Related papers: Intrinsic convergence properties of entropic sampl…
The entropy of a quantum system is a measure of its randomness, and has applications in measuring quantum entanglement. We study the problem of measuring the von Neumann entropy, $S(\rho)$, and R\'enyi entropy, $S_\alpha(\rho)$ of an…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Entropy regularization is an efficient technique for encouraging exploration and preventing a premature convergence of (vanilla) policy gradient methods in reinforcement learning (RL). However, the theoretical understanding of…
Consider a two-class classification problem where the number of features is much larger than the sample size. The features are masked by Gaussian noise with mean zero and covariance matrix $\Sigma$, where the precision matrix…
In this paper, we first propose a unified framework for analyzing the stability of the phaseless operators for both amplitude and intensity measurement on an arbitrary geometric set, thereby characterizing the robust performance of phase…
In a wireless sensor network, data from various sensors are gathered to estimate the system-state of the process system. However, adversaries aim at distorting the system-state estimate, for which they may infiltrate sensors or position…
Stochastic policies (also known as relaxed controls) are widely used in continuous-time reinforcement learning algorithms. However, executing a stochastic policy and evaluating its performance in a continuous-time environment remain open…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
We describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models. The density of states is modified at each step when the energy…
Model-free reinforcement learning attempts to find an optimal control action for an unknown dynamical system by directly searching over the parameter space of controllers. The convergence behavior and statistical properties of these…
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…
The rapid growth of entanglement under unitary time evolution is the primary bottleneck for modern tensor-network techniques--such as Matrix Product States (MPS)--when computing time-dependent expectation values. This {entanglement barrier}…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
A cornerstone of numerical homogenization is the equivalence of the microscopic and the macroscopic energy densities, which is referred to as Hill-Mandel condition. Among these coupling conditions, the cases of periodic, linear displacement…
We propose a method of computing and studying entanglement quantities in non-Hermitian systems by use of a biorthogonal basis. We find that the entanglement spectrum characterizes the topological properties in terms of the existence of…
The recovery of an unknown density matrix of large size requires huge computational resources. The recent Factored Gradient Descent (FGD) algorithm and its variants achieved state-of-the-art performance since they could mitigate the…
Flatness of sampled data systems can be characterized by a simple property. They must admit the transformation to special representations, which are the series or partial series connection of a Brunovsky normal form and a complement. It is…
The statistical mechanics characterization of a finite subsystem embedded in an infinite system is a fundamental question of quantum physics. Nevertheless, a full closed form { for all required entropic measures} does not exist in the…
As far as we know, there is no flat-histogram algorithm to sample the stationary distribution of non-equilibrium stochastic processes. The present work addresses this gap by introducing a generalization of the Wang-Landau algorithm, applied…
Test-time adaptation (TTA) may fail to improve or even harm the model performance when test data have: 1) mixed distribution shifts, 2) small batch sizes, 3) online imbalanced label distribution shifts. This is often a key obstacle…