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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 study a second-order approach to policy optimization in reinforcement learning. Existing second-order methods often suffer from suboptimal sample complexity or rely on unrealistic assumptions about importance sampling. To…

Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…

Interference prediction and resource allocation are critical challenges in mission-critical applications where stringent latency and reliability constraints must be met. This paper proposes a novel Gaussian process regression (GPR)-based…

We study the optimal sample complexity of variable selection in linear regression under general design covariance, and show that subset selection is optimal while under standard complexity assumptions, efficient algorithms for this problem…

Among the major difficulties that one may encounter when estimating parameters in a nonlinear regression model are the nonuniqueness of the estimator, its instability with respect to small perturbations of the observations and the presence…

This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained $\ell_1$ minimization approach,…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

We present a dynamic programming algorithm for selecting a representative subset of size $k$ from a given set with $n$ points such that the Riesz $s$-energy is near minimized. While NP-hard in general dimensions, the one-dimensional case…

Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…

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…

Optimal allocation of scarce resources is a common problem for decision makers faced with choosing a limited number of locations for intervention. Spatiotemporal prediction models could make such decisions data-driven. A recent performance…

The gradient mapping norm is a strong and easily verifiable stopping criterion for first-order methods on composite problems. When the objective exhibits the quadratic growth property, the gradient mapping norm minimization problem can be…

Modern aerospace guidance systems demand rigorous constraint satisfaction, optimal performance, and computational efficiency. Traditional analytical methods struggle to simultaneously satisfy these requirements. While data driven methods…

Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing…

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…

Curating a desirable dataset for training has been the core of building highly capable large language models (Touvron et al., 2023; Achiam et al., 2023; Team et al.,2024). Gradient influence scores (Pruthi et al., 2020; Xia et al., 2024)…

In this paper we give a completely new approach to the problem of covariate selection in linear regression. A covariate or a set of covariates is included only if it is better in the sense of least squares than the same number of Gaussian…

Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…

In multi-objective decision planning and learning, much attention is paid to producing optimal solution sets that contain an optimal policy for every possible user preference profile. We argue that the step that follows, i.e, determining…