Related papers: Structured Sparse Regression via Greedy Hard-Thres…

Machine learning and statistics typically focus on building models that capture the vast majority of the data, possibly ignoring a small subset of data as "noise" or "outliers." By contrast, here we consider the problem of jointly…

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…

Sparsity helps reduce the computational complexity of deep neural networks by skipping zeros. Taking advantage of sparsity is listed as a high priority in next generation DNN accelerators such as TPU. The structure of sparsity, i.e., the…

We develop tools for selective inference in the setting of group sparsity, including the construction of confidence intervals and p-values for testing selected groups of variables. Our main technical result gives the precise distribution of…

Classification and probability estimation are fundamental tasks with broad applications across modern machine learning and data science, spanning fields such as biology, medicine, engineering, and computer science. Recent development of…

We propose a new iterative greedy algorithm for reconstructions of sparse signals with or without noisy perturbations in compressed sensing. The proposed algorithm, called \emph{subspace thresholding pursuit} (STP) in this paper, is a…

Unions of subspaces provide a powerful generalization to linear subspace models for collections of high-dimensional data. To learn a union of subspaces from a collection of data, sets of signals in the collection that belong to the same…

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…

Probabilistic Coalition Structure Generation (PCSG) is NP-hard and can be recast as an $l_0$-type sparse recovery problem by representing coalition structures as sparse coefficient vectors over a coalition-incidence design. A natural…

The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying…

Neural networks (NNs) are primarily developed within the frequentist statistical framework. Nevertheless, frequentist NNs lack the capability to provide uncertainties in the predictions, and hence their robustness can not be adequately…

In this paper, the problem of training a classifier on a dataset with incomplete features is addressed. We assume that different subsets of features (random or structured) are available at each data instance. This situation typically occurs…

Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. The data representations learned with the models are often…

Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…

We consider high-dimensional multiclass classification by sparse multinomial logistic regression. Unlike binary classification, in the multiclass setup one can think about an entire spectrum of possible notions of sparsity associated with…

The performance of trained neural networks is robust to harsh levels of pruning. Coupled with the ever-growing size of deep learning models, this observation has motivated extensive research on learning sparse models. In this work, we focus…

High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of…

In high-dimensional linear models, sparsity is often exploited to reduce variability and achieve parsimony. Equi-sparsity, where one assumes that predictors can be aggregated into groups sharing the same effects, is an alternative…

We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…