相关论文: Detecting approximate replicate components of a hi…

We study the problem nonparametric classification with repeated observations. Let $\bX$ be the $d$ dimensional feature vector and let $Y$ denote the label taking values in $\{1,\dots ,M\}$. In contrast to usual setup with large sample size…

We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…

Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of ``components.'' Typically, these components are linear combinations of the rows and columns of the matrix, and are thus…

We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…

The bifactor model and its extensions are multidimensional latent variable models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psychological…

This study addresses the challenge of accurately identifying multi-task contention types in high-dimensional system environments and proposes a unified contention classification framework that integrates representation transformation,…

This paper provides a comprehensive estimation framework via nuclear norm plus $l_1$ norm penalization for high-dimensional approximate factor models with a sparse residual covariance. The underlying assumptions allow for non-pervasive…

We consider algorithmic problems in the setting in which the input data has been partitioned arbitrarily on many servers. The goal is to compute a function of all the data, and the bottleneck is the communication used by the algorithm. We…

This paper develops the inferential theory for latent factor models estimated from large dimensional panel data with missing observations. We propose an easy-to-use all-purpose estimator for a latent factor model by applying principal…

We consider a similarity measure between two sets $A$ and $B$ of vectors, that balances the average and maximum cosine distance between pairs of vectors, one from set $A$ and one from set $B$. As a motivation for this measure, we present…

Large-scale Hierarchical Classification (HC) involves datasets consisting of thousands of classes and millions of training instances with high-dimensional features posing several big data challenges. Feature selection that aims to select…

Estimating graphical model structure from high-dimensional and undersampled data is a fundamental problem in many scientific fields. Existing approaches, such as GLASSO, latent variable GLASSO, and latent tree models, suffer from high…

Latent factor models are the canonical statistical tool for exploratory analyses of low-dimensional linear structure for an observation matrix with p features across n samples. We develop a structured Bayesian group factor analysis model…

Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…

A randomized algorithm for computing a data sparse representation of a given rank structured matrix $A$ (a.k.a. an $H$-matrix) is presented. The algorithm draws on the randomized singular value decomposition (RSVD), and operates under the…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…

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…

We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…

We build a simple diagnostic criterion for approximate factor structure in large cross-sectional equity datasets. Given a model for asset returns with observable factors, the criterion checks whether the error terms are weakly…