GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation

By Edward Meeds, Max Welling. 2014

127 citations recorded by the source corpus.

Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging. The Approximate Bayesian Computation (ABC) framework is the standard statistical tool to handle these likelihood free problems, but they require a very large number of simulations. In this work we develop two new ABC sampling algorithms that significantly reduce the number of simulations necessary for posterior inference. Both algorithms use confidence estimates for the accept probability in the Metropolis Hastings step to adaptively choose the number of necessary simulations. Our GPS-ABC algorithm stores the information obtained from every simulation in a Gaussian process which acts as a surrogate function for the simulated statistics. Experiments on a challenging realistic biological problem illustrate the potential of these algorithms.

Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

K2-ABC: Approximate Bayesian Computation with Infinite Dimensional Summary Statistics via Kernel Embeddings (2015, methodology): “2B), and therefore inference with those data is very challenging as noted in (Meeds & Welling, 2014).”
Likelihood-free MCMC with Approximate Likelihood Ratios (2019, methodology): “Active simulation strategies such as BOLFI [52] and others [53, 54] achieve this by employing Bayesian optimization to make efﬁcient use of the simulator.”
Likelihood-Free Inference by Ratio Estimation (2016, methodology): “The synthetic likelihood approach is applicable to a diverse set of problems (Meeds and Welling, 2014; Price et al., 2017), but the Gaussianity assumption may not always hold and the original method does not include a mechanism for choosing summary statistics automatically.”
Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models (2015, methodology): “There are also connections to the body of work on Bayesian analysis of computer codes (for an introduction to this field of research, see for example the paper by O’Hagan, 2006): Sacks et al. (1989) and Currin et al.”
Hamiltonian ABC (2015, methodology): “We use = {1/2, 1/2, 1/2, 1/2, 1/4, 1/4, 1/4, 1/4, 3/4, 3/4} (slightly different from [14]) and S = 10 for all experiments (this means that there are S random seeds).”
Flexible statistical inference for mechanistic models of neural dynamics (2017, methodology): “Synthetic-likelihood methods [28, 21, 29] approximate the likelihood p(x|θ) using multivariate Gaussians fitted to repeated simulations given θ (see [30, 31] for generalisations).”
Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows (2018, methodology): “Gaussian Process Surro-gate ABC [49] employs a Gaussian process to model the dependence of ( m θ , S θ ) on θ , and uses the uncertainty in the GP to decide whether to run more simulations to estimate ( m θ , S θ ).”
Likelihood-free MCMC with Amortized Approximate Ratio Estimators (2019, methodology): “Active simulation strategies such as BOLFI (Gutmann & Corander, 2016) and others (Ong et al., 2017; Meeds & Welling, 2014) achieve this through Bayesian optimization.”
Fast $\epsilon$-free Inference of Simulation Models with Bayesian Conditional Density Estimation (2016, methodology): “More recently, Meeds and Welling [14] used a Gaussian process model to interpolate Gaussian likelihood approximations between different θ’s.”
Likelihood-free inference with emulator networks (2018, methodology): “In order to exploit smoothness of likelihood functions across the parameter space, the use of Gaussian Processes ( GP s) has been proposed [13].”