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We introduce a novel framework for clustering a collection of tall matrices based on their column spaces, a problem we term Subspace Clustering of Subspaces (SCoS). Unlike traditional subspace clustering methods that assume vectorized data,…

Spatial regression or geographically weighted regression models have been widely adopted to capture the effects of auxiliary information on a response variable of interest over a region. In contrast, relationships between response and…

This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…

Determining company similarity is a vital task in finance, underpinning risk management, hedging, and portfolio diversification. Practitioners often rely on sector and industry classifications such as SIC and GICS codes to gauge similarity,…

Stepped wedge cluster randomized trials (SW-CRTs) with binary outcomes are increasingly used in prevention and implementation studies. Marginal models represent a flexible tool for analyzing SW-CRTs with population-averaged interpretations,…

Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…

Sparse Inverse Covariance Estimation (SICE) is useful in many practical data analyses. Recovering the connectivity, non-connectivity graph of covariates is classified amongst the most important data mining and learning problems. In this…

In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity." Classical sparse regression…

This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori…

This work is motivated by analyses of longitudinal data collected from participants in the Quebec Longitudinal Study of Child Development (QLSCD) and the Quebec Newborn Twin Study (QNTS) to identify important genetic predictors for…

Canonical correlation analysis (CCA) describes the associations between two sets of variables by maximizing the correlation between linear combinations of the variables in each data set. However, in high-dimensional settings where the…

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…

Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among…

This paper proposes a Sequential Monte Carlo approach for the Bayesian estimation of mixed causal and noncausal models. Unlike previous Bayesian estimation methods developed for these models, Sequential Monte Carlo offers extensive…

A novel method is proposed for the exact posterior mean and covariance of the random effects given the response in a generalized linear mixed model (GLMM) when the response does not follow normal. The research solves a long-standing problem…

We propose a rate equation approach to compute two vertex correlations in scale-free growing network models based in the preferential attachment mechanism. The formalism, based on previous work of Szab\'o \textit{et al.} [Phys. Rev. E…

This paper extends the idea of decoupling shrinkage and sparsity for continuous priors to Bayesian Quantile Regression (BQR). The procedure follows two steps: In the first step, we shrink the quantile regression posterior through state of…

We consider a collection of prediction experiments, which are clustered in the sense that groups of experiments ex- hibit similar relationship between the predictor and response variables. The experiment clusters as well as the regres- sion…

This work introduces 4 novel probabilistic and reinforcement-driven methods for association rule mining (ARM): Gaussian process-based association rule mining (GPAR), Bayesian ARM (BARM), multi-armed bandit based ARM (MAB-ARM), and…

We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…