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While there has been much interest in adapting conventional clustering procedures---and in higher dimensions, persistent homology methods---to directed networks, little is known about the convergence of such methods. In order to even…

The study of self-normalized processes plays a crucial role in a wide range of applications, from sequential decision-making to econometrics. While the behavior of self-normalized concentration has been widely investigated for scalar-valued…

We study compressed sensing when the sampling vectors are chosen from the rows of a unitary matrix. In the literature, these sampling vectors are typically chosen randomly; the use of randomness has enabled major empirical and theoretical…

We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.

We obtain moment and Gaussian bounds for general Lipschitz functions evaluated along the sample path of a Markov chain. We treat Markov chains on general (possibly unbounded) state spaces via a coupling method. If the first moment of the…

This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…

We show that the mixing times of random walks on compact groups can be used to obtain concentration inequalities for the respective Haar measures. As an application, we derive a concentration inequality for the empirical distribution of…

A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial…

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…

Non-maximum suppression (NMS) is used in virtually all state-of-the-art object detection pipelines. While essential object detection ingredients such as features, classifiers, and proposal methods have been extensively researched…

We prove that probability laws of certain multidimensional semimartingales which includes time-inhomogenous diffusions, under suitable assumptions, satisfy Quadratic Transportation Cost Inequality under the uniform metric. From this we…

This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series of random matrices to…

Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…

Concentration inequalities for the sample mean, like those due to Bernstein, Hoeffding, and Bentkus, are valid for any sample size but overly conservative, yielding confidence intervals that are unnecessarily wide. The central limit theorem…

The performance of tensor network methods has seen constant improvements over the last few years. We add to this effort by introducing a new algorithm that efficiently applies tree tensor network operators to tree tensor network states…

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…

In a recent article [A. Kurcz et al., Phys. Rev. A 81, 063821 (2010)] we predicted an energy concentrating mechanism in composite quantum systems. Its result is a non-zero stationary state photon emission rate even in the absence of…

Recent work has shown that self-attention can serve as a basic building block for image recognition models. We explore variations of self-attention and assess their effectiveness for image recognition. We consider two forms of…

Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…

Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs…