2 research outputs found
Automatic regenerative simulation via non-reversible simulated tempering
Simulated Tempering (ST) is an MCMC algorithm for complex target
distributions that operates on a path between the target and a more amenable
reference distribution. Crucially, if the reference enables i.i.d. sampling, ST
is regenerative and can be parallelized across independent tours. However, the
difficulty of tuning ST has hindered its widespread adoption. In this work, we
develop a simple nonreversible ST (NRST) algorithm, a general theoretical
analysis of ST, and an automated tuning procedure for ST. A core contribution
that arises from the analysis is a novel performance metric -- Tour
Effectiveness (TE) -- that controls the asymptotic variance of estimates from
ST for bounded test functions. We use the TE to show that NRST dominates its
reversible counterpart. We then develop an automated tuning procedure for NRST
algorithms that targets the TE while minimizing computational cost. This
procedure enables straightforward integration of NRST into existing
probabilistic programming languages. We provide extensive experimental evidence
that our tuning scheme improves the performance and robustness of NRST
algorithms on a diverse set of probabilistic models
autoMALA: Locally adaptive Metropolis-adjusted Langevin algorithm
Selecting the step size for the Metropolis-adjusted Langevin algorithm (MALA)
is necessary in order to obtain satisfactory performance. However, finding an
adequate step size for an arbitrary target distribution can be a difficult task
and even the best step size can perform poorly in specific regions of the space
when the target distribution is sufficiently complex. To resolve this issue we
introduce autoMALA, a new Markov chain Monte Carlo algorithm based on MALA that
automatically sets its step size at each iteration based on the local geometry
of the target distribution. We prove that autoMALA has the correct invariant
distribution, despite continual automatic adjustments of the step size. Our
experiments demonstrate that autoMALA is competitive with related
state-of-the-art MCMC methods, in terms of the number of log density
evaluations per effective sample, and it outperforms state-of-the-art samplers
on targets with varying geometries. Furthermore, we find that autoMALA tends to
find step sizes comparable to optimally-tuned MALA when a fixed step size
suffices for the whole domain.Comment: Fix Fig.