Related papers: The CLT in high dimensions: quantitative bounds vi…
Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To…
We investigate the multivariate central limit theorem for nonlinear statistics by means of Stein's method and Slepian's smart path interpolation method. Based on certain difference operators in theory of concentration inequalities, we…
We consider point particle that collides with a periodic array of hard-core elastic scatterers where the length of the free flights is unbounded (the infinite-horizon Lorentz gas, LG). The Bleher central limit theorem (CLT) states that the…
Stochastic gradient descent (SGD) has emerged as the quintessential method in a data scientist's toolbox. Using SGD for high-stakes applications requires, however, careful quantification of the associated uncertainty. Towards that end, in…
We introduce a unified framework to estimate the convergence of Markov chains to equilibrium in Wasserstein distance. The framework can provide convergence bounds with rates ranging from polynomial to exponential, all derived from a…
We revisited the central limit theorem (CLT) for stochastic gradient descent (SGD) type methods, including the vanilla SGD, momentum SGD and Nesterov accelerated SGD methods with constant or vanishing damping parameters. By taking advantage…
The article presents new entropic continuity bounds for conditional expectations and conditional covariance matrices. These bounds are expressed in terms of the relative entropy between different coupling distributions. Our approach…
Maxwell's velocity distribution is known to be universally valid across systems and phases. Here we present a new and general derivation that uses the central limit theorem (CLT) of the probability theory. This essentially uses the idea…
We consider the rates of convergence of the quenched central limit theorem for hitting times of one-dimensional random walks in a random environment. Previous results had identified polynomial upper bounds for the rates of decay which are…
Lloyd's algorithm is an iterative method that solves the quantization problem, i.e. the approximation of a target probability measure by a discrete one, and is particularly used in digital applications. This algorithm can be interpreted as…
We develop a new methodology for model-based clustering. Optimizing the log-likelihood provides a principled statistical framework for clustering, with solutions found via the EM algorithm. However, because the log-likelihood is nonconvex,…
We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random…
Recent work has proposed the use of a composite hypothesis Hoeffding test for statistical anomaly detection. Setting an appropriate threshold for the test given a desired false alarm probability involves approximating the false alarm…
We revisit the question of characterizing the convergence rate of plug-in estimators of optimal transport costs. It is well known that an empirical measure comprising independent samples from an absolutely continuous distribution on…
A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…
We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the…
Designing large coupling memory quasi-cyclic spatially-coupled LDPC (QC-SC-LDPC) codes with low error floors requires eliminating specific harmful substructures (e.g., short cycles) induced by edge spreading and lifting. Building on our…
Using martingale methods, we provide bounds for the entropy of a probability measure on $\mathbb {R}^d$ with the right-hand side given in a certain integral form. As a corollary, in the one-dimensional case, we obtain a weighted log-Sobolev…
This article deals with the error estimates for numerical approximations of the entropy solutions of coupled systems of nonlocal hyperbolic conservation laws. The systems can be strongly coupled through the nonlocal coefficient present in…
The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d.…