Related papers: IMP: A Message-Passing Algorithmfor Matrix Complet…
The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completion problem are based on singular value thresholding and…
Vector Approximate Message Passing (VAMP) provides the means of solving a linear inverse problem in a Bayes-optimal way assuming the measurement operator is sufficiently random. However, VAMP requires implementing the linear minimum mean…
We consider the estimation of an i.i.d.\ random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message…
Machine learning techniques for Recommendation System (RS) and Classification has become a prime focus of research to tackle the problem of information overload. RS are software tools that aim at making informed decisions about the services…
Approximate message passing is an iterative algorithm for compressed sensing and related applications. A solid theory about the performance and convergence of the algorithm exists for measurement matrices having iid entries of zero mean.…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
Message passing (MP) is a computational technique used to find approximate solutions to a variety of problems defined on networks. MP approximations are generally accurate in locally tree-like networks but require corrections to maintain…
Matrix completion refers to completing a low-rank matrix from a few observed elements of its entries and has been known as one of the significant and widely-used problems in recent years. The required number of observations for exact…
We investigate the low rank matrix completion problem in an online setting with ${M}$ users, ${N}$ items, ${T}$ rounds, and an unknown rank-$r$ reward matrix ${R}\in \mathbb{R}^{{M}\times {N}}$. This problem has been well-studied in the…
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 work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…
Efficiently finding the maximum a posteriori (MAP) configuration of a graphical model is an important problem which is often implemented using message passing algorithms. The optimality of such algorithms is only well established for…
The ubiquity of approximately sparse data has led a variety of com- munities to great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying…
Although Recommender Systems have been comprehensively studied in the past decade both in industry and academia, most of current recommender systems suffer from the following issues: 1) The data sparsity of the user-item matrix seriously…
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…
In this paper, we study the popularly dubbed matrix completion problem, where the task is to "fill in" the unobserved entries of a matrix from a small subset of observed entries, under the assumption that the underlying matrix is of…
In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation constraint. NMU results are…
We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…
Gaussian Process (GP) formulation of continuoustime trajectory offers a fast solution to the motion planning problem via probabilistic inference on factor graph. However, often the solution converges to in-feasible local minima and the…
We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the…