Related papers: Ordinal Optimisation for the Gaussian Copula Model
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
We consider Bayesian optimization using Gaussian Process models, also referred to as kernel-based bandit optimization. We study the methodology of exploring the domain using random samples drawn from a distribution. We show that this random…
Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…
We consider the 1D Expected Improvement optimization based on Gaussian processes having spectral densities converging to zero faster than exponentially. We give examples of problems where the optimization trajectory is not dense in the…
Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random…
We develop two new stochastic Gauss-Newton algorithms for solving a class of non-convex stochastic compositional optimization problems frequently arising in practice. We consider both the expectation and finite-sum settings under standard…
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…
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…
The problem of obtaining optimal projections for performing discriminant analysis with Gaussian class densities is studied. Unlike in most existing approaches to the problem, the focus of the optimisation is on the multinomial likelihood…
We propose an algorithm to approximate solutions of global optimization problems in Sobolev spaces that follows the spirit of Consensus-based algorithms in finite dimensions. The main ingredient are Gaussian processes. In fact, we exploit…
We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…
We obtain an optimal bound for a Gaussian approximation of a large class of vector-valued random processes. Our results provide a substantial generalization of earlier results that assume independence and/or stationarity. Based on the decay…
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
Use copula to model dependency of variable extends multivariate gaussian assumption. In this paper we first empirically studied copula regression model with continous response. Both simulation study and real data study are given. Secondly…
We present randomized algorithms for sampling the standard Gaussian distribution restricted to a convex set and for estimating the Gaussian measure of a convex set, in the general membership oracle model. The complexity of integration is…
We study the problem of causal discovery through targeted interventions. Starting from few observational measurements, we follow a Bayesian active learning approach to perform those experiments which, in expectation with respect to the…
We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are "sub-Gaussian"~even when the randomness of the…