Related papers: Group Lasso merger for sparse prediction with high…

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

Multiresponse data with complex group structures in both responses and predictors arises in many fields, yet, due to the difficulty in identifying complex group structures, only a few methods have been studied on this problem. We propose a…

We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on…

The increasing complexity of deep learning recommendation models (DLRM) has led to a growing need for large-scale distributed systems that can efficiently train vast amounts of data. In DLRM, the sparse embedding table is a crucial…

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…

Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…

Regularized m-estimators are widely used due to their ability of recovering a low-dimensional model in high-dimensional scenarios. Some recent efforts on this subject focused on creating a unified framework for establishing oracle bounds,…

High-order clustering aims to classify objects in multiway datasets that are prevalent in various fields such as bioinformatics, recommendation systems, and social network analysis. Such data are often sparse and high-dimensional, posing…

Despite widespread adoption in practice, guarantees for the LASSO and Group LASSO are strikingly lacking in settings beyond statistical problems, and these algorithms are usually considered to be a heuristic in the context of sparse convex…

In high dimensional regression, feature clustering by their effects on outcomes is often as important as feature selection. For that purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) are used…

This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…

Robust clustering of high-dimensional data is an important topic because clusters in real datasets are often heavy-tailed and/or asymmetric. Traditional approaches to model-based clustering often fail for high dimensional data, e.g., due to…

In this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, and where only a few of them are assumed to be active. In such a situation, the group Lasso is an at- tractive method for…

It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…

Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…

Although the sparse multinomial logistic regression (SMLR) has provided a useful tool for sparse classification, it suffers from inefficacy in dealing with high dimensional features and manually set initial regressor values. This has…

In the presence of grouped covariates, we propose a framework for boosting that allows to enforce sparsity within and between groups. By using component-wise and group-wise gradient boosting at the same time with adjusted degrees of…

Gaussian Markov random fields are used in a large number of disciplines in machine vision and spatial statistics. The models take advantage of sparsity in matrices introduced through the Markov assumptions, and all operations in inference…

Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network…