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In this paper, we study the maximum entropy sampling problem (MESP) and its variants. MESP seeks to identify a small subset of variables that maximizes the determinant of a covariance submatrix, and is a fundamental model in optimal…
Based on a factorization of an input covariance matrix, we define a mild generalization of an upper bound of Nikolov (2015) and Li and Xie (2020) for the NP-Hard constrained maximum-entropy sampling problem (CMESP). We demonstrate that this…
This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix of a prespecified size from a covariance matrix. MESP has been widely applied to many areas, including…
The maximum-entropy remote sampling problem (MERSP) is to select a subset of s random variables from a set of n random variables, so as to maximize the information concerning a set of target random variables that are not directly…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
The maximum-entropy sampling problem is the NP-hard problem of maximizing the (log) determinant of an order-$s$ principle submatrix of a given order $n$ covariance matrix $C$. Exact algorithms are based on a branch-and-bound framework. The…
The generalized maximum-entropy sampling problem (GMESP) is to select an order-$s$ principal submatrix from an order-$n$ covariance matrix, to maximize the product of its $t$ greatest eigenvalues, $0<t\leq s <n$. Introduced more than 25…
The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…
The constrained generalized maximum-entropy sampling problem (CGMESP) is to select an order-s principal submatrix from an order-n covariance matrix, subject to some linear side constraints, so as to maximize the product of its t greatest…
The NP-hard maximum-entropy sampling problem (MESP) seeks a maximum (log-)determinant principal submatrix, of a given order, from an input covariance matrix $C$. We give an efficient dynamic-programming algorithm for MESP when $C$ (or its…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
Sampling from constrained distributions has a wide range of applications, including in Bayesian optimization and robotics. Prior work establishes convergence and feasibility guarantees for constrained sampling, but assumes that the feasible…
Modern deep neural networks achieved remarkable progress in medical image segmentation tasks. However, it has recently been observed that they tend to produce overconfident estimates, even in situations of high uncertainty, leading to…
The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…
We study the bootstrap for the maxima of the sums of independent random variables, a problem of high relevance to many applications in modern statistics. Since the consistency of bootstrap was justified by Gaussian approximation in…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…
Given a set of discrete probability distributions, the minimum entropy coupling is the minimum entropy joint distribution that has the input distributions as its marginals. This has immediate relevance to tasks such as entropic causal…
We study best-policy identification for finite-horizon risk-sensitive reinforcement learning under the entropic risk measure. Recent work established a constant gap in the exponential horizon dependence between lower and upper bounds on the…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the…