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Given a set of items and a set of evaluators who all individually rank them, how do we aggregate these evaluations into a single societal ranking? Work in social choice and statistics has produced many aggregation methods for this problem,…

We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Mat\'{e}rn kernel and the squared exponential…

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…

Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…

This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched…

Directed information and its causally conditioned variations are often used to measure causal influences between random processes. In practice, these quantities must be measured from data. Non-asymptotic error bounds for these estimates are…

This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected…

We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…

Probabilistic sampling-based algorithms, such as the probabilistic roadmap (PRM) and the rapidly-exploring random tree (RRT) algorithms, represent one of the most successful approaches to robotic motion planning, due to their strong…

Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…

Parameter estimation is crucial for modeling, tracking, and control of complex dynamical systems. However, parameter uncertainties can compromise system performance under a controller relying on nominal parameter values. Typically,…

When, in terms of the number of data points, the size of a dataset exceeds available computing resources, or when labeling is expensive, an attractive solution consists of selecting only some of the data points (subdata) for further…

We present a planning framework for minimising the deterministic worst-case error in sparse Gaussian process (GP) regression. We first derive a universal worst-case error bound for sparse GP regression with bounded noise using interpolation…

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…

Probabilistic models are often used to make predictions in regions of the data space where no observations are available, but it is not always clear whether such predictions are well-informed by previously seen data. In this paper, we…

Selective prediction, where a model has the option to abstain from making a decision, is crucial for machine learning applications in which mistakes are costly. In this work, we focus on distributional regression and introduce a framework…

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…

Model selection aims to find the best model in terms of accuracy, interpretability or simplicity, preferably all at once. In this work, we focus on evaluating model performance of Gaussian process models, i.e. finding a metric that provides…

Gaussian process regression uses data measured at sensor locations to reconstruct a spatially dependent function with quantified uncertainty. However, if only a limited number of sensors can be deployed, it is important to determine how to…