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Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…

Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…

Higher-order lensing statistics contain a wealth of cosmological information that is not captured by second-order statistics. Stage-III lensing surveys have sufficient statistical power to significantly detect cumulant-based statistics up…

In fiber optic sensing, time delays induced by polarization mode dispersion can distort signals in systems relying on phase or intensity variations for measurement, degrading performance, especially in long distance, high-precision…

We prove optimal convergence results of a stochastic particle method for computing the classical solution of a multivariate McKean-Vlasov equation, when the measure variable is in the drift, following the classical approach of [BT97,…

In this paper, we present a variational inference algorithm that decomposes a signal into multiple groups of related spectral lines. The spectral lines in each group are associated with a group parameter common to all spectral lines within…

All 21-cm signal experiments rely on electronic receivers that affect the data via both multiplicative and additive biases through the receiver's gain and noise temperature. While experiments attempt to remove these biases, the residuals of…

Dimensionality reduction is critical for deploying dense retrieval systems at scale, yet mainstream post-hoc methods face a fundamental trade-off: principal component analysis (PCA) preserves dominant variance but underutilizes…

We present a novel methodology that combines graph and dense segmentation techniques by jointly learning both point and pixel contour representations, thereby leveraging the benefits of each approach. This addresses deficiencies in typical…

A number of recent works have proposed to solve the line spectral estimation problem by applying off-the-grid extensions of sparse estimation techniques. These methods are preferable over classical line spectral estimation algorithms…

We summarize our recent determination [1] of the spectral density of the Wilson operator in the p-regime of Wilson chiral perturbation theory. We discuss the range of validity of our formula and a possible extension to our computation in…

We propose a new method for the estimation of parameters of hidden diffusion processes. Based on parametrization of the transition matrix, the Baum-Welch algorithm is improved. The algorithm is compared to the particle filter in application…

A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral…

Estimation problems in wireless sensor networks typically involve gathering and processing data from distributed sensors to infer the state of an environment at the fusion center. However, not all measurements contribute significantly to…

The second-order dependence structure of purely nondeterministic stationary process is described by the coefficients of the famous Wold representation. These coefficients can be obtained by factorizing the spectral density of the process.…

Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…

Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…

A continuous-time nonlinear regression model with L\'evy-driven linear noise process is considered. Sufficient conditions of consistency and asymptotic normality of the Whittle estimator for the parameter of the noise spectral density are…

This paper studies two spectrum estimation methods for the case that the samples are obtained at a rate lower than the Nyquist rate. The first method is the correlogram method for undersampled data. The algorithm partitions the spectrum…

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…