arXiv subjects

Matthew Ludkin

Publications and source records attributed to Matthew Ludkin.

3 recordsLinked to original sources

arXiv2021

The Apogee to Apogee Path Sampler

Amongst Markov chain Monte Carlo algorithms, Hamiltonian Monte Carlo (HMC) is often the algorithm of choice for complex, high-dimensional target distributions; however, its efficiency is notoriously sensitive to the choice of the integration-time tuning parameter, $T$. When integrating both forward and backward in time using the same leapfrog integration step as HMC, the set of local maxima in the potential along a path, or apogees, is the same whatever point (position and momentum) along the path is chosen to initialise the integration. We present the Apogee to Apogee Path Sampler (AAPS), which utilises this invariance to create a simple yet generic methodology for constructing a path, proposing a point from it and accepting or rejecting that proposal so as to target the intended distribution. We demonstrate empirically that AAPS has a similar efficiency to HMC but is much more robust to the setting of its equivalent tuning parameter, the number of apogees that the path crosses.

stat.CO↗

arXiv2020

Inference for a generalised stochastic block model with unknown number of blocks and non-conjugate edge models

The stochastic block model (SBM) is a popular model for capturing community structure and interaction within a network. Network data with non-Boolean edge weights is becoming commonplace; however, existing analysis methods convert such data to a binary representation to apply the SBM, leading to a loss of information. A generalisation of the SBM is considered, which allows edge weights to be modelled in their recorded state. An effective reversible jump Markov chain Monte Carlo sampler is proposed for estimating the parameters and the number of blocks for this generalised SBM. The methodology permits non-conjugate distributions for edge weights, which enable more flexible modelling than current methods as illustrated on synthetic data, a network of brain activity and an email communication network.

stat.ME↗

arXiv2019

Hug and Hop: a discrete-time, non-reversible Markov chain Monte-Carlo algorithm

We introduced the Hug and Hop Markov chain Monte Carlo algorithm for estimating expectations with respect to an intractable distribution. The algorithm alternates between two kernels: Hug and Hop. Hug is a non-reversible kernel that repeatedly applies the bounce mechanism from the recently proposed Bouncy Particle Sampler to produce a proposal point far from the current position, yet on almost the same contour of the target density, leading to a high acceptance probability. Hug is complemented by Hop, which deliberately proposes jumps between contours and has an efficiency that degrades very slowly with increasing dimension. There are many parallels between Hug and Hamiltonian Monte Carlo using a leapfrog integrator, including the order of the integration scheme, however Hug is also able to make use of local Hessian information without requiring implicit numerical integration steps, and its performance is not terminally affected by unbounded gradients of the log-posterior. We test Hug and Hop empirically on a variety of toy targets and real statistical models and find that it can, and often does, outperform Hamiltonian Monte Carlo.

stat.CO↗