The Distributional Uncertainty of the SHAP score in Explainable Machine Learning

Attribution scores reflect how important the feature values in an input entity are for the output of a machine learning model. One of the most popular attribution scores is the SHAP score, which is an instantiation of the general Shapley value used in coalition game theory. The definition of this score relies on a probability distribution on the entity population. Since the exact distribution is generally unknown, it needs to be assigned subjectively or be estimated from data, which may lead to misleading feature scores. In this paper, we propose a principled framework for reasoning on SHAP scores under unknown entity population distributions. In our framework, we consider an uncertainty region that contains the potential distributions, and the SHAP score of a feature becomes a function defined over this region. We study the basic problems of finding maxima and minima of this function, which allows us to determine tight ranges for the SHAP scores of all features. In particular, we pinpoint the complexity of these problems, and other related ones, showing them to be NP-complete. Finally, we present experiments on a real-world dataset, showing that our framework may contribute to a more robust feature scoring.

Attribution-Scores in Data Management and Explainable Machine Learning

We describe recent research on the use of actual causality in the definition of responsibility scores as explanations for query answers in databases, and for outcomes from classification models in machine learning. In the case of databases, useful connections with database repairs are illustrated and exploited. Repairs are also used to give a quantitative measure of the consistency of a database. For classification models, the responsibility score is properly extended and illustrated. The efficient computation of Shap-score is also analyzed and discussed. The emphasis is placed on work done by the author and collaborators.

From Database Repairs to Causality in Databases and Beyond

We describe some recent approaches to score-based explanations for query answers in databases. The focus is on work done by the author and collaborators. Special emphasis is placed on the use of counterfactual reasoning for score specification and computation. Several examples that illustrate the flexibility of these methods are shown.

Opening Up the Neural Network Classifier for Shap Score Computation

We address the problem of efficiently computing Shap explanation scores for classifications with machine learning models. With this goal, we show the transformation of binary neural networks (BNNs) for classification into deterministic and decomposable Boolean circuits, for which knowledge compilation techniques are used. The resulting circuit is treated as an open-box model, to compute Shap scores by means of a recent efficient algorithm for this class of circuits. Detailed experiments show a considerable gain in performance in comparison with computing Shap directly on the BNN treated as a black-box model.

Attribution-Scores and Causal Counterfactuals as Explanations in Artificial Intelligence

In this expository article we highlight the relevance of explanations for artificial intelligence, in general, and for the newer developments in {\em explainable AI}, referring to origins and connections of and among different approaches. We describe in simple terms, explanations in data management and machine learning that are based on attribution-scores, and counterfactuals as found in the area of causality. We elaborate on the importance of logical reasoning when dealing with counterfactuals, and their use for score computation.

Answer-Set Programs for Repair Updates and Counterfactual Interventions

We briefly describe -- mainly through very simple examples -- different kinds of answer-set programs with annotations that have been proposed for specifying: database repairs and consistent query answering; secrecy view and query evaluation with them; counterfactual interventions for causality in databases; and counterfactual-based explanations in machine learning.

Reasoning about Counterfactuals and Explanations: Problems, Results and Directions

There are some recent approaches and results about the use of answer-set programming for specifying counterfactual interventions on entities under classification, and reasoning about them. These approaches are flexible and modular in that they allow the seamless addition of domain knowledge. Reasoning is enabled by query answering from the answer-set program. The programs can be used to specify and compute responsibility-based numerical scores as attributive explanations for classification results.

Second-Order Specifications and Quantifier Elimination for Consistent Query Answering in Databases

Consistent answers to a query from a possibly inconsistent database are answers that are simultaneously retrieved from every possible repair of the database. Repairs are consistent instances that minimally differ from the original inconsistent instance. It has been shown before that database repairs can be specified as the stable models of a disjunctive logic program. In this paper we show how to use the repair programs to transform the problem of consistent query answering into a problem of reasoning w.r.t. a theory written in second-order predicate logic. It also investigated how a first-order theory can be obtained instead by applying second-order quantifier elimination techniques.

Extending Sticky-Datalog+/- via Finite-Position Selection Functions: Tractability, Algorithms, and Optimization

Weakly-Sticky(WS) Datalog+/- is an expressive member of the family of Datalog+/- program classes that is defined on the basis of the conditions of stickiness and weak-acyclicity. Conjunctive query answering (QA) over the WS programs has been investigated, and its tractability in data complexity has been established. However, the design and implementation of practical QA algorithms and their optimizations have been open. In order to fill this gap, we first study Sticky and WS programs from the point of view of the behavior of the chase procedure. We extend the stickiness property of the chase to that of generalized stickiness of the chase (GSCh) modulo an oracle that selects (and provides) the predicate positions where finitely values appear during the chase. Stickiness modulo a selection function S that provides only a subset of those positions defines sch(S), a semantic subclass of GSCh. Program classes with selection functions include Sticky and WS, and another syntactic class that we introduce and characterize, namely JWS, of jointly-weakly-sticky programs, which contains WS. The selection functions for these last three classes are computable, and no external, possibly non-computable oracle is needed. We propose a bottom-up QA algorithm for programs in the class sch(S), for a general selection function S. As a particular case, we obtain a polynomial-time QA algorithm for JWS and weakly-sticky programs. Unlike WS, JWS turns out to be closed under magic-sets query optimization. As a consequence, both the generic polynomial-time QA algorithm and its magic-set optimization can be particularized and applied to WS.

Answer-Set Programs for Reasoning about Counterfactual Interventions and Responsibility Scores for Classification

We describe how answer-set programs can be used to declaratively specify counterfactual interventions on entities under classification, and reason about them. In particular, they can be used to define and compute responsibility scores as attribution-based explanations for outcomes from classification models. The approach allows for the inclusion of domain knowledge and supports query answering. A detailed example with a naive-Bayes classifier is presented.