The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation

By Chris J. Oates, Theodore Papamarkou, Mark A. Girolami. 2016

60 citations recorded by the source corpus.

ABSTRACT Approximation of the model evidence is well known to be challenging. One promising approach is based on thermodynamic integration, but a key concern is that the thermodynamic integral can suffer from high variability in many applications. This article considers the reduction of variance that can be achieved by exploiting control variates in this setting. Our methodology applies whenever the gradient of both the log-likelihood and the log-prior with respect to the parameters can be efficiently evaluated. Results obtained on regression models and popular benchmark datasets demonstrate a significant and sometimes dramatic reduction in estimator variance and provide insight into the wider applicability of control variates to evidence estimation. Supplementary materials for this article are available online.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, background): “Details are reserved for a future publication (Oates et al., 2016).”
Convergence rates for a class of estimators based on Stein’s method (2016, background): “Control variates can alternatively be constructed based on gradient information on the sampling distribution [2,31,35,36].”
Control Functionals for Quasi-Monte Carlo Integration (2015, methodology): “The methods that we describe are immediately applicable in a range of applications including marginalisation of hyper-parameters in classification [10], probabilistic inference for differential equations [28, 5], computation of model evidence [21] and approximation of the partition function in socia”
Bayesian Probabilistic Numerical Methods (2017, methodology): “Higher-order quadrature rules and variance reduction techniques can be used, but were not implemented for this work (Oates et al., 2016b).”