Related papers: Analytical Forms for Most Likely Matrices Derived …
This paper studies the problem of completing a low-rank matrix from a few of its random entries with the aid of prior information. We suggest a strategy to incorporate prior information into the standard matrix completion procedure by…
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
Predicting unobserved entries of a partially observed matrix has found wide applicability in several areas, such as recommender systems, computational biology, and computer vision. Many scalable methods with rigorous theoretical guarantees…
This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
We revisit the classical problem of inverting dimension-reducing linear mappings using the maximum entropy (MaxEnt) criterion. In the literature, solutions are problem-dependent, inconsistent, and use different entropy measures. We propose…
In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from…
This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results…
During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…
We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and…
One of the main objectives of science is the recognition of a general pattern in a particular phenomenon in some particular regime. In this work, this is achieved with the analytical expression for the optimal protocol that minimizes the…
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…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
Humans are adept at uncovering abstract associations in the world around them, yet the underlying mechanisms remain poorly understood. Intuitively, learning the higher-order structure of statistical relationships should involve complex…
This work investigates a new approach to find closed form analytical approximate solution of linear initial value problems. Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite…
The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…
We propose a general method for optimally approximating an arbitrary matrix $\mathbf{M}$ by a structured matrix $\mathbf{T}$ (circulant, Toeplitz/Hankel, etc.) and examine its use for estimating the spectra of genomic linkage disequilibrium…
This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This…
Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…