Related papers: Empirical Bayes Linked Matrix Decomposition
In recent years, a number of methods have been developed for the dimension reduction and decomposition of multiple linked high-content data matrices. Typically these methods assume that just one dimension, rows or columns, is shared among…
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization,…
Multiple imputation has become one of the standard methods in drawing inferences in many incomplete data applications. Applications of multiple imputation in relatively more complex settings, such as high-dimensional clustered data, require…
Advances in molecular "omics'" technologies have motivated new methodology for the integration of multiple sources of high-content biomedical data. However, most statistical methods for integrating multiple data matrices only consider data…
Bayesian matrix factorization (BMF) is a powerful tool for producing low-rank representations of matrices and for predicting missing values and providing confidence intervals. Scaling up the posterior inference for massive-scale matrices is…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…
Real-world clinical problems are often characterized by multimodal data, usually associated with incomplete views and limited sample sizes in their cohorts, posing significant limitations for machine learning algorithms. In this work, we…
Several modern applications require the integration of multiple large data matrices that have shared rows and/or columns. For example, cancer studies that integrate multiple omics platforms across multiple types of cancer, pan-omics…
With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent…
Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine.…
In this paper, we propose a probabilistic model for computing an interpolative decomposition (ID) in which each column of the observed matrix has its own priority or importance, so that the end result of the decomposition finds a set of…
We introduce a flexible framework for high-dimensional matrix estimation to incorporate side information for both rows and columns. Existing approaches, such as inductive matrix completion, often impose restrictive structure-for example, an…
This study proposes a new Bayesian approach to infer binary treatment effects. The approach treats counterfactual untreated outcomes as missing observations and infers them by completing a matrix composed of realized and potential untreated…
This paper presents a new modeling strategy for joint unsupervised analysis of multiple high-throughput biological studies. As in Multi-study Factor Analysis, our goals are to identify both common factors shared across studies and…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
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…
Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…