An Axiomatisation of the Banzhaf Value and Interaction Index for Multichoice Games

Ridaoui, Mustapha; Grabisch, Michel; Labreuche, Christophe

doi:10.1007/978-3-030-00202-2_12

Cited by 7 publications

(4 citation statements)

References 20 publications

(26 reference statements)

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“…Why not additivity and efficiency? Actually, we do not expect the Variational Values to satisfy the additivity and efficiency axioms due to the following reasons: 1) Similar as what Ridaoui et al (2018) argues, efficiency and additivity do not make sense for certain games. Let us consider feature valuation in the simple classification problem, which can be viewed as a voting game (N, F(S)): each feature participates in the coalition in order to vote for the classification result to be true or false.…”

Section: Axiomatisation Of Variational Valuesmentioning

confidence: 98%

Energy-Based Learning for Cooperative Games, with Applications to Valuation Problems in Machine Learning

Bian¹,

Rong²,

Xu³

et al. 2021

Preprint

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Valuation problems, such as attribution-based feature interpretation, data valuation and model valuation for ensembles, become increasingly more important in many machine learning applications. Such problems are commonly addressed via well-known gametheoretic criteria, such as the Shapley value or Banzhaf index. In this work, we present a novel energy-based treatment for cooperative games, with a theoretical justification by the maximum entropy framework. Surprisingly, by conducting variational inference of the energy-based model, we recover classical game-theoretic valuation criteria through conducting one-step gradient ascent for maximizing the mean-field ELBO objective. This observation also verifies the rationality of existing criteria, as they are all trying to decouple the correlations among the players through the mean-field approach. By running gradient ascent for multiple steps, we achieve a trajectory of the valuations, among which we define the valuation with the best conceivable decoupling error as the Variational Index. We experimentally demonstrate that the proposed Variational Index enjoys intriguing properties on certain synthetic and real-world valuation problems.

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Section: Axiomatisation Of Variational Valuesmentioning

confidence: 98%

Energy-Based Learning for Cooperative Games, with Applications to Valuation Problems in Machine Learning

Bian¹,

Rong²,

Xu³

et al. 2021

Preprint

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show abstract

“…To ensure the fairness of data valuation functions, a common approach in CGT is axiomatization, where a list of axioms is provided to be fulfilled by data valuation functions. There are four important axioms that are commonly agreed to be fair (Covert, Lundberg, and Lee 2021;Ridaoui, Grabisch, and Labreuche 2018;Sim, Xu, and Low 2022): Linearity, Dummy Player, Interchangeability and Monotonicity (refer to App. A for their respective definition and connection to fairness).…”

Section: Semivalue-based Data Valuationmentioning

confidence: 99%

“…This mandates model owners to delete the data and their impact from trained models without undue delay (Magdziarczyk 2019) upon request or after a stipulated time (Ong 2018). While these regulations have led to intensive research on machine unlearning (Bourtoule et al 2021;Chen et al 2021;Sekhari et al 2021) to efficiently remove the impact of deleted data from trained models, to our knowledge, no work has considered the impact of data deletions on data valuation.…”

Section: Introductionmentioning

confidence: 99%

DeRDaVa: Deletion-Robust Data Valuation for Machine Learning

Tian,

Sim,

Fan

et al. 2024

AAAI

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Data valuation is concerned with determining a fair valuation of data from data sources to compensate them or to identify training examples that are the most or least useful for predictions. With the rising interest in personal data ownership and data protection regulations, model owners will likely have to fulfil more data deletion requests. This raises issues that have not been addressed by existing works: Are the data valuation scores still fair with deletions? Must the scores be expensively recomputed? The answer is no. To avoid recomputations, we propose using our data valuation framework DeRDaVa upfront for valuing each data source's contribution to preserving robust model performance after anticipated data deletions. DeRDaVa can be efficiently approximated and will assign higher values to data that are more useful or less likely to be deleted. We further generalize DeRDaVa to Risk-DeRDaVa to cater to risk-averse/seeking model owners who are concerned with the worst/best-cases model utility. We also empirically demonstrate the practicality of our solutions.

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“…When the symmetry axiom is removed, the quasivalue and the weighted value have been studied (Shapley, 1953a;Banzhaf III, 1964;Gilboa and Monderer, 1991;Monderer et al, 1992). When the efficiency axiom is removed, the semivalue has been studied (Dubey and Weber, 1977;Dubey et al, 1981;Ridaoui et al, 2018). We refer to Monderer and Samet (2002b) for a complementary literature review of variations of Shapley value.…”

Section: Related Workmentioning

confidence: 99%

Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning

Kwon¹,

Zou²

2021

Preprint

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Data Shapley has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. It can effectively identify helpful or harmful data points for a learning algorithm. In this paper, we propose Beta Shapley, which is a substantial generalization of Data Shapley. Beta Shapley arises naturally by relaxing the efficiency axiom of the Shapley value, which is not critical for machine learning settings. Beta Shapley unifies several popular data valuation methods and includes data Shapley as a special case. Moreover, we prove that Beta Shapley has several desirable statistical properties and propose efficient algorithms to estimate it. We demonstrate that Beta Shapley outperforms state-of-the-art data valuation methods on several downstream ML tasks such as: 1) detecting mislabeled training data; 2) learning with subsamples; and 3) identifying points whose addition or removal have the largest positive or negative impact on the model.

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An Axiomatisation of the Banzhaf Value and Interaction Index for Multichoice Games

Cited by 7 publications

References 20 publications

Energy-Based Learning for Cooperative Games, with Applications to Valuation Problems in Machine Learning

Energy-Based Learning for Cooperative Games, with Applications to Valuation Problems in Machine Learning

DeRDaVa: Deletion-Robust Data Valuation for Machine Learning

Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning

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