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We develop Bayesian nonparametric models for spatially indexed data of mixed type. Our work is motivated by challenges that occur in environmental epidemiology, where the usual presence of several confounding variables that exhibit complex…
Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…
Recently, 3D Gaussian Splatting (3DGS) has demonstrated impressive novel view synthesis results, while allowing the rendering of high-resolution images in real-time. However, leveraging 3D Gaussians for surface reconstruction poses…
We propose a new method for simplification of Gaussian process (GP) models by projecting the information contained in the full encompassing model and selecting a reduced number of variables based on their predictive relevance. Our results…
3D Gaussian Splatting (3DGS) has revolutionized 3D scene representation with superior efficiency and quality. While recent adaptations for computed tomography (CT) show promise, they struggle with severe artifacts under highly sparse-view…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
3D Gaussian Splatting (3DGS) has recently emerged as a powerful scene representation and is increasingly used for visual localization and pose refinement. However, despite its high-quality differentiable rendering, the robustness of…
3D Gaussian Splatting (3DGS) has emerged as a powerful approach for 3D scene reconstruction using 3D Gaussians. However, neither the centers nor surfaces of the Gaussians are accurately aligned to the object surface, complicating their…
This article presents an Integral Gaussian Process (IntegralGP) framework for volumetric estimation of subterranean properties in mineral deposits. It provides a unified representation for data with different spatial supports, which enables…
An understanding of the energy dependence of gamma-ray sources can yield important information on the underlying emission mechanisms. However, despite the detection of energy-dependent morphologies in many TeV sources, we lack a proper…
Environmental and individualistic variables affect the rate of human decomposition in complex ways. These effects complicate the estimation of the postmortem interval (PMI) based on observed decomposition characteristics. In this work, we…
Three-dimensional tomography of hadrons can be investigated by generalized parton distributions (GPDs), transverse-momentum-dependent parton distributions (TMDs), and generalized distribution amplitudes (GDAs). The GDA studies had been only…
Physics-constrained machine learning is emerging as an important topic in the field of machine learning for physics. One of the most significant advantages of incorporating physics constraints into machine learning methods is that the…
3D Gaussian Splatting (3DGS) has emerged as a leading technique for novel view synthesis, demonstrating exceptional rendering efficiency. \replaced[]{Well-reconstructed surfaces can be characterized by low configurational entropy, where…
3D scene modeling techniques serve as the bedrocks in the geospatial engineering and computer science, which drives many applications ranging from automated driving, terrain mapping, navigation, virtual, augmented, mixed, and extended…
3D maps are increasingly useful for many applications such as drone navigation, emergency services, and urban planning. However, creating 3D maps and keeping them up-to-date using existing technologies, such as laser scanners, is expensive.…
The widespread adoption of AI models, especially foundation models (FMs), has made a profound impact on numerous domains. However, it also raises significant ethical concerns, including bias issues. Although numerous efforts have been made…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…
Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…