Related papers: A Multi-Resolution Model for Non-Gaussian Random F…

To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this…

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…

Engineering simulations using boundary-value partial differential equations often implicitly assume that the uncertainty in the location of the boundary has a negligible impact on the output of the simulation. In this work, we develop a…

Analyzing spatially varying effects is pivotal in geographic analysis. However, accurately capturing and interpreting this variability is challenging due to the increasing complexity and non-linearity of geospatial data. Recent advancements…

We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…

Machine learning of multi-dimensional potential energy surfaces, from purely ab initio datasets, has seen substantial progress in the past years. Gaussian processes, a popular regression method, have been very successful at producing…

Robotics applications often rely on scene reconstructions to enable downstream tasks. In this work, we tackle the challenge of actively building an accurate map of an unknown scene using an RGB-D camera on a mobile platform. We propose a…

The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where…

We propose a Bayesian model for mixed ordinal and continuous multivariate data to evaluate a latent spatial Gaussian process. Our proposed model can be used in many contexts where mixed continuous and discrete multivariate responses are…

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…

Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…

Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location-scale mixture of Gaussian kernels is the golden standard, both having nice…

Multi-model ensemble analysis integrates information from multiple climate models into a unified projection. However, existing integration approaches based on model averaging can dilute fine-scale spatial information and incur bias from…

This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on $\mathbb{R}^2$ based on dense observations of a single realization of the deformed random field. Under this framework we…

The mean-field theory for two-layer neural networks considers infinitely wide networks that are linearly parameterized by a probability measure over the parameter space. This nonparametric perspective has significantly advanced both the…

The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…

Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…

Rendering novel view images in dynamic scenes is a crucial yet challenging task. Current methods mainly utilize NeRF-based methods to represent the static scene and an additional time-variant MLP to model scene deformations, resulting in…