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We focus on the problem of estimating the change in the dependency structures of two $p$-dimensional Gaussian Graphical models (GGMs). Previous studies for sparse change estimation in GGMs involve expensive and difficult non-smooth…

Substantial research on structured sparsity has contributed to analysis of many different applications. However, there have been few Bayesian procedures among this work. Here, we develop a Bayesian model for structured sparsity that uses a…

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…

Outlying observations can be challenging to handle and adversely affect subsequent analyses, especially in data with increasing dimensional complexity. Although outliers are not always undesired anomalies in the data and may possess…

Although freeform devices with complex internal structures promise drastic increases in performance, the discreteness of the set of available materials presents challenges for gradient-based optimization necessary for the efficient…

Bayesian multidimensional scaling (BMDS) is a probabilistic dimension reduction tool that allows one to model and visualize data consisting of dissimilarities between pairs of objects. Although BMDS has proven useful within, e.g., Bayesian…

A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

We consider a framework for determining and estimating the conditional pairwise relationships of variables when the observed samples are contaminated with measurement error in high dimensional settings. Assuming the true underlying…

We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…

We consider online change detection of high dimensional data streams with sparse changes, where only a subset of data streams can be observed at each sensing time point due to limited sensing capacities. On the one hand, the detection…

This paper considers the problem of networks reconstruction from heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well known that parameter estimation in this context is challenging due to large numbers of variables…

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…

Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point…

Ensembles of decision trees are a useful tool for obtaining for obtaining flexible estimates of regression functions. Examples of these methods include gradient boosted decision trees, random forests, and Bayesian CART. Two potential…

We present a new class of methods for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We derive…

A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…

Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world…

This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…

Motivation: Recent advances in technology for brain imaging and high-throughput genotyping have motivated studies examining the influence of genetic variation on brain structure. Wang et al. (Bioinformatics, 2012) have developed an approach…