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Hamiltonian Monte Carlo (HMC) is a popular Markov Chain Monte Carlo (MCMC) algorithm to sample from an unnormalized probability distribution. A leapfrog integrator is commonly used to implement HMC in practice, but its performance can be…
We consider two approaches to balanced truncation of stochastic linear systems, which follow from different generalizations of the reachability Gramian of deterministic systems. Both preserve mean-square asymptotic stability, but only the…
Gaussian processes are widely used for accurate emulation of unknown surfaces in sequential design of expensive simulation experiments. Integrated mean squared error (IMSE) is an effective acquisition function for sequential designs based…
In this paper, we investigate the mean-square convergence of a novel symplectic local discontinuous Galerkin method in L^2-norm for stochastic linear Schroedinger equation with multiplicative noise. It is shown that the mean-square error is…
A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
This paper is concerned with linear stochastic Hamiltonian (LSH) systems subject to random external forces. Their dynamics are modelled by linear stochastic differential equations, parameterised by stiffness, mass, damping and coupling…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
In this paper, we have established a unified framework of multistage parameter estimation. We demonstrate that a wide variety of statistical problems such as fixed-sample-size interval estimation, point estimation with error control,…
We consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions…
This paper introduces a novel distributed optimization technique for networked systems, which removes the dependency on specific parameter choices, notably the learning rate. Traditional parameter selection strategies in distributed…
We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is…
Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler…
We analyze the mixing time of Metropolized Hamiltonian Monte Carlo (HMC) with the leapfrog integrator to sample from a distribution on $\mathbb{R}^d$ whose log-density is smooth, has Lipschitz Hessian in Frobenius norm and satisfies…
Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305--320] as a general simulation and optimization algorithm. In this paper, we propose to improve its…
Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of…
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…
As is well known, both sampling from the posterior and computing the mean of the posterior in Gaussian process regression reduces to solving a large linear system of equations. We study the use of stochastic gradient descent for solving…
Much recent research has been conducted in the area of Bayesian learning, particularly with regard to the optimization of hyper-parameters via Gaussian process regression. The methodologies rely chiefly on the method of maximizing the…