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Based on the idea of randomized coordinate descent of $\alpha$-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a…
Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
The integration and transfer of information from multiple sources to multiple targets is a core motive of neural systems. The emerging field of partial information decomposition (PID) provides a novel information-theoretic lens into these…
Inspired by applications in weighted polynomial approximation problems, we study an optimal mass distribution problem. Given a gauge function $h$ and a positive "roof" function $R$ compactly supported in $\mathbb{R}^n$, we are interested in…
We consider Scherk-Schwarz compactifications of M-theory (toroidal compactifications with a non-trivial spin structure) in various dimensions and find isolated critical points of the potential on the moduli space. We demonstrate this by…
The Linear Quadratic Gaussian (LQG) controller is known to be inherently fragile to model misspecifications common in real-world situations. We consider discrete-time partially observable stochastic linear systems and provide a…
The paper deals with studying a connection of the Littlewood--Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions. It is shown that the values at zero of the concentration…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
In this paper, we have studied various mixed distributions generated by two uniform distributions: first, where the supports are two connected line segments, and second, where the supports are two disconnected line segments. For these mixed…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…
Given two discrete random variables $X$ and $Y,$ with probability distributions ${\bf p}=(p_1, \ldots , p_n)$ and ${\bf q}=(q_1, \ldots , q_m)$, respectively, denote by ${\cal C}({\bf p}, {\bf q})$ the set of all couplings of ${\bf p}$ and…
We consider the problem of distributed feature quantization, where the goal is to enable a pretrained classifier at a central node to carry out its classification on features that are gathered from distributed nodes through communication…
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…
In this paper, we consider a distributionally robust optimization (DRO) model in which the ambiguity set is defined as the set of distributions whose Kullback-Leibler (KL) divergence to an empirical distribution is bounded. Utilizing the…
Recent work in machine learning community proposed multiple methods for performing lossy compression (quantization) of large matrices. This quantization is important for accelerating matrix multiplication (main component of large language…
This paper presents a detailed theoretical analysis of the Langevin Monte Carlo sampling algorithm recently introduced in Durmus et al. (Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau, 2016)…
A lot of effort has been invested into characterizing the convergence rates of gradient based algorithms for non-linear convex optimization. Recently, motivated by large datasets and problems in machine learning, the interest has shifted…
Kiefer and Wolfowitz [Z. Wahrsch. Verw. Gebiete 34 (1976) 73--85] showed that if $F$ is a strictly curved concave distribution function (corresponding to a strictly monotone density $f$), then the Maximum Likelihood Estimator $\hat{F}_n$,…
In this paper, we propose a primal-dual splitting algorithm for a broad class of structured composite monotone inclusions that involve finitely many set-valued operators, compositions of set-valued operators with bounded linear operators,…