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A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC),…
We present a new algorithm for estimating the star discrepancy of arbitrary point sets. Similar to the algorithm for discrepancy approximation of Winker and Fang [SIAM J. Numer. Anal. 34 (1997), 2028--2042] it is based on the optimization…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
Randomized smoothing (RS) is an effective and scalable technique for constructing neural network classifiers that are certifiably robust to adversarial perturbations. Most RS works focus on training a good base model that boosts the…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
In this paper, we develop a symmetric accelerated stochastic Alternating Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
A novel movable-element enabled simultaneously transmitting and reflecting surface (ME-STARS) communication system is proposed, where ME-STARS elements positions can be adjusted to enhance the degress-of-freedom for transmission and…
We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a…
In this paper, we revisit the problem of private stochastic convex optimization. We propose an algorithm based on noisy mirror descent, which achieves optimal rates both in terms of statistical complexity and number of queries to a…
This paper studies decentralized stochastic nonconvex optimization problem over row-stochastic networks. We consider the heavy-tailed gradient noise which is empirically observed in many popular real-world applications. Specifically, we…
This paper presents Sparse Gradient Descent as a solution for variable selection in convex piecewise linear regression, where the model is given as the maximum of $k$-affine functions $ x \mapsto \max_{j \in [k]} \langle a_j^\star, x…
It is known that evolution strategies in continuous domains might not converge in the presence of noise. It is also known that, under mild assumptions, and using an increasing number of resamplings, one can mitigate the effect of additive…
We design and analyze an algorithm for first-order stochastic optimization of a large class of functions on $\mathbb{R}^d$. In particular, we consider the \emph{variationally coherent} functions which can be convex or non-convex. The…
We introduce a class of convex equivolume partitions. Expected star discrepancy results are compared for stratified samples under these partitions, including simple random samples. There are four main parts of our results. First, among…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative…
This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…
The sum-rate performance of simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted full-duplex (FD) communication systems is investigated. The reflection and transmission coefficients of STAR-RIS…