Related papers: Subgroup Identification with Latent Factor Structu…

In this paper, a subgroup least squares and a convex clustering are introduced for inferring a partially heterogenous linear regression that has potential application in the areas of precision marketing and precision medicine. The…

In this paper, we focus on exploiting the group structure for large-dimensional factor models, which captures the homogeneous effects of common factors on individuals within the same group. In view of the fact that datasets in…

The alternating direction method of multipliers (ADMM) has been widely adopted in low-rank approximation and low-order model identification tasks; however, the performance of nonconvex ADMM is highly reliant on the choice of penalty…

Sparse feature selection has been demonstrated to be effective in handling high-dimensional data. While promising, most of the existing works use convex methods, which may be suboptimal in terms of the accuracy of feature selection and…

In this paper, we propose a novel element-wise subset selection method for the alternating least squares (ALS) algorithm, focusing on low-rank matrix factorization involving matrices with missing values, as commonly encountered in…

Discovering and clustering subspaces in high-dimensional data is a fundamental problem of machine learning with a wide range of applications in data mining, computer vision, and pattern recognition. Earlier methods divided the problem into…

Group-prior based regularization method has led to great successes in various image processing tasks, which can usually be considered as a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear…

Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…

In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…

We introduce a general tensor model suitable for data analytic tasks for {\em heterogeneous} datasets, wherein there are joint low-rank structures within groups of observations, but also discriminative structures across different groups. To…

Group imbalance, resulting from inadequate or unrepresentative data collection methods, is a primary cause of representation bias in datasets. Representation bias can exist with respect to different groups of one or more protected…

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require…

Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a…

The alternating direction method of multipliers (ADMM) has been applied successfully in a broad spectrum of areas. Moreover, it was shown in the literature that ADMM is closely related to the Douglas-Rachford operator-splitting method, and…

We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…

In this paper, we study a constrained minimization problem that arise from materials science to determine the dislocation (line defect) structure of grain boundaries. The problems aims to minimize the energy of the grain boundary with…

We solve the compressive sensing problem via convolutional factor analysis, where the convolutional dictionaries are learned {\em in situ} from the compressed measurements. An alternating direction method of multipliers (ADMM) paradigm for…

Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…

Community detection is a crucial task in network analysis that can be significantly improved by incorporating subject-level information, i.e. covariates. However, current methods often struggle with selecting tuning parameters and analyzing…

Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…