Caching and Interpolated Likelihoods: Accelerating Cosmological Monte Carlo Markov Chains

TL;DR

This paper introduces a novel polynomial interpolation method to speed up cosmological parameter estimation with MCMC, achieving 2-4x acceleration without precomputed training sets.

Contribution

The paper presents InterpMC, a new interpolation-based algorithm that accelerates MCMC sampling in cosmology by replacing expensive likelihood evaluations with polynomial approximations.

Findings

Achieves 2-4x speedup in parameter estimation

Applicable to any smooth likelihood surface

Open-source implementation as a CosmoMC patch

Abstract

We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free parameters and computationally expensive to evaluate. We generate a high-order interpolating polynomial for the log-likelihood using the first points gathered by the Markov chains as a training set. This polynomial then accurately computes the majority of the likelihoods needed in the latter parts of the chains. We implement a simple version of this algorithm as a patch (InterpMC) to CosmoMC and show that it accelerates parameter estimatation by a factor of between two and four for well-converged chains. The current code is primarily intended as a "proof of concept", and we argue that there is considerable room for further performance gains. Unlike other approaches to accelerating parameter fits, we make no use of precomputed training sets or special choices of variables, and InterpMC is almost entirely transparent to the user.