Related papers: Diffusion approximations and control variates for …
This work is motivated by the need to study the impact of data uncertainties and material imperfections on the solution to optimal control problems constrained by partial differential equations. We consider a pathwise optimal control…
Motivated by applications arising in networked systems, this work examines controlled regime-switching systems that stem from a mean-variance formulation. A main point is that the switching process is a hidden Markov chain. An additional…
Markov chain Monte Carlo methods such as Gibbs sampling and simple forms of the Metropolis algorithm typically move about the distribution being sampled via a random walk. For the complex, high-dimensional distributions commonly encountered…
Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is…
This paper presents a method to leverage arbitrary neural network architecture for control variates. Control variates are crucial in reducing the variance of Monte Carlo integration, but they hinge on finding a function that both correlates…
Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use…
Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary…
Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations…
In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the…
Proposals for Metropolis-Hastings MCMC derived by discretizing Langevin diffusion or Hamiltonian dynamics are examples of stochastic autoregressive proposals that form a natural wider class of proposals with equivalent computability. We…
Although the mean-variance control was initially formulated for financial portfolio management problems in which one wants to maximize expected return and control the risk, our motivations also stem from highway vehicle platoon controls…
Langevin Monte Carlo (LMC) algorithms are popular Markov Chain Monte Carlo (MCMC) methods to sample a target probability distribution, which arises in many applications in machine learning. Inspired by regime-switching stochastic…
Recent studies on diffusion-based sampling methods have shown that Langevin Monte Carlo (LMC) algorithms can be beneficial for non-convex optimization, and rigorous theoretical guarantees have been proven for both asymptotic and finite-time…
Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
Sampling from score-based diffusion models incurs bias due to both time discretisation and the approximation of the score function. A common strategy for reducing this bias is to apply corrector steps based on the unadjusted Langevin…
Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stochastic gradients…
In this paper we build on previous work which uses inferences techniques, in particular Markov Chain Monte Carlo (MCMC) methods, to solve parameterized control problems. We propose a number of modifications in order to make this approach…
This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…
We estimate the parameter of a stationary time series process by minimizing the integrated weighted mean squared error between the empirical and simulated characteristic function, when the true characteristic functions cannot be explicitly…