In Markov chain Monte Carlo sampling, light-tailed target distributions present something of a poisoned chalice: their light tails offer good confinement, and tend to imply good mixing properties for natural continuous-time dynamics, but the steepness of their tail decay means that they often fall outside of the scope of modern quantitative convergence theory. For usual gradient-based samplers, this reflects a genuine instability issue, whereby Metropolis acceptance rates can degrade badly. In this work, we study the gradient-free random-walk Metropolis sampler, and show that for a wide range of light-tailed targets, the acceptance probability remains stable for reasonable choices of proposal variance, from which effective and favourable mixing time estimates can be deduced. The analysis relies on a simple relationship between the first and second derivatives of the log-density of the target distribution.
We study a non-reversible random walk advected by the symmetric simple exclusion process, so that the walk has a local drift of opposite sign when sitting atop an occupied or an empty site. We prove that the back-tracking probability of the walk exhibits a sharp transition as the density
\rho
of particles in th...
Guillaume Conchon-Kerjan, Daniel Kious, Pierre-François Rodriguez· Journal of the European Math...· 0 citations
Langevin-based Markov chain Monte Carlo (MCMC) algorithms use gradient information to improve sampling, particularly in high dimensions. Classical optimal scaling theory for these algorithms has largely focused on the Metropolis-Hastings (MH) acceptance rule. However, there has been a recent surge in acceptance rules b...
Some of the sharpest challenges in sampling from the energy functions of physical systems arise at phase transitions, where the density of states changes abruptly and many sampling algorithms stall. Nested sampling is a particle method that traverses the density of states under a hard energy constraint and is known to...
We study the annealed survival probability of a random walk in an inhomogeneous Poisson environment of mobile traps on $\mathbb{Z}^d$. In dimensions $d=1,2$, we determine the asymptotics for the annealed survival probability of the walker under suitable assumptions on the average trap intensity and study how inhomogene...
This work introduces an algorithm for learning Boltzmann distributions that does not require any true samples for training and establishes a new method for sample-free learning of complex physical distributions.
V. Kanaujia, Vipul Arora· Trans. Mach. Learn. Res.· 1 citation
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