Various methods based on the Shapley value have enjoyed notable success in recent years within the field of Explainable AI (XAI), in particular as feature selection mechanisms and for providing feature attributions for explaining machine learning models. Nevertheless, recent studies have raised concerns regarding the use of the Shapley value in this framework. In this paper, we delve deeper into these limitations through the lens of the axiomatic analysis of the Shapley value and its implications in the realm of machine learning. Leveraging on specific examples of classification models, we compare the effects of axioms for the Shapley value with other axioms for ranking methods based on a coalitional framework, where features are the “players” and the worth of a coalition of features corresponds to their predictive capacity. As an alternative feature selection method we pay particular attention to the lex-cel, a social ranking solution introduced in the recent literature at the intersection between coalitional games and social choice theory. Our analysis suggests that axioms characterizing the lex-cel, under certain circumstances, are more suitable for ranking features in machine learning models, compared to axioms satisfied by the Shapley value. Furthermore, through experiments conducted on public datasets, we show that the lex-cel outperforms some commonly employed feature selection algorithms based on the Shapley value, in particular with respect to the capacity of selecting less redundant features. An approximated version of the lex-cel, showing a satisfactory compromise between scalability of the approach and selection performance, is also presented and discussed.

Biochemical networks are models of biological functions and processes in biomedicine. Hierarchical decomposition simplifies complex biochemical networks by partitioning them into smaller blocks (modules), facilitating computationally intensive analyses and providing deeper insights into cellular processes and regulatory mechanisms. We introduce a novel algorithm for the hierarchical decomposition of large-scale biochemical systems. By using causality and information flow as organizing principles, our approach combines strongly connected components with $r$-causality to identify and structure manageable network blocks. Benchmarking against a comprehensive database of biochemical reaction networks demonstrates the computational efficiency and scalability of our algorithm. To ensure broad applicability, we integrate our algorithm into tools that support standardized Systems Biology Markup Language (SBML) formats, facilitating its use in biochemical modeling workflows.

Optimizing over the efficient set of a discrete multi-objective problem is a challenging issue. The main reason is that, unlike when optimizing over the feasible set, the efficient set is implicitly characterized. Therefore, methods designed for this purpose iteratively generate efficient solutions by solving appropriate single-objective problems. However, the number of efficient solutions can be quite large and the problems to be solved can be difficult practically. Thus, the challenge is both to minimize the number of iterations and to reduce the difficulty of the problems to be solved at each iteration. In this paper, a new enumeration scheme is proposed. By introducing some constraints and optimizing over projections of the search region, potentially large parts of the search space can be discarded, drastically reducing the number of iterations. Moreover, the single-objective programs to be solved can be guaranteed to be feasible, and a starting solution can be provided allowing warm start resolutions. This results in a fast algorithm that is simple to implement. Experimental computations on two standard multi-objective instance families show that our approach seems to perform significantly faster than the state of the art algorithm.

In this paper, we propose a generic algorithm to compute exactly the set of nondominated points for multiobjective discrete optimization problems. Our algorithm extends the ε-constraint method, originally designed for the biobjective case only, to solve problems with two or more objectives. For this purpose, our algorithm splits the search space into zones that can be investigated separately by solving an integer program. We also propose refinements, which provide extra information on several zones, allowing us to detect, and discard, empty parts of the search space without checking them by solving the associated integer programs. This results in a limited number of calls to the integer solver. Moreover, we can provide a feasible starting solution before solving every program, which significantly reduces the time spent for each resolution. The resulting algorithm is fast and simple to implement. It is compared with previous state-of-the-art algorithms and is seen to outperform them significantly on the experimented problem instances.