Related papers: Sparse Reduced-Rank Regression for Simultaneous Ra…

Network modeling of high-dimensional time series data is a key learning task due to its widespread use in a number of application areas, including macroeconomics, finance and neuroscience. While the problem of sparse modeling based on…

In this paper, we study the trace regression when a matrix of parameters B* is estimated via the convex relaxation of a rank-regularized regression or via regularized non-convex optimization. It is known that these estimators satisfy…

Sparse representation-based classification (SRC), proposed by Wright et al., seeks the sparsest decomposition of a test sample over the dictionary of training samples, with classification to the most-contributing class. Because it assumes…

Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…

A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…

We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique…

Identifying co-varying causal elements in very high dimensional feature space with internal structures, e.g., a space with as many as millions of linearly ordered features, as one typically encounters in problems such as whole genome…

This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when…

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…

This paper considers sparse spiked covariance matrix models in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of…

Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $\ell_{1,\infty}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression…

A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…

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…

Personalization of machine learning (ML) predictions for individual users/domains/enterprises is critical for practical recommendation systems. Standard personalization approaches involve learning a user/domain specific embedding that is…

We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a…

In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…

Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…

Feature selection identifies subsets of informative features and reduces dimensions in the original feature space, helping provide insights into data generation or a variety of domain problems. Existing methods mainly depend on feature…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…