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A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty,…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Multi-task learning is frequently used to model a set of related response variables from the same set of features, improving predictive performance and modeling accuracy relative to methods that handle each response variable separately.…
Sparse linear regression is a vast field and there are many different algorithms available to build models. Two new papers published in Statistical Science study the comparative performance of several sparse regression methodologies,…
We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…
One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while…
Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a given dictionary. This paper resorts to exponential…
In ecological studies niche overlap is often used to quantify species interaction and dynamics. This paper develops a robust, nonparametric statistical framework for quantifying and analyzing multivariate niche overlap. Parametric methods…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
In this paper we consider high-dimensional multiclass classification by sparse multinomial logistic regression. We propose first a feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
A variety of machine learning tasks---e.g., matrix factorization, topic modelling, and feature allocation---can be viewed as learning the parameters of a probability distribution over bipartite graphs. Recently, a new class of models for…
Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…
In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…
The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…