Related papers: Low-Rank Graphon Estimation: Theory and Applicatio…
The graphon (W-graph), including the stochastic block model as a special case, has been widely used in modeling and analyzing network data. This random graph model is well-characterized by its graphon function, and estimation of the graphon…
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…
We study the interplay between surrogate methods for structured prediction and techniques from multitask learning designed to leverage relationships between surrogate outputs. We propose an efficient algorithm based on trace norm…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
This paper studies the inference about linear functionals of high-dimensional low-rank matrices. While most existing inference methods would require consistent estimation of the true rank, our procedure is robust to rank misspecification,…
Deep linear networks trained with gradient descent yield low rank solutions, as is typically studied in matrix factorization. In this paper, we take a step further and analyze implicit rank regularization in autoencoders. We show greedy…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
We study stochastic differential games with $N$ players, where interactions are determined by sequences of graphs in which the number of neighbours of each node remains bounded as $N$ grows, such as chain graphs or lattices. Our main goal…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
We consider static finite-player network games and their continuum analogs, graphon games. Existence and uniqueness results are provided, as well as convergence of the finite-player network game optimal strategy profiles to their analogs…
This paper proposes the estimation of a smooth graphon model for network data analysis using principles of the EM algorithm. The approach considers both variability with respect to ordering the nodes of a network and smooth estimation of…
We study multi-agent general-sum Markov games with nonlinear function approximation. We focus on low-rank Markov games whose transition matrix admits a hidden low-rank structure on top of an unknown non-linear representation. The goal is to…
Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In…
Bayesian predictive synthesis provides a coherent Bayesian framework for combining multiple predictive distributions, or agents, into a single updated prediction, extending Bayesian model averaging to allow general pooling of full…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic…