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Accurate learning of system dynamics is becoming increasingly crucial for advanced control and decision-making in engineering. However, real-world systems often exhibit multiple channels and highly nonlinear transition dynamics, challenging…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
We investigate the merits of replication, and provide methods for optimal design (including replicates), with the goal of obtaining globally accurate emulation of noisy computer simulation experiments. We first show that replication can be…
The Kennedy and O'Hagan (KOH) calibration framework uses coupled Gaussian processes (GPs) to meta-model an expensive simulator (first GP), tune its ``knobs" (calibration inputs) to best match observations from a real physical/field…
Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
Flexible and scalable decentralized learning solutions are fundamentally important in the application of multi-agent systems. While several recent approaches introduce (ensembles of) kernel machines in the distributed setting, Bayesian…
This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each…
Gaussian processes~(Kriging) are interpolating data-driven models that are frequently applied in various disciplines. Often, Gaussian processes are trained on datasets and are subsequently embedded as surrogate models in optimization…
Inspired by the developments in quantum computing, building domain-specific classical hardware to solve computationally hard problems has received increasing attention. Here, by introducing systematic sparsification techniques, we…
This paper presents a simple and efficient method to convolve an image with a Gaussian kernel. The computation is performed in a constant number of operations per pixel using running sums along the image rows and columns. We investigate the…
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…
In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as…
With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…