Related papers: Semiparametric Cross Entropy for rare-event simula…
Minimizing cross-entropy is a widely used method for training artificial neural networks. Many training procedures based on backpropagation use cross-entropy directly as their loss function. Instead, this theoretical essay investigates a…
Estimating rare events in complex systems is a key challenge in reliability analysis. The challenge grows in multimodal problems, where traditional methods often rely on a small set of design points and risk overlooking critical failure…
The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically…
Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted…
Given a sequence composed of a limit number of characters, we try to "read" it as a "text". This involves to segment the sequence into "words". The difficulty is to distinguish good segmentation from enormous number of random ones.Aiming at…
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…
Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…
The domination problem and several of its variants (total domination, 2-domination and secure domination) are considered. These problems have various real-world applications, but are NP-hard to solve to provable optimality, making fast…
Covariate balance is a conventional key diagnostic for methods used estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm with the Cross-Entropy (CE) method for non smooth constrained optimization. The CE method is used as a Search step by the MADS algorithm. The result of…
Enhanced sampling methods typically require predefined collective variables (CVs) that presuppose knowledge of reaction coordinates, restricting the discovery of unanticipated transition mechanisms or intermediates. Here, we show that a…
In this paper, a safe and learning-based control framework for model predictive control (MPC) is proposed to optimize nonlinear systems with a non-differentiable objective function under uncertain environmental disturbances. The control…
The method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is guided by intuition gained from the…
This work deals with the solution of a non-convex optimization problem to enhance the performance of an energy harvesting device, which involves a nonlinear objective function and a discontinuous constraint. This optimization problem, which…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…