arXiv subjects

Yinchen Luo

Publications and source records attributed to Yinchen Luo.

4 recordsLinked to original sources

arXiv2026

Rényi mixing bounds for kinetic samplers via $L^2$ hypocoercivity

We study convergence in Rényi divergence of order two for underdamped Langevin dynamics, the bouncy particle sampler, and the Zigzag sampler, for a target $e^{-U}$ on $\mathbb R^d$ that satisfies a logarithmic Sobolev inequality, with $\nabla^2U$ bounded below by a possibly negative constant and, for the Zigzag sampler, also bounded above. For initial laws whose Rényi divergence from equilibrium is at most $R$, we show that it decays exponentially, at a rate that depends on $R$. With the friction or refreshment rate chosen according to $R$, the time needed to reach a fixed accuracy in total variation or in Rényi divergence is of order $\sqrt{R\log R}$ at fixed dimension and target parameters, improving the linear dependence obtained by directly converting exponential $L^2$ decay. The key idea is to use the logarithmic Sobolev inequality for the position target in place of the usual spatial spectral-gap estimate in the $L^2$ hypocoercivity argument. For the bouncy particle and Zigzag samplers, this order is sharp for the Rényi divergence on a one-dimensional Gaussian target, uniformly in the refreshment rate. For the Zigzag sampler in dimension at least two, Gaussian examples show that the mixing-time bound is sharp up to logarithmic factors in the worst case over strongly convex targets, in both the initial divergence and the upper Hessian bound; in particular, strong convexity alone does not give a uniform mixing bound.

math.PR↗

arXiv2026

Entropy hypocoercivity and query complexity for the bouncy particle sampler

We study convergence in relative entropy of the bouncy particle sampler with Gaussian velocity refreshment, for a target $e^{-U}$ on $\mathbb R^d$ with $U$ $m$-strongly convex and $L$-smooth, and condition number $κ=L/m$. For initial laws with bounded density relative to equilibrium, we show that the relative entropy decays exponentially up to an arbitrary additive error $δ$, with a rate that depends only logarithmically on the density bound and on $δ$. From a Gaussian cold start and with a suitably chosen refreshment rate, the relative entropy falls below $δ$ after time $\widetilde O(\sqrt{d/m})$. Combined with exact simulation by windowed thinning, this gives an expected gradient-query complexity of $\widetilde O(d\sqrtκ)$, improving the $\widetilde O(d^2\sqrtκ)$ bound based on $L^2$ hypocoercivity.

math.PR↗

arXiv2026

Windowed thinning and query complexity for the bouncy particle and Zigzag samplers

Let $μ(d x)\propto e^{-U(x)} d x$ on $\R^d$, where $U$ is $m$-strongly convex and $L$-smooth, and denote by $κ=L/m$ the condition number. We consider windowed thinning, an exact simulation method for the bouncy particle sampler and the coordinate Zigzag process. The method divides a trajectory into deterministic windows and uses a gradient evaluation at the beginning of each window to construct a tractable local envelope for the event rate. Combining this construction with quantitative mixing estimates and finite-time bounds on the expected numbers of bounces and flips yields query complexity guarantees from a Gaussian cold start. For total-variation error $\varepsilon$, the expected query counts are $O(κ^{1/2}d\,(d\logκ+\log\frac1\varepsilon))$ gradient queries for the bouncy particle sampler and $O(κd^{1/4}(d\logκ+\log\frac1\varepsilon))$ full-gradient equivalents for Zigzag, where $d$ coordinate-partial queries count as one equivalent.

math.NA↗

arXiv2025

A generalized discontinuous Hamilton Monte Carlo for transdimensional sampling

In this paper, we propose a discontinuous Hamilton Monte Carlo (DHMC) to sample from dimensional varying distributions, and particularly the grand canonical ensemble. The DHMC was proposed in [Biometrika, 107(2)] for discontinuous potential where the variable has a fixed dimension. When the dimension changes, there is no clear explanation of the volume-preserving property, and the conservation of energy is also not necessary. We use a random sampling for the extra dimensions, which corresponds to a measure transform. We show that when the energy is corrected suitably for the trans-dimensional Hamiltonian dynamics, the detailed balance condition is then satisfied. For the grand canonical ensemble, such a procedure can be explained very naturally to be the extra free energy change brought by the newly added particles, which justifies the rationality of our approach. To sample the grand canonical ensemble for interacting particle systems, the DHMC is then combined with the random batch method to yield an efficient sampling method. In experiments, we show that the proposed DHMC combined with the random batch method generates samples with much less correlation when compared with the traditional Metropolis-Hastings method.

math.NA↗