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Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…

We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical…

Study of neural networks with infinite width is important for better understanding of the neural network in practical application. In this work, we derive the equivalence of the deep, infinite-width maxout network and the Gaussian process…

Adding inequality constraints (e.g. boundedness, monotonicity, convexity) into Gaussian processes (GPs) can lead to more realistic stochastic emulators. Due to the truncated Gaussianity of the posterior, its distribution has to be…

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement,…

Gaussian Process Motion Planning (GPMP) is a widely used framework for generating smooth trajectories within a limited compute time--an essential requirement in many robotic applications. However, traditional GPMP approaches often struggle…

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

In this work, we introduce a real-time capable algorithm for considering monotonicity assumptions for recursive Gaussian Process regression (RGP). Therefore, we present how to efficiently calculate the RGP gradients online. Then, we utilize…

Machine learning (ML) techniques have recently gained significant attention for solving compliance minimization (CM) problems. However, these methods typically provide poor feature boundaries, are very expensive, and lack a systematic…

Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We…

Complex computer codes are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this problem consists in replacing cpu-time expensive…

The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear model reduction method that operates on fully discretized computational models. It achieves dimension reduction by a Petrov--Galerkin projection associated with…

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global…

Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same…

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

In this paper, we consider the Gaussian process (GP) bandit optimization problem in a non-stationary environment. To capture external changes, the black-box function is allowed to be time-varying within a reproducing kernel Hilbert space…

Gaussian Process (GP) models have also become extremely useful for optimization under uncertainty algorithms, especially where the objective functions are costly to compute. Yet, the more classical methods usually adopt strategies that, in…

We propose a variable decomposition algorithm -greedy block coordinate descent (GBCD)- in order to make dense Gaussian process regression practical for large scale problems. GBCD breaks a large scale optimization into a series of small…