Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods

By Nial Friel, Antonietta Mira, Chris J. Oates. 2014

26 citations recorded by the source corpus.

Many popular statistical models for complex phenomena are intractable, in the sense that the likelihood function cannot easily be evaluated. Bayesian estimation in this setting remains challenging, with a lack of computa- tional methodology to fully exploit modern processing capabilities. In this paper we introduce novel control variates for intractable likelihoods that can dramati- cally reduce the Monte Carlo variance of Bayesian estimators. We prove that our control variates are well-defined and provide a positive variance reduction. Fur- thermore, we show how to optimise these control variates for variance reduction. The methodology is highly parallel and offers a route to exploit multi-core pro- cessing architectures that complements recent research in this direction. Indeed, our work shows that it may not be necessary to parallelise the sampling process itself in order to harness the potential of massively multi-core architectures. Simu- lation results presented on the Ising model, exponential random graph models and non-linear stochastic differential equation models support our theoretical findings.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, methodology): “An extension should be possible to models with unknown, parameter-dependent normalizing constants, which include for example Markov random fields (Everitt, 2012) and random-network models (Friel et al., 2015).”
The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation (2016, background): “For a large class of intractable likelihood models, Friel, Mira, and Oates (2014b) showed how to obtain a stochastic approximation to ZV control variates that could be directly leveraged within our methodology.”