Hamiltonian ABC

By Edward Meeds, Robert Leenders, Max Welling. 2015

32 citations recorded by the source corpus.

Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively low-dimensional problems. We introduce Hamiltonian ABC (HABC), a set of likelihood-free algorithms that apply recent advances in scaling Bayesian learning using Hamiltonian Monte Carlo (HMC) and stochastic gradients. We find that a small number forward simulations can effectively approximate the ABC gradient, allowing Hamiltonian dynamics to efficiently traverse parameter spaces. We also describe a new simple yet general approach of incorporating random seeds into the state of the Markov chain, further reducing the random walk behavior of HABC. We demonstrate HABC on several typical ABC problems, and show that HABC samples comparably to regular Bayesian inference using true gradients on a high-dimensional problem from machine learning.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families (2015, methodology): “There have been efforts to mimic HMC’s behaviour using stochastic gradients from mini-batches in Big Data [7], or stochastic finite differences in ABC [8].”
Flexible statistical inference for mechanistic models of neural dynamics (2017, methodology): “More efficient variants make use of a Markov-Chain Monte-Carlo [23, 24] or Sequential Monte-Carlo (SMC) samplers [25, 26].”
A Markov Jump Process for More Efficient Hamiltonian Monte Carlo (2015, methodology): “tion techniques [16], Hamiltonian annealed importance sampling [17], split HMC [18], tempered trajectories [9], novel discrete time transition rules [10, 19, 20], stochastic gradient variants on HMC [21], HMC for approximate Bayesian computation [22], and new approximate Hamiltonian integrators [23]”
Asymptotically exact inference in differentiable generative models (2016, methodology): “Hamiltonian ABC [22], also proposes applying HMC to perform inference in simulator models as considered here.”
Adversarial Variational Optimization of Non-Differentiable Simulators (2017, methodology): “The prevalence and signiﬁcance of this problem has motivated an active research eﬀort in so-called likelihood-free inference algorithms such as Approximate Bayesian Computation (ABC) and density estimation-by-comparison algorithms [1–6].”
Mining gold from implicit models to improve likelihood-free inference (2018, methodology): “Most established inference methods, such as ABC and techniques based on neural density estimation, only use samples of observables from the simulator.”
Optimization Monte Carlo: Efficient and Embarrassingly Parallel Likelihood-Free Inference (2015, unknown): “This assumption has been used previously in ABC, ﬁrst in “coupled ABC” [16] and also in an application of Hamiltonian dynamics to ABC [15].”
Fast $\epsilon$-free Inference of Simulation Models with Bayesian Conditional Density Estimation (2016, methodology): “Hamiltonian ABC [15] improves upon MCMC-ABC by using stochastically estimated gradients in order to explore the parameter space more efficiently.”
Likelihood-free MCMC with Approximate Likelihood Ratios (2019, background): “Current likelihood-free implementations of HMC rely on ﬁnite differences to estimate this gradient [16].”
Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows (2018, methodology): “A basic implementation of ABC would simulate parameters from the prior; more sophisticated variants such as Markov Chain Monte Carlo ABC [47, 51, 69] and Sequential Monte Carlo ABC [6, 10, 70, 76] guide future simulations based on previously accepted parameters.”