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Prior beliefs about the latent function to shape inductive biases can be incorporated into a Gaussian Process (GP) via the kernel. However, beyond kernel choices, the decision-making process of GP models remains poorly understood. In this…

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…

Recent advancements in Gaussian Splatting (3DGS) have introduced various modifications to the original kernel, resulting in significant performance improvements. However, many of these kernel changes are incompatible with existing datasets…

Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…

In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the \emph{inverse regression} method under strong mixing condition. This method is based on estimation of the…

Kernel methods such as kernel ridge regression and Gaussian process regressions with Matern type kernels have been increasingly used, in particular, to fit potential energy surfaces (PES) and density functionals, and for materials…

Learning the kernel functions used in kernel methods has been a vastly explored area in machine learning. It is now widely accepted that to obtain 'good' performance, learning a kernel function is the key challenge. In this work we focus on…

Gaussian Process (GP) regression has seen widespread use in robotics due to its generality, simplicity of use, and the utility of Bayesian predictions. The predominant implementation of GP regression is a nonparameteric kernel-based…

Gaussian processes are widely used for accurate emulation of unknown surfaces in sequential design of expensive simulation experiments. Integrated mean squared error (IMSE) is an effective acquisition function for sequential designs based…

Dynamic positron emission tomography (PET) reconstruction often presents high noise due to the use of short duration frames to describe the kinetics of the radiotracer. Here we introduce a new method to calculate a kernel matrix to be used…

Data-driven models of robot motion constructed using principles from Geometric Mechanics have been shown to produce useful predictions of robot motion for a variety of robots. For robots with a useful number of DoF, these geometric…

To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

Symmetry, where certain features remain invariant under geometric transformations, can often serve as a powerful prior in designing convolutional neural networks (CNNs). While conventional CNNs inherently support translational equivariance,…

Accurately representing the sound field with the high spatial resolution is critical for immersive and interactive sound field reproduction technology. To minimize experimental effort, data-driven methods have been proposed to estimate…

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…

This work addresses the problem of non-rigid registration of 3D scans, which is at the core of shape modeling techniques. Firstly, we propose a new kernel based on geodesic distances for the Gaussian Process Morphable Models (GPMMs)…

Direct design of a robot's rendered dynamics, such as in impedance control, is now a well-established control mode in uncertain environments. When the physical interaction port variables are not measured directly, dynamic and kinematic…

Gaussian processes (GPs) are powerful probabilistic models that define flexible priors over functions, offering strong interpretability and uncertainty quantification. However, GP models often rely on simple, stationary kernels which can…

Since most inverse problems arising in scientific and engineering applications are ill-posed, prior information about the solution space is incorporated, typically through regularization, to establish a well-posed problem with a unique…