Optimization Monte Carlo: Efficient and Embarrassingly Parallel Likelihood-Free Inference

By Edward Meeds, Max Welling. 2015

36 citations recorded by the source corpus.

We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a vector of random numbers u, in such a way that the outcome, knowing u, is deterministic. For each instantiation of u we run an optimization procedure to minimize the distance between summary statistics of the simulator and the data. After reweighing these samples using the prior and the Jacobian (accounting for the change of volume in transforming from the space of summary statistics to the space of parameters) we show that this weighted ensemble represents a Monte Carlo estimate of the posterior distribution. The procedure can be run embarrassingly parallel (each node handling one sample) and anytime (by allocating resources to the worst performing sample). The procedure is validated on six experiments.

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

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Citations in the corpus

Fast $\epsilon$-free Inference of Simulation Models with Bayesian Conditional Density Estimation (2016, methodology): “Here, MDNs make more efﬁcient use of simulations than Monte Carlo ABC methods.”
Asymptotically exact inference in differentiable generative models (2016, methodology): “Our method also diﬀers in treating all inputs to a generator equivalently; while the Optimisation Monte Carlo authors similarly identify the simulator models as deterministic functions they distinguish between parameters and random inputs, optimising the ﬁrst and independently sampling the latter.”
Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows (2018, methodology): “Optimization Monte Carlo [50] directly optimizes parameter samples so as to generate data similar to x o .”