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Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets.…

In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…

We propose an L1-penalized algorithm for fitting high-dimensional generalized linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as an extension of generalized linear models for clustered observations. This…

Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…

In variable selection, a selection rule that prescribes the permissible sets of selected variables (called a "selection dictionary") is desirable due to the inherent structural constraints among the candidate variables. Such selection rules…

Mixed-effect models are very popular for analyzing data with a hierarchical structure, e.g. repeated observations within subjects in a longitudinal design, patients nested within centers in a multicenter design. However, recently, due to…

Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…

Efficient methods for large-scale security constrained unit commitment (SCUC) problems have long been an important research topic and a challenge especially in market clearing computation. For large-scale SCUC, the Lagrangian relaxation…

We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…

Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…

We propose novel first-order stochastic approximation algorithms for canonical correlation analysis (CCA). Algorithms presented are instances of inexact matrix stochastic gradient (MSG) and inexact matrix exponentiated gradient (MEG), and…

Consider the normal linear regression setup when the number of covariates p is much larger than the sample size n, and the covariates form correlated groups. The response variable y is not related to an entire group of covariates in all or…

We propose a variable decomposition algorithm -greedy block coordinate descent (GBCD)- in order to make dense Gaussian process regression practical for large scale problems. GBCD breaks a large scale optimization into a series of small…

Granger causality analysis (GCA) provides a powerful tool for uncovering the patterns of brain connectivity mechanism using neuroimaging techniques. Conventional GCA applies two different mathematical theories in a two-stage scheme: (1) the…

Significant advances in biotechnology have allowed for simultaneous measurement of molecular data points across multiple genomic and transcriptomic levels from a single tumor/cancer sample. This has motivated systematic approaches to…

We propose a method for estimating coefficients in multivariate regression when there is a clustering structure to the response variables. The proposed method includes a fusion penalty, to shrink the difference in fitted values from…

Block-wise sparse attention offers significant efficiency gains for long-context modeling, yet existing methods often suffer from low selection fidelity and cumulative contextual loss by completely discarding unselected blocks. To address…

This paper considers canonical correlation analysis for two longitudinal variables that are possibly sampled at different time resolutions with irregular grids. We modeled trajectories of the multivariate variables using random effects and…

Multi-cellular programs (MCPs) are coordinated patterns of gene expression across interacting cell types that collectively drive complex biological processes such as tissue development and immune responses. While MCPs are typically…

While meta-analyzing retrospective cancer patient cohorts, an investigation of differences in the expressions of target oncogenes across cancer subtypes is of substantial interest because the results may uncover novel tumorigenesis…