Related papers: Estimation of the Shapley value by ergodic samplin…

Importance sampling (IS) is a Monte Carlo technique that relies on weighted samples, simulated from a proposal distribution, to estimate intractable integrals. The quality of the estimators improves with the number of samples. However, for…

This paper introduces GeoShapley, a game theory approach to measuring spatial effects in machine learning models. GeoShapley extends the Nobel Prize-winning Shapley value framework in game theory by conceptualizing location as a player in a…

Data analytics allows an analyst to gain insight into underlying populations through the use of various computational approaches, including Monte Carlo methods. This paper discusses an approach to apply Monte Carlo methods to hedonic games.…

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…

Cooperative game theory methods, notably Shapley values, have significantly enhanced machine learning (ML) interpretability. However, existing explainable AI (XAI) frameworks mainly attribute average model predictions, overlooking…

The multilevel Monte Carlo method is applied to an academic example in the field of electromagnetism. The method exhibits a reduced variance by assigning the samples to multiple models with a varying spatial resolution. For the given…

Data valuation, especially quantifying data value in algorithmic prediction and decision-making, is a fundamental problem in data trading scenarios. The most widely used method is to define the data Shapley and approximate it by means of…

We investigate the use of a stratified sampling approach for LIME Image, a popular model-agnostic explainable AI method for computer vision tasks, in order to reduce the artifacts generated by typical Monte Carlo sampling. Such artifacts…

In Markov Chain Monte Carlo (MCMC) simulations, the thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the…

We consider game-theoretically secure distributed protocols for coalition games that approximate the Shapley value with small multiplicative error. Since all known existing approximation algorithms for the Shapley value are randomized, it…

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…

We study a class of two-player zero-sum stochastic games known as \textit{blind stochastic games}, where players neither observe the state nor receive any information about it during the game. A central concept for analyzing long-duration…

Probabilistic values, including Shapley values and semivalues, provide a model-agnostic framework to attribute the behavior of a black-box model to data points or features, with a wide range of applications including explainable artificial…

As data emerges as a vital driver of technological and economic advancements, a key challenge is accurately quantifying its value in algorithmic decision-making. The Shapley value, a well-established concept from cooperative game theory,…

We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…

Over the last few years, the Shapley value, a solution concept from cooperative game theory, has found numerous applications in machine learning. In this paper, we first discuss fundamental concepts of cooperative game theory and axiomatic…

Let $T:X\to X $ and $S:Y \to Y$ be continuous maps defined on compact sets. Let $$\varphi_i(\mu,\nu)=\int_{X \times Y} A_i(x,y) d\mu(x) d\nu(y)\;\;{for} \;\; i=1,2,$$ where $\mu$ is $T$-invariant and $\nu$ is $S$-invariant, be pay-off…

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo…

Cohort Shapley value is a model-free method of variable importance grounded in game theory that does not use any unobserved and potentially impossible feature combinations. We use it to evaluate algorithmic fairness, using the well known…

We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…