相关论文: A remark on unified error exponents: Hypothesis te…

In the simple quantum hypothesis testing problem, upper bounds on the error probabilities are shown based on a key operator inequality between a density operator and its pinching. Concerning the error exponents, the upper bounds lead to a…

Compressing word embeddings is important for deploying NLP models in memory-constrained settings. However, understanding what makes compressed embeddings perform well on downstream tasks is challenging---existing measures of compression…

Determining the minimum density of a covering of $\mathbb{R}^{n}$ by Euclidean unit balls as $n\to\infty$ is a major open problem, with the best known results being the lower bound of $\left(\mathrm{e}^{-3/2}+o(1)\right)n$ by Coxeter, Few…

For each positive integer n this paper considers a one-parameter family of complex-valued measures on the symmetric group S_n, depending on a complex parameter z. For parameter values z=p^f a prime power, this measure describes splitting…

Feature allocation models generalize species sampling models by allowing every observation to belong to more than one species, now called features. Under the popular Bernoulli product model for feature allocation, given $n$ samples, we…

Gaussian boson sampling (GBS) is a promising protocol for demonstrating quantum computational advantage. One of the key steps for proving classical hardness of GBS is the so-called ``hiding conjecture'', which asserts that one can ``hide''…

A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…

The study of finite approximations of probability measures has a long history. In (Xu and Berger, 2017), the authors focus on constrained finite approximations and, in particular, uniform ones in dimension $d=1$. The present paper gives an…

The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…

Bob predicts a future observation based on a sample of size one. Alice can draw a sample of any size before issuing her prediction. How much better can she do than Bob? Perhaps surprisingly, under a large class of loss functions, which we…

We investigate volume-element sampling strategies for the stochastic homogenization of particle-reinforced composites and show, via computational experiments, that an improper treatment of particles intersecting the boundary of the…

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…

We consider a new method for estimating the parameters of univariate Gaussian mixture models. The method relies on a nonparametric density estimator $\hat{f}_n$ (typically a kernel estimator). For every set of Gaussian mixture components,…

We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the…

Assessing whether two datasets are distributionally consistent is central to modern scientific analysis, particularly as generative artificial intelligence produces synthetic data whose fidelity must be validated against real observations…

We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…

Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…

In a previous work, a simple approach to derive the jamming packing fraction of a hard-sphere mixture from the knowledge of the random close-packing fraction of the monocomponent system was proposed. Now, an extension of that approach is…

Given the widespread use of lossless compression algorithms to approximate algorithmic (Kolmogorov-Chaitin) complexity, and that lossless compression algorithms fall short at characterizing patterns other than statistical ones not different…