field of formal explainable AI. Recent detailed accounts are available [56], [59].…”

“…Progress in formal XAI. Figure 4 summarizes the progress observed in recent years for computing one explanation [56], [59]. For several families of classifiers there exist practical efficient solutions, either in theory or in practice.…”