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The ultimate goal of most scientific studies is to understand the underlying causal mechanism between the involved variables. Structural causal models (SCMs) are widely used to represent such causal mechanisms. Given an SCM, causal queries…

Masked Image Modeling (MIM) techniques have redefined the landscape of computer vision, enabling pre-trained models to achieve exceptional performance across a broad spectrum of tasks. Despite their success, the full potential of MIM-based…

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…

With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of…

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models,…

Experimental data is often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are…

We propose a new modeling framework for highly-multivariate spatial processes that synthesizes ideas from recent multiscale and spectral approaches with graphical models. The basis graphical lasso writes a univariate Gaussian process as a…

This paper contributes to the multivariate analysis of marked spatio-temporal point process data by introducing different partial point characteristics and extending the spatial dependence graph model formalism. Our approach yields a…

Complex systems with intricate causal dependencies challenge accurate prediction. Effective modeling requires precise physical process representation, integration of interdependent factors, and incorporation of multi-resolution…

Spatiotemporal forecasting is critical in applications such as traffic prediction, climate modeling, and environmental monitoring. However, the prevalence of missing data in real-world sensor networks significantly complicates this task. In…

Global Storm-Resolving Models (GSRMs) have gained widespread interest because of the unprecedented detail with which they resolve the global climate. However, it remains difficult to quantify objective differences in how GSRMs resolve…

The goal of system identification is to learn about underlying physics dynamics behind the time-series data. To model the probabilistic and nonparametric dynamics model, Gaussian process (GP) have been widely used; GP can estimate the…

Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…

We consider the problem of optimizing a vector-valued objective function $\boldsymbol{f}$ sampled from a Gaussian Process (GP) whose index set is a well-behaved, compact metric space $({\cal X},d)$ of designs. We assume that…

Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention. We develop SigGPDE, a new scalable sparse variational inference framework…

We propose a novel Bayesian framework for changepoint detection in large-scale spherical spatiotemporal data, with broad applicability in environmental and climate sciences. Our approach models changepoints as spatially dependent…

The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes…

Supervised Machine Learning (SML) algorithms, such as Gradient Boosting, Random Forest, and Neural Networks, have become popular in recent years due to their superior predictive performance over traditional statistical methods. However,…

This paper introduces the Gaussian multi-Graphical Model, a model to construct sparse graph representations of matrix- and tensor-variate data. We generalize prior work in this area by simultaneously learning this representation across…