相关论文: Estimation of the Shapley value by ergodic samplin…

We establish, for the first time, a connection between stochastic games and multiparameter eigenvalue problems, using the theory developed by Shapley and Snow (1950). This connection provides new results, new proofs, and new tools for…

We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies. Given a positive real $\epsilon$, let us call a stochastic game $\epsilon$-ergodic, if its values from any two initial…

Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…

Measuring contributions is a classical problem in cooperative game theory where the Shapley value is the most well-known solution concept. In this paper, we establish the convergence property of the Shapley value in parametric Bayesian…

Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…

We propose the study of computing the Shapley value for a new class of cooperative games that we call budgeted games, and investigate in particular knapsack budgeted games, a version modeled after the classical knapsack problem. In these…

The method proposed by Bernardo and Smith [2000] to approximate reference priors by simulation was analyzed with the objective of improving the procedure in order to obtain consistent estimators and to allow the estimation of asymptotic…

In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an algorithm that…

Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…

We present a new method for conducting Monte Carlo inference in graphical models which combines explicit search with generalized importance sampling. The idea is to reduce the variance of importance sampling by searching for significant…

Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…

Investing efficiently in future research to improve policy decisions is an important goal. Expected Value of Sample Information (EVSI) can be used to select the specific design and sample size of a proposed study by assessing the benefit of…

Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…

The Shapley value is a common tool in game theory to evaluate the importance of a player in a cooperative setting. In a geometric context, it provides a way to measure the contribution of a geometric object in a set towards some function on…

We show that in any $n$-player $m$-action normal-form game, we can obtain an approximate equilibrium by sampling any mixed-action equilibrium a small number of times. We study three types of equilibria: Nash, correlated and coarse…

Shapley values are among the most popular tools for explaining predictions of blackbox machine learning models. However, their high computational cost motivates the use of sampling approximations, inducing a considerable degree of…

It is often necessary to make sampling-based statistical inference about many probability distributions in parallel. Given a finite computational resource, this article addresses how to optimally divide sampling effort between the samplers…

Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values…

In this paper, we consider convex stochastic optimization problems arising in machine learning applications (e.g., risk minimization) and mathematical statistics (e.g., maximum likelihood estimation). There are two main approaches to solve…

The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…