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Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
We introduce Prob-GParareal, a probabilistic extension of the GParareal algorithm designed to provide uncertainty quantification for the Parallel-in-Time (PinT) solution of (ordinary and partial) differential equations (ODEs, PDEs). The…
Contraction theory formulates the analysis of nonlinear systems in terms of Jacobian matrices. Although this provides the potential to develop a linear matrix inequality (LMI) framework for nonlinear control design, conditions are imposed…
A majority of experimental disciplines face the challenge of exploring large and high-dimensional parameter spaces in search of new scientific discoveries. Materials science is no exception; the wide variety of synthesis, processing, and…
We develop an online probabilistic metric-semantic mapping approach for mobile robot teams relying on streaming RGB-D observations. The generated maps contain full continuous distributional information about the geometric surfaces and…
The study of multimodality has garnered significant interest in fields where the analysis of interactions among multiple information sources can enhance predictive modeling, data fusion, and interpretability. Partial information…
In this paper, we introduce a novel theoretical framework for Gaussian process regression error analysis, leveraging a function-space decomposition. Based on this framework, we develop a weighted Jacobi iterative method that utilizes…
In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are…
Task learning in neural networks typically requires finding a globally optimal minimizer to a loss function objective. Conventional designs of swarm based optimization methods apply a fixed update rule, with possibly an adaptive step-size…
Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions…
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…
Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes…
Adaptive sampling based on Gaussian process regression (GPR) has already been applied with considerable success to generate boundary test scenarios for multi-UAV systems (MUS). One of the key techniques in such researches is leveraging the…
Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…
Gaussian processes (GPs) are non-parametric Bayesian models that are widely used for diverse prediction tasks. Previous work in adding strong privacy protection to GPs via differential privacy (DP) has been limited to protecting only the…
Retinal prostheses restore vision by electrically stimulating surviving neurons, but calibrating perceptual thresholds (i.e., the minimum stimulus intensity required for perception) remains a time-intensive challenge, especially for…
Parameter shift rules (PSRs) are key techniques for efficient gradient estimation in variational quantum eigensolvers (VQEs). In this paper, we propose its Bayesian variant, where Gaussian processes with appropriate kernels are used to…
Regressions created from experimental or simulated data enable the construction of metamodels, widely used in a variety of engineering applications. Many engineering problems involve multi-parametric physics whose corresponding…
We derive criteria for the selection of datapoints used for data-driven reduced-order modeling and other areas of supervised learning based on Gaussian process regression (GPR). While this is a well-studied area in the fields of active…
Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…