相关论文: Biwhitening Reveals the Rank of a Count Matrix

In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…

We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…

We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…

Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries.…

The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…

We study the statistical decision process of detecting the signal from a `signal+noise' type matrix model with an additive Wigner noise. We propose a hypothesis test based on the linear spectral statistics of the data matrix, which does not…

High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…

We study the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of rank-one measurements using sensing vectors composed of i.i.d. standard Gaussian entries, which are possibly corrupted by arbitrary outliers.…

We study symmetric spiked matrix models with respect to a general class of noise distributions. Given a rank-1 deformation of a random noise matrix, whose entries are independently distributed with zero mean and unit variance, the goal is…

We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood,…

Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially…

The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…

We consider the problem of estimating a rank-1 signal corrupted by structured rotationally invariant noise, and address the following question: how well do inference algorithms perform when the noise statistics is unknown and hence Gaussian…

This work explores non-negative low-rank matrix factorization based on regularized Poisson models (PF or "Poisson factorization" for short) for recommender systems with implicit-feedback data. The properties of Poisson likelihood allow a…

How can we discern whether the covariance operator of a stochastic process is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for…

Recommender system is a widely adopted technology in a diversified class of product lines. Modern day recommender system approaches include matrix factorization, learning to rank and deep learning paradigms, etc. Unlike many other…

Principal component analysis (PCA) is a foundational tool in modern data analysis, and a crucial step in PCA is selecting the number of components to keep. However, classical selection methods (e.g., scree plots, parallel analysis, etc.)…

Boolean matrix factorization (BMF) is a popular and powerful technique for inferring knowledge from data. The mining result is the Boolean product of two matrices, approximating the input dataset. The Boolean product is a disjunction of…

We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to…

The comparison of benchmark error sets is an essential tool for the evaluation of theories in computational chemistry. The standard ranking of methods by their Mean Unsigned Error is unsatisfactory for several reasons linked to the…