Related papers: A Bayesian Approach for Noisy Matrix Completion: O…
We study the problem of exact completion for $m \times n$ sized matrix of rank $r$ with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces (which we call…
Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…
We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are characterized by an equivalent Gaussian model with an effective…
We consider the statistical inference for noisy incomplete binary (or 1-bit) matrix. Despite the importance of uncertainty quantification to matrix completion, most of the categorical matrix completion literature focuses on point estimation…
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…
A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…
Matrix completion aims to estimate missing entries in a data matrix, using the assumption of a low-complexity structure (e.g., low rank) so that imputation is possible. While many effective estimation algorithms exist in the literature,…
Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference,…
Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary…
In this paper we develop a theory of matrix completion for the extreme case of noisy 1-bit observations. Instead of observing a subset of the real-valued entries of a matrix M, we obtain a small number of binary (1-bit) measurements…
We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…
This paper studies the problem of learning Bayesian networks from continuous observational data, generated according to a linear Gaussian structural equation model. We consider an $\ell_0$-penalized maximum likelihood estimator for this…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
We study the problem of matrix completion in this paper. A spectral scaled Student prior is exploited to favour the underlying low-rank structure of the data matrix. We provide a thorough theoretical investigation for our approach through…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…
Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…