Publicaciones

AUTHORS

Leopoldo Bertossi, Mikaël Monet, Pablo Barceló, Marcelo Arenas

ABSTRACT

Scores based on Shapley values are widely used for providing explanations to classification results over machine learning models. A prime example of this is the influential SHAP-score, a version of the Shapley value that can help explain the result of a learned model on a specific entity by assigning a score to every feature. While in general computing Shapley values is a computationally intractable problem, it has recently been claimed that the SHAP-score can be computed in polynomial time over the class of decision trees. In this paper, we provide a proof of a stronger result over Boolean models: the SHAP-score can be computed in polynomial time over deterministic and decomposable Boolean circuits. Such circuits, also known as tractable Boolean circuits, generalize a wide range of Boolean circuits and binary decision diagrams classes, including binary decision trees, Ordered Binary Decision Diagrams (OBDDs) and Free Binary Decision Diagrams (FBDDs). We also establish the computational limits of the notion of SHAP-score by observing that, under a mild condition, computing it over a class of Boolean models is always polynomially as hard as the model counting problem for that class. This implies that both determinism and decomposability are essential properties for the circuits that we consider, as removing one or the other renders the problem of computing the SHAP-score intractable (namely, #P

AUTHORS

Leopoldo Bertossi, Mikaël Monet, Pablo Barceló, Marcelo Arenas

AUTHORS

Benny Kimelfeld, Moshe Sebag, Ester Livshits, Leopoldo Bertossi

ABSTRACT

Database tuples can be seen as players in the game of jointly realizing the answer to a query. Some tuples may contribute more than others to the outcome, which can be a binary value in the case of a Boolean query, a number for a numerical aggregate query, and so on. To quantify the contributions of tuples, we use the Shapley value that was introduced in cooperative game theory and has found applications in a plethora of domains. Specifically, the Shapley value of an individual tuple quantifies its contribution to the query. We investigate the applicability of the Shapley value in this setting, as well as the computational aspects of its calculation in terms of complexity, algorithms, and approximation.

AUTHORS

Leopoldo Bertossi

ABSTRACT

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

AUTHORS

Gabriela Reyes, Leopoldo Bertossi

ABSTRACT

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.

AUTHORS

Leopoldo Bertossi, Mostafa Milani

ABSTRACT

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.

AUTHORS

Leopoldo Bertossi

ABSTRACT

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.

AUTHORS

Leopoldo Bertossi

ABSTRACT

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.

2022, Publisher: Logical Methods in Computer Science, Link>

AUTHORS

AUTHORS

Leopoldo Bertossi

ABSTRACT

We propose answer-set programs that specify and compute counterfactual interventions on entities that are input on a classification model. In relation to the outcome of the model, the resulting counterfactual entities serve as a basis for the definition and computation of causality-based explanation scores for the feature values in the entity under classification, namely responsibility scores. The approach and the programs can be applied with black-box models, and also with models that can be specified as logic programs, such as rule-based classifiers. The main focus of this study is on the specification and computation of best counterfactual entities, that is, those that lead to maximum responsibility scores. From them one can read off the explanations as maximum responsibility feature values in the original entity. We also extend the programs to bring into the picture semantic or domain knowledge. We show how the approach could be extended by means of probabilistic methods, and how the underlying probability distributions could be modified through the use of constraints. Several examples of programs written in the syntax of the DLV ASP-solver, and run with it, are shown.

AUTHORS

Eduardo Cerpa, Gildas Besancon, Christophe Prieur, Constantinos Kitsos

ABSTRACT

This paper is about the stabilization of a cascade system of $n$ linear Korteweg--de Vries equations in a bounded interval. It considers an output feedback control placed at the left endpoint of the last equation, while the output involves only the solution to the first equation. The boundary control problems investigated include two cases: a classical control on the Dirichlet boundary condition and a less standard one on its second-order derivative. The feedback control law utilizes the estimated solutions of a high-gain observer system, and the output feedback control leads to stabilization for any $n$ for the first boundary conditions case and for $n=2$ for the second one.