arXiv research

Sparse reduced-rank regression selects variables and ranks via manifold optimization.

Robust sparse reduced rank regression for high-dimensional data with heavy-tailed noise.

New method improves cross-validation for sparse reduced rank regression models.

Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high dimensionality. It is likely that only a few views are relevant to prediction, an…

We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across groups, and a sparse linear combination of the dictionary elements is estimated…

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The problem is formulated to minimize the least squares loss with a sparsity-induci…

Proposes a model to relate a tensor feature to a univariate outcome using sparse and low-rank components.

This paper studies robust regression in the settings of Huber's $ε$-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of $ε$-contamination models for various regression problems including nonpa…

Sparse symmetric tensor regression reduces brain connectivity complexity.

New method for multiclass classification reduces error bounds.

New convex relaxations solve sparse regression problems efficiently.

The paper examines how kernel approximations affect Gaussian process regression in large data applications.

Reduced-rank method improves least-squares regression under output regularity.

SLTR model preserves tensor structure and reduces prediction time costs.

Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.

RFM reduces feature space for linear models, improving sparse recovery.

We present a novel method for exact hierarchical sparse polynomial regression. Our regressor is that degree $r$ polynomial which depends on at most $k$ inputs, counting at most $\ell$ monomial terms, which minimizes the sum of the squares of its prediction errors. The previous hierarchical sparse specification aligns w…

We consider the problem of modeling multivariate time series with parsimonious dynamical models which can be represented as sparse dynamic Bayesian networks with few latent nodes. This structure translates into a sparse plus low rank model. In this paper, we propose a Gaussian regression approach to identify such a mod…

Extends RRR to capture nonlinear interactions in multi-response regression.

FasTR efficiently solves sparse and unit-rank tensor regression problems.

Proposes a new method for multivariate functional regression.

We solve robust regression and matrix completion problems with sparse and low-rank models.

New model encodes multivariate signals more efficiently with sparsity and low-rank constraints.

Randomized algorithm solves vector-valued regression problems with low-rank operators.

We address the problem of general supervised learning when data can only be accessed through an (indefinite) similarity function between data points. Existing work on learning with indefinite kernels has concentrated solely on binary/multi-class classification problems. We propose a model that is generic enough to hand…

The paper proposes a method to estimate tensor regression parameters using low-rank and sparse Tucker decompositions.

In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, called path thresholding (PaTh), that transforms any tuning parameter-dependent sparse regression algorithm into an asymptotically tuning-fre…

Sparse tensor additive regression models tensor covariates for scalar responses.

Paper develops a new algorithm for sparse signal recovery.

Improved GCNs for non-sparse graphs with low-rank filters.

A new method combines multiple cancer datasets to improve analysis.

Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.

Improved Frank-Wolfe for sparse/low-rank problems.

A new algorithm speeds up sparse regression for discovering equations from data.

Bagging improves sparse regression performance, especially with reduced sampling ratios.

In the past decade, sparse and low-rank recovery have drawn much attention in many areas such as signal/image processing, statistics, bioinformatics and machine learning. To achieve sparsity and/or low-rankness inducing, the $\ell_1$ norm and nuclear norm are of the most popular regularization penalties due to their co…

We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a $q$-dimensional response, with a shared $p$-dimensional predictor variable. To control the complexity of the model, we employ a functional fo…

Unified framework HASSLE-free decomposes large model weights into sparse and low-rank components.

LORIS model estimates main and interaction effects in large data frames.

This work tackles sparse coding in DLRA for interpretable multiway data.

We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor selection and rank reduction are the most popular strategies for obtaining lower-d…

Efficient tensor kernel method reduces memory usage and computational cost for sparse regression.

Efficiently selects predictors in sparse regression without approximations.

New algorithm solves $\ell_0$-norm constrained multilinear logistic regression for tensor data.

We prove, using the subspace embedding guarantee in a black box way, that one can achieve the spectral norm guarantee for approximate matrix multiplication with a dimensionality-reducing map having $m = O(\tilde{r}/\varepsilon^2)$ rows. Here $\tilde{r}$ is the maximum stable rank, i.e. squared ratio of Frobenius and op…

Spectral algorithm reduces samples needed for multitask regression.

Improved Frank-Wolfe algorithm speeds up training of differentially private LASSO models.

The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a low-rank-cum-Markov approximation (LMA) of the GP model that is novel in leveraging the dual computational advantages stemming from complementing a low-rank appro…