Related papers: Empirical Bayes 1-bit matrix completion

Boolean Matrix Factorization (BMF) aims to find an approximation of a given binary matrix as the Boolean product of two low-rank binary matrices. Binary data is ubiquitous in many fields, and representing data by binary matrices is common…

Binary matrix factorisation is an essential tool for identifying discrete patterns in binary data. In this paper we consider the rank-k binary matrix factorisation problem (k-BMF) under Boolean arithmetic: we are given an n x m binary…

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use…

Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…

In this paper we adopt the familiar sparse, high-dimensional linear regression model and focus on the important but often overlooked task of prediction. In particular, we consider a new empirical Bayes framework that incorporates data in…

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…

A general framework based on Gaussian models and a MAP-EM algorithm is introduced in this paper for solving matrix/table completion problems. The numerical experiments with the standard and challenging movie ratings data show that the…

We develop a class of minimax estimators for a normal mean matrix under the Frobenius loss, which generalizes the James--Stein and Efron--Morris estimators. It shrinks the Schatten norm towards zero and works well for low-rank matrices. We…

Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of…

We address estimation of one-parameter unitary gates for qubit systems and seek for optimal probes and measurements. Single- and two-qubit probes are analyzed in details focusing on precision and stability of the estimation procedure.…

We propose a principled framework for nonparametric empirical Bayes (EB) estimation, based on the idea that the prior should be consistent with the observed posterior and that Bayesian updating should be stable. Focusing on discretized…

Motivated by applications in tissue-wide association studies (TWAS), we develop a flexible and theoretically grounded empirical Bayes approach for integrating %vector-valued outcomes data obtained from different sources. We propose a linear…

Many statistical problems involve data from thousands of parallel cases. Each case has some associated effect size, and most cases will have no effect. It is often important to estimate the effect size and the local or tail-area false…

We consider estimation of a normal mean matrix under the Frobenius loss. Motivated by the Efron--Morris estimator, a generalization of Stein's prior has been recently developed, which is superharmonic and shrinks the singular values towards…

We propose an efficient family of algorithms to learn the parameters of a Bayesian network from incomplete data. In contrast to textbook approaches such as EM and the gradient method, our approach is non-iterative, yields closed form…

Empirical Bayes inference is based on estimation of the parameters of an a priori distribution from the observed data. The estimation technique of the parameters of the prior, called hyperparameters, is based on the marginal distribution…

In this paper we study the problem of bilinear regression and we further address the case when the response matrix contains missing data that referred as the problem of inductive matrix completion. We propose a quasi-Bayesian approach first…

We consider the low rank matrix completion problem over finite fields. This problem has been extensively studied in the domain of real/complex numbers, however, to the best of authors' knowledge, there exists merely one efficient algorithm…

We introduce Bayesian Bits, a practical method for joint mixed precision quantization and pruning through gradient based optimization. Bayesian Bits employs a novel decomposition of the quantization operation, which sequentially considers…

When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…