Related papers: Optimal Gaussian Approximation for Multiple Time S…
Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select appropriate parameters for the covariance kernel. However,…
Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage to the solutions that fit observations on average, but they do not pay attention to…
In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…
The paper deals with the expected maxima of continuous Gaussian processes $X = (X_t)_{t\ge 0}$ that are H\"older continuous in $L_2$-norm and/or satisfy the opposite inequality for the $L_2$-norms of their increments. Examples of such…
Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical…
There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…
Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
In this paper, we establish optimal rates of adaptive estimation of a vector in the multi-reference alignment model, a problem with important applications in fields such as signal processing, image processing, and computer vision, among…
We revisit a result of Mittal--Ylvisaker that states that the rescaled maximum of a stationary sequence of Gaussian random variables has a Gaussian limit if correlations decay sufficiently slowly. Taking a new approach we relax the…
The Gaussian process (GP) model, which has been extensively applied as priors of functions, has demonstrated excellent performance. The specification of a large number of parameters affects the computational efficiency and the feasibility…
This article derives quantitative limit theorems for multivariate Poisson and Poisson process approximations. Employing the solution of Stein's equation for Poisson random variables, we obtain an explicit bound for the multivariate Poisson…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
This paper mainly addresses the optimization of $p$-th moment of $\mathbb{R}^n$-valued random variable. Through an ingenious approximation mechanism, one transforms the maximization problem into a sequence of minimization problems, which…
An important task of uncertainty quantification is to identify {the probability of} undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian…
Gaussian process modeling is a standard tool for building emulators for computer experiments, which are usually used to study deterministic functions, for example, a solution to a given system of partial differential equations. This work…
This paper proposes a new class of real-time optimization schemes to overcome system-model mismatch of uncertain processes. This work's novelty lies in integrating derivative-free optimization schemes and multi-fidelity Gaussian processes…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…
The Gaussian process bandit is a problem in which we want to find a maximizer of a black-box function with the minimum number of function evaluations. If the black-box function varies with time, then time-varying Bayesian optimization is a…