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Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…

Computation · Statistics 2022-03-01 Charles C. Margossian , Michael Betancourt

We propose an unbiased Monte-Carlo estimator for $\mathbb{E}[g(X_{t_1}, \cdots, X_{t_n})]$, where $X$ is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a…

Probability · Mathematics 2016-03-08 Pierre Henry-Labordere , Xiaolu Tan , Nizar Touzi

This paper discusses how two classes of approximate computation algorithms can be adapted, in a modular fashion, to achieve exact statistical inference from differentially private data products. Considered are approximate Bayesian…

Computation · Statistics 2022-09-28 Ruobin Gong

The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…

Statistics Theory · Mathematics 2017-12-15 Radislav Vaisman , Robert Salomone , Dirk P. Kroese

The paper deals with stochastic difference-of-convex functions (DC) programs, that is, optimization problems whose the cost function is a sum of a lower semicontinuous DC function and the expectation of a stochastic DC function with respect…

Numerical Analysis · Mathematics 2020-12-14 Le Thi Hoai An , Huynh Van Ngai , Pham Dinh Tao , Luu Hoang Phuc Hau

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…

Computation · Statistics 2015-05-20 Tim Salimans , Diederik P. Kingma , Max Welling

Indirect inference requires simulating realisations of endogenous variables from the model under study. When the endogenous variables are discontinuous functions of the model parameters, the resulting indirect inference criterion function…

Economics · Quantitative Finance 2019-07-11 David T. Frazier , Tatsushi Oka , Dan Zhu

In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…

Computation · Statistics 2017-10-30 Ajay Jasra , Kengo Kamatani , Kody Law , Yan Zhou

We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…

Dynamical Systems · Mathematics 2019-01-30 Omar Kebiri , Lara Neureither , Carsten Hartmann

This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a…

Machine Learning · Statistics 2020-09-30 Shakir Mohamed , Mihaela Rosca , Michael Figurnov , Andriy Mnih

Starting from the radiative transfer equation and its usual boundary conditions, the objective of this work is to design Monte Carlo algorithms estimating the specific intensity spatial and angular derivatives as well as its geometric…

The theme of the present paper is numerical integration of $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the…

Numerical Analysis · Mathematics 2023-06-21 Leszek Plaskota , Paweł Przybyłowicz , Łukasz Stępień

Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…

Computational Physics · Physics 2023-08-28 Shi-Xin Zhang , Zhou-Quan Wan , Hong Yao

Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…

Numerical Analysis · Mathematics 2018-06-15 Yuji Nakatsukasa

Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…

Probability · Mathematics 2009-10-23 Benjamin Jourdain , Jérôme Lelong

In applications of imprecise probability, analysts must compute lower (or upper) expectations, defined as the infimum of an expectation over a set of parameter values. Monte Carlo methods consistently approximate expectations at fixed…

Computation · Statistics 2021-03-05 Nicholas Syring , Ryan Martin

We provide a framework which admits a number of ``marginal'' sequential Monte Carlo (SMC) algorithms as particular cases -- including the marginal particle filter [Klaas et al., 2005, in: Proceedings of Uncertainty in Artificial…

Computation · Statistics 2023-03-08 Francesca R. Crucinio , Adam M. Johansen

In this work we develop an effective Monte Carlo method for estimating sensitivities, or gradients of expectations of sufficiently smooth functionals, of a reflected diffusion in a convex polyhedral domain with respect to its defining…

Probability · Mathematics 2017-12-01 David Lipshutz , Kavita Ramanan

This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…

Optimization and Control · Mathematics 2017-11-08 Andreas Van Barel , Stefan Vandewalle

This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…

Probability · Mathematics 2021-09-21 Côme Huré , Huyên Pham , Achref Bachouch , Nicolas Langrené