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When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating errors may become inadequate. We present an iterative…

In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a…

For linear regression models with cross-section or panel data, it is natural to assume that the disturbances are clustered in two dimensions. However, the finite-sample properties of two-way cluster-robust tests and confidence intervals are…

We propose a new class of multiplier bootstraps for count functionals, ranging from a fast, approximate linear bootstrap tailored to sparse, massive graphs to a quadratic bootstrap procedure that offers refined accuracy for smaller, denser…

The Information bottleneck method is an unsupervised non-parametric data organization technique. Given a joint distribution P(A,B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are…

We prove new probabilistic upper bounds on generalization error of complex classifiers that are combinations of simple classifiers. Such combinations could be implemented by neural networks or by voting methods of combining the classifiers,…

For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…

Large-scale distributed training of deep neural networks suffer from the generalization gap caused by the increase in the effective mini-batch size. Previous approaches try to solve this problem by varying the learning rate and batch size…

We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…

Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with high-dimensional random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter,…

Simulating scalar wave propagation in strongly heterogeneous media comes at a steep computational cost, and the widely used approach to simplification - split-step operators - sacrifices accuracy. The recently proposed multi-layer Born…

Imputation methods play a critical role in enhancing the quality of practical time-series data, which often suffer from pervasive missing values. Recently, diffusion-based generative imputation methods have demonstrated remarkable success…

To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown…

This article presents a new spectral analysis approach for dispersion error and a methodology to numerically evaluate it. In practice, this new analysis allows the numerical study of dispersion errors on all types of mesh and for multiple…

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…

Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most…

In network science, researchers often use mutual information to understand the difference between network partitions produced by community detection methods. Here we extend the use of mutual information to covers, that is, the cases where a…

Recent stochastic gradient methods that have appeared in the literature base their efficiency and global convergence properties on a suitable control of the variance of the gradient batch estimate. This control is typically achieved by…

In a fixed-confidence pure exploration problem in stochastic multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions. We are…

Model-based reinforcement learning is one approach to increase sample efficiency. However, the accuracy of the dynamics model and the resulting compounding error over modelled trajectories are commonly regarded as key limitations. A natural…