Related papers: Improving sampling by modifying the effective diff…
We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace…
Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…
To sample from a general target distribution $p_*\propto e^{-f_*}$ beyond the isoperimetric condition, Huang et al. (2023) proposed to perform sampling through reverse diffusion, giving rise to Diffusion-based Monte Carlo (DMC).…
We propose a reflection-free Langevin framework for sampling and optimization on compact polyhedra. The method is based on the inverse Hessian of the logarithmic barrier, which defines a Dikin--Langevin diffusion whose drift and noise adapt…
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…
The exact estimation of latent variable models with big data is known to be challenging. The latents have to be integrated out numerically, and the dimension of the latent variables increases with the sample size. This paper develops a…
In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly…
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…
Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…
Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the…
Various Markov chain Monte Carlo (MCMC) methods are studied to improve upon random walk Metropolis sampling, for simulation from complex distributions. Examples include Metropolis-adjusted Langevin algorithms, Hamiltonian Monte Carlo, and…
Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge…
Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, the canonical Euler-Maruyama discretization of the Langevin diffusion process, also named as Langevin Monte Carlo (LMC), studied…
We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…
Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where…
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…
We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in…
There is a lack of methodological results to design efficient Markov chain Monte Carlo (MCMC) algorithms for statistical models with discrete-valued high-dimensional parameters. Motivated by this consideration, we propose a simple framework…
A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and…
Algorithms based on discretizing Langevin diffusion are popular tools for sampling from high-dimensional distributions. We develop novel connections between such Monte Carlo algorithms, the theory of Wasserstein gradient flow, and the…