Kengo Kamatani

ISM, Japan

Non-reversible guided Metropolis kernel

Statistics Seminar

26th February 2021, 9:00 am – 9:45 am,

We construct a class of non-reversible Metropolis kernels as
a multivariate extension of the guided-walk kernel proposed by
Gustafson, 1998.
The main idea of our method is to introduce a projection that maps a
state space to a totally ordered group.
By using Haar measure, we construct a novel Markov kernel termed
Haar-mixture reversible kernel,
which is of interest in its own right. This is achieved by inducing a
topological structure to the totally ordered group.
Our proposed method, the guided Metropolis kernel, is constructed by
using the Haar-mixture reversible kernel as a proposal kernel.
The proposed non-reversible kernel at least 10 times better than the
random-walk Metropolis kernel and Hamiltonian Monte Carlo kernel for
the logistic regression and a discretely observed stochastic process
in terms of effective sample size per second.

This is joint work with Xiaolin Song (Osaka University).

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