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Regression analysis is commonly conducted in survey sampling. However, existing methods fail when the relationships vary across different areas or domains. In this paper, we propose a unified framework to study the group-wise covariate…

The supersymmetric Poisson Sigma model is studied as a possible worldsheet realization of generalized complex geometry. Generalized complex structures alone do not guarantee non-manifest N=(2,1) or N=(2,2) supersymmetry, but a certain…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

Model correction is essential for reliable PDE learning when the governing physics is misspecified due to simplified assumptions or limited observations. In the machine learning literature, existing correction methods typically operate in…

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…

We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss…

This paper proposes a general framework to estimate coefficients of generalized polynomial chaos (gPC) used in uncertainty quantification via rotational sparse approximation. In particular, we aim to identify a rotation matrix such that the…

Computer models are used to model complex processes in various disciplines. Often, a key source of uncertainty in the behavior of complex computer models is uncertainty due to unknown model input parameters. Statistical computer model…

Chain Event Graphs (CEGs) are a widely applicable class of probabilistic graphical model that can represent context-specific independence statements and asymmetric unfoldings of events in an easily interpretable way. Existing model…

Extreme precipitation events occurring over large spatial domains pose substantial threats to societies because they can trigger compound flooding, landslides, and infrastructure failures across wide areas. A hybrid framework for spatial…

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…

We address the problem of robust estimation of sparse high dimensional tensor elliptical graphical model. Most of the research focus on tensor graphical model under normality. To extend the tensor graphical model to more heavy-tailed…

In the analysis of count data often the equidispersion assumption is not suitable, hence the Poisson regression model is inappropriate. As a generalization of the Poisson distribution, the COM-Poisson distribution can deal with under-,…

Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…

Spatial confounding is how is called the confounding between fixed and spatial random effects. It has been widely studied and it gained attention in the past years in the spatial statistics literature, as it may generate unexpected results…

The present paper is about estimation and prediction in high-dimensional additive models under a sparsity assumption ($p\gg n$ paradigm). A PAC-Bayesian strategy is investigated, delivering oracle inequalities in probability. The…

We propose a scalable framework for inference in an inhomogeneous Poisson process modeled by a continuous sigmoidal Cox process that assumes the corresponding intensity function is given by a Gaussian process (GP) prior transformed with a…

Symmetric positive definite~(SPD) matrices have shown important value and applications in statistics and machine learning, such as FMRI analysis and traffic prediction. Previous works on SPD matrices mostly focus on discriminative models,…

Motivated by the need for computationally tractable spatial methods in neuroimaging studies, we develop a distributed and integrated framework for estimation and inference of Gaussian process model parameters with ultra-high-dimensional…

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…