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Although deep convolutional neural networks (CNNs) have demonstrated remarkable performance on multiple computer vision tasks, researches on adversarial learning have shown that deep models are vulnerable to adversarial examples, which are…
We investigate the adaptive robust control framework for portfolio optimization and loss-based hedging under drift and volatility uncertainty. Adaptive robust problems offer many advantages but require handling a double optimization problem…
Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…
Quantum Monte Carlo (QMC) methods offer exact solutions for quantum many-body systems but face severe limitations in fermionic systems like atomic nuclei due to the sign problem. While sign-problem-free QMC algorithms exist and provide…
On the base of a Feynman-Kac--type formula involving Poisson stochastic processes, recently a Monte Carlo algorithm has been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We…
Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…
We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster…
Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…
Monte Carlo algorithms are a foundational pillar of modern computational science, yet their effective application hinges on a deep understanding of their performance trade offs. This paper presents a critical analysis of the evolution of…
We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures…
Fixed-node diffusion Monte Carlo (DMC) is a stochastic algorithm for finding the lowest energy many-fermion wave function with the same nodal surface as a chosen trial function. It has proved itself among the most accurate methods available…
Sequential Monte Carlo (SMC) methods represent a classical set of techniques to simulate a sequence of probability measures through a simple selection/mutation mechanism. However, the associated selection functions and mutation kernels…
Methods for generating sequences of surrogates approximating fine scale models of two-phase random heterogeneous media are presented that are designed to adaptively control the modeling error in key quantities of interest (QoIs). For…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
Stochastic partial differential equations (SPDEs) are often difficult to solve numerically due to their low regularity and high dimensionality. These challenges limit the practical use of computer-aided studies and pose significant barriers…
We consider the task of MCMC sampling from a distribution defined on a discrete space. Building on recent insights provided in [Zan19], we devise a class of efficient continuous-time, non-reversible algorithms which make active use of the…
For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…
Markov Chain Monte Carlo (MCMC) underlies both statistical physics and combinatorial optimization, but mixes slowly near critical points and in rough landscapes. Parallel Tempering (PT) improves mixing by swapping replicas across…
This article was motivated by the desire to improve Markov chain Monte Carlo methods for spatial survival models in which the locations of individuals in space are known. For a dataset comprising information on n individuals, standard…
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…