Related papers: Minimising MCMC variance via diffusion limits, wit…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
I show how any reversible Markov chain on a finite state space that is irreducible, and hence suitable for estimating expectations with respect to its invariant distribution, can be used to construct a non-reversible Markov chain on a…
We introduce an algorithm to systematically improve the efficiency of parallel tempering Monte Carlo simulations by optimizing the simulated temperature set. Our approach is closely related to a recently introduced adaptive algorithm that…
We present here two novel algorithms for simulated tempering simulations, which break detailed balance condition (DBC) but satisfy the skewed detailed balance to ensure invariance of the target distribution. The irreversible methods we…
In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…
We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrisation defined through…
This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
Markov chain Monte Carlo (MCMC) methods are frequently used to approximately simulate high-dimensional, multimodal probability distributions. In adaptive MCMC methods, the transition kernel is changed "on the fly" in the hope to speed up…
We propose a sampling-based framework for finite-horizon trajectory and policy optimization under differentiable dynamics by casting controller design as inference. Specifically, we minimize a KL-regularized expected trajectory cost, which…
Motivated in part by a problem in simulated tempering (a form of Markov chain Monte Carlo) we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel from the origin…
Autocorrelations in MCMC chains increase the variance of the estimators they produce. We propose the occlusion process to mitigate this problem. It is a process that sits upon an existing MCMC sampler, and occasionally replaces its samples…
We present discrete-time approximation of optimal control policies for infinite horizon discounted/ergodic control problems for controlled diffusions in $\Rd$\,. In particular, our objective is to show near optimality of optimal policies…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
This paper proposes an adaptive stochastic Model Predictive Control (MPC) strategy for stable linear time invariant systems in the presence of bounded disturbances. We consider multi-input multi-output systems that can be expressed by a…
Markov chain Monte Carlo(MCMC) is a popular approach to sample from high dimensional distributions, and the asymptotic variance is a commonly used criterion to evaluate the performance. While most popular MCMC algorithms are reversible,…
Inexact methods for model predictive control (MPC), such as real-time iterative schemes or time-distributed optimization, alleviate the computational burden of exact MPC by providing suboptimal solutions. While the asymptotic stability of…
We establish finite sample bounds for the error of standard and waste-free SMC samplers. Our results cover estimates of both expectations and normalising constants of the target distributions. We consider first an arbitrary sequence of…