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In this paper we investigate the problem of quantifying the contribution of each variable to the satisfying assignments of a Boolean function based on the Shapley value. Our main result is a polynomial-time equivalence between computing…

Databases · Computer Science 2023-06-27 Ahmet Kara , Dan Olteanu , Dan Suciu

The attribution problem, that is the problem of attributing a model's prediction to its base features, is well-studied. We extend the notion of attribution to also apply to feature interactions. The Shapley value is a commonly used method…

Computer Science and Game Theory · Computer Science 2020-02-11 Kedar Dhamdhere , Ashish Agarwal , Mukund Sundararajan

The ubiquitous use of Shapley values in eXplainable AI (XAI) has been triggered by the tool SHAP, and as a result are commonly referred to as SHAP scores. Recent work devised examples of machine learning (ML) classifiers for which the…

Machine Learning · Computer Science 2024-12-20 Olivier Letoffe , Xuanxiang Huang , Joao Marques-Silva

The Shapley value was originally introduced in cooperative game theory as a wealth distribution mechanism. It has since found use in knowledge representation and databases for the purpose of assigning scores to formulas and database tuples…

Artificial Intelligence · Computer Science 2026-02-26 Meghyn Bienvenu , Diego Figueira , Pierre Lafourcade

Shapley-based data valuation provides a principled way to quantify the contribution of training data, but its high computational cost makes it impractical in dynamic settings where tasks and training players evolve. Existing methods treat…

Machine Learning · Computer Science 2026-05-21 Xuan Yang , Hsi-Wen Chen , Ming-Syan Chen , Jian Pei

We propose probabilistic Shapley inference (PSI), a novel probabilistic framework to model and infer sufficient statistics of feature attributions in flexible predictive models, via latent random variables whose mean recovers Shapley…

Machine Learning · Computer Science 2025-09-09 Mert Ketenci , Iñigo Urteaga , Victor Alfonso Rodriguez , Noémie Elhadad , Adler Perotte

Graphs are commonly used in machine learning to model relationships between instances. Consider the task of predicting the political preferences of users in a social network; to solve this task one should consider, both, the features of…

Machine Learning · Computer Science 2026-01-06 Clemens Damke , Eyke Hüllermeier

The concept of probabilistic values, such as Beta Shapley values and weighted Banzhaf values, has gained recent attention in applications like feature attribution and data valuation. However, exact computation of these values is often…

Machine Learning · Computer Science 2024-11-01 Weida Li , Yaoliang Yu

Shapley values are ubiquitous in interpretable Machine Learning due to their strong theoretical background and efficient implementation in the SHAP library. Computing these values previously induced an exponential cost with respect to the…

Machine Learning · Computer Science 2022-12-06 Gabriel Laberge , Yann Pequignot

Shapley effects are attracting increasing attention as sensitivity measures. When the value function is the conditional variance, they account for the individual and higher order effects of a model input. They are also well defined under…

Computation · Statistics 2021-10-13 Elmar Plischke , Giovanni Rabitti , Emanuele Borgonovo

What is the value of an individual model in an ensemble of binary classifiers? We answer this question by introducing a class of transferable utility cooperative games called \textit{ensemble games}. In machine learning ensembles,…

Machine Learning · Computer Science 2021-06-14 Benedek Rozemberczki , Rik Sarkar

We consider an investment process that includes a number of features, each of which can be active or inactive. Our goal is to attribute or decompose an achieved performance to each of these features, plus a baseline value. There are many…

Computational Finance · Quantitative Finance 2021-02-12 Nicholas Moehle , Stephen Boyd , Andrew Ang

Machine learning models are widely applied in various fields. Stakeholders often use post-hoc feature importance methods to better understand the input features' contribution to the models' predictions. The interpretation of the importance…

Machine Learning · Statistics 2024-04-19 Bitya Neuhof , Yuval Benjamini

Shapley value-based methods have become foundational in explainable artificial intelligence (XAI), offering theoretically grounded feature attributions through cooperative game theory. However, in practice, particularly in vision tasks, the…

Artificial Intelligence · Computer Science 2026-02-20 Xiangyu Zhou , Chenhan Xiao , Yang Weng

Large Language Models (LLMs) are increasingly used in systems that retrieve and summarize content from multiple sources, such as search engines and AI assistants. While these systems enhance user experience through coherent summaries, they…

Computation and Language · Computer Science 2026-01-08 Zikun Ye , Hema Yoganarasimhan

Multi-label classification is a type of classification task, it is used when there are two or more classes, and the data point we want to predict may belong to none of the classes or all of them at the same time. In the real world, many…

Machine Learning · Computer Science 2021-04-26 Shikun Chen

Queries with aggregation and arithmetic operations, as well as incomplete data, are common in real-world database, but we lack a good understanding of how they should interact. On the one hand, systems based on SQL provide ad-hoc rules for…

Databases · Computer Science 2022-11-02 Marco Console , Leonid Libkin , Liat Peterfreund

Recent studies have examined the computational complexity of computing Shapley additive explanations (also known as SHAP) across various models and distributions, revealing their tractability or intractability in different settings.…

Machine Learning · Computer Science 2025-02-19 Reda Marzouk , Shahaf Bassan , Guy Katz , Colin de la Higuera

Deep Neural Networks (DNNs) have demonstrated strong capacity in supporting a wide variety of applications. Shapley value has emerged as a prominent tool to analyze feature importance to help people understand the inference process of deep…

Machine Learning · Statistics 2025-02-19 Xiaolei Lu

Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…

Soft Condensed Matter · Physics 2012-01-18 Aaron S. Keys , Christopher R. Iacovella , Sharon C. Glotzer