Related papers: Robust Reduced Rank Regression
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
Parameter estimation of mixture regression model using the expectation maximization (EM) algorithm is highly sensitive to outliers. Here we propose a fast and efficient robust mixture regression algorithm, called Component-wise Adaptive…
Numerous modern optimization and machine learning algorithms rely on subgradient information being trustworthy and hence, they may fail to converge when such information is corrupted. In this paper, we consider the setting where subgradient…
In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…
Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to…
Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…
Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…
The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…
Reduced-rank (RR) regression may be interpreted as a dimensionality reduction technique able to reveal complex relationships among the data parsimoniously. However, RR regression models typically overlook any potential group structure among…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
Heterogeneous data are now ubiquitous in many applications in which correctly identifying the subgroups from a heterogeneous population is critical. Although there is an increasing body of literature on subgroup detection, existing methods…
We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a…
In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible…
Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper…
Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal…
This study deals with the problem of outliers in ordinal response model, which is a regression on ordered categorical data as the response variable. ``Outlier" means that the combination of ordered categorical data and its covariates is…
In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…
Low rank model arises from a wide range of applications, including machine learning, signal processing, computer algebra, computer vision, and imaging science. Low rank matrix recovery is about reconstructing a low rank matrix from…