Parallel tempering with equi-energy moves

Abstract

The Equi-Energy Sampler (EES) introduced by Kou et al. [2006] is based on a population of chains which are updated by local moves and global moves, also called equi-energy jumps. The state space is partitioned into energy rings, and the current state of a chain can jump to a past state of an adjacent chain that has an energy level close to its level. This algorithm has been developed to facilitate global moves between different chains, resulting in a good exploration of the state space by the target chain. This method seems to be more efficient than the classical Parallel Tempering (PT) algorithm. However it is difficult to use in combination with a Gibbs sampler and it necessitates increased storage. In this paper we propose an adaptation of this EES that combines PT with the principle of swapping between chains with same levels of energy. This adaptation, that we shall call Parallel Tempering with Equi-Energy Moves (PTEEM), keeps the original idea of the EES method while ensuring good theoretical properties, and practical implementation. Performances of the PTEEM algorithm are compared with those of the EES and of the standard PT algorithms in the context of mixture models, and in a problem of identification of transcription factor binding motifs.

State-dependent swap strategies and automatic reduction of number of temperatures in adaptive parallel tempering algorithm

“…We find out that in comparison with the previous results (Kou et al 2006;Baragatti et al 2013) we do not observe significant differences between strategies both based on classical Parallel Tempering approach and the Equi Energy type moves: they all provide similarly good quality results. We conclude that a good choice of temperatures schedule is far more important than the way how differently tempered chains interact.…”

“…1. Our studies on swap strategies that depend on the current state are motivated by a seminal paper on Equi-Energy sampler by Kou et al (2006), further adopted to Parallel Tempering algorithm by Baragatti et al (2013).…”

“…value of log-density). The Baragatti et al (2013), also requires specification of the Energy Rings. In order to circumvent this hindrance we propose using state-dependent swap strategies that perform Equi-Energy-like moves within the Parallel Tempering algorithm framework.…”

“…Letting p ij (x) ∝ 1 {x j ∈H x i } we note that the swap acceptance probability is reduced to (7). In the end we obtain an algorithm proposed by Baragatti et al (2013).…”

“…We study the impact of different distributions on potential steps and call them Strategies. Our choice of strategies is driven by solutions already known to the literature (Kou et al 2006) and used within Parallel Tempering algorithm by Baragatti et al (2013). The novelty of our approach stems from an alternative implementation of Equi Energy moves that renders the algorithm parameters free, i.e.…”