arXiv subjects

Hai-Dang Dau

Publications and source records attributed to Hai-Dang Dau.

5 recordsLinked to original sources

arXiv2026

A coupling-based approach to f-divergences diagnostics for Markov chain Monte Carlo

A long-standing gap exists between the theoretical analysis of Markov chain Monte Carlo convergence, which is often based on statistical divergences, and the diagnostics used in practice. We introduce the first general convergence diagnostics for Markov chain Monte Carlo based on any $f$-divergence, allowing users to directly monitor, among others, the Kullback-Leibler and the $χ^2$ divergences as well as the Hellinger and the total variation distances. Our approach rests on a coupling-based "weight harmonization" scheme that produces direct, computable, and consistent importance weights for interacting Markov chains with respect to their target distribution. Beyond their use as convergence diagnostics, these weights are consistent estimates of the Radon-Nikodym derivative $\mathrm{d}π/\mathrm{d} μ_t$, a richer object than the convergence bounds alone, with natural applications to importance-weighted inference. We show how such weightings can provide upper bounds to any $f$-divergence, prove that these bounds tighten over time and converge to zero as the chains approach stationarity, and demonstrate that, while more conservative than existing coupling-based total variation estimators, our method remains a practical and broadly applicable diagnostic tool.

stat.CO↗

arXiv2026

Accelerated Parallel Tempering via Neural Transports

Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target distributions. Parallel Tempering (PT) enhances MCMC's sample efficiency through annealing and parallel computation, propagating samples from tractable reference distributions to intractable targets via state swapping across interpolating distributions. The effectiveness of PT is limited by the often minimal overlap between adjacent distributions in challenging problems, which requires increasing the computational resources to compensate. We introduce a framework that accelerates PT by leveraging neural samplers -- including normalising flows, diffusion models, and controlled diffusions -- to reduce the required overlap. Our approach utilises neural samplers in parallel, circumventing the computational burden of neural samplers while preserving the asymptotic consistency of classical PT. We demonstrate theoretically and empirically on a variety of multimodal sampling problems that our method improves sample quality, reduces the computational cost compared to classical PT, and enables efficient free energy/normalising constant estimation.

stat.ML↗

arXiv2024

Particle Denoising Diffusion Sampler

Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by estimating the time-reversal of this diffusion using score matching ideas. We follow here a similar strategy to sample from unnormalized probability densities and compute their normalizing constants. However, the time-reversed diffusion is here simulated by using an original iterative particle scheme relying on a novel score matching loss. Contrary to standard denoising diffusion models, the resulting Particle Denoising Diffusion Sampler (PDDS) provides asymptotically consistent estimates under mild assumptions. We demonstrate PDDS on multimodal and high dimensional sampling tasks.

stat.ML↗

arXiv2023

On backward smoothing algorithms

In the context of state-space models, skeleton-based smoothing algorithms rely on a backward sampling step which by default has a $\mathcal O(N^2)$ complexity (where $N$ is the number of particles). Existing improvements in the literature are unsatisfactory: a popular rejection sampling -- based approach, as we shall show, might lead to badly behaved execution time; another rejection sampler with stopping lacks complexity analysis; yet another MCMC-inspired algorithm comes with no stability guarantee. We provide several results that close these gaps. In particular, we prove a novel non-asymptotic stability theorem, thus enabling smoothing with truly linear complexity and adequate theoretical justification. We propose a general framework which unites most skeleton-based smoothing algorithms in the literature and allows to simultaneously prove their convergence and stability, both in online and offline contexts. Furthermore, we derive, as a special case of that framework, a new coupling-based smoothing algorithm applicable to models with intractable transition densities. We elaborate practical recommendations and confirm those with numerical experiments.

stat.CO↗

arXiv2021

Waste-free Sequential Monte Carlo

A standard way to move particles in a SMC sampler is to apply several steps of a MCMC (Markov chain Monte Carlo) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of the intermediate steps are discarded and thus wasted somehow. We propose a new, waste-free SMC algorithm which uses the outputs of all these intermediate MCMC steps as particles. We establish that its output is consistent and asymptotically normal. We use the expression of the asymptotic variance to develop various insights on how to implement the algorithm in practice. We develop in particular a method to estimate, from a single run of the algorithm, the asymptotic variance of any particle estimate. We show empirically, through a range of numerical examples, that waste-free SMC tends to outperform standard SMC samplers, and especially so in situations where the mixing of the considered MCMC kernels decreases across iterations (as in tempering or rare event problems).

stat.CO↗