Efficient Acquisition Rules for Model-Based Approximate Bayesian Computation
By Marko Jarvenpaa, Michael U Gutmann, Arijus Pleska, Aki Vehtari, Pekka Marttinen. 2017
72 citations recorded by the source corpus.
Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly. To reduce the computational cost, Bayesian optimisation (BO) and surrogate models such as Gaussian processes have been proposed. Bayesian optimisation enables one to intelligently decide where to evaluate the model next but common BO strategies are not designed for the goal of estimating the posterior distribution. Our paper addresses this gap in the literature. We propose to compute the uncertainty in the ABC posterior density, which is due to a lack of simulations to estimate this quantity accurately, and define a loss function that measures this uncertainty. We then propose to select the next evaluation location to minimise the expected loss. Experiments show that the proposed method often produces the most accurate approximations as compared to common BO strategies.
Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Gilles Louppe
- George Papamakarios
- Iain Murray
- Joeri Hermans
- Jakob H. Macke
- David S. Greenberg
- Volodimir Begy
- Marcel Nonnenmacher
In Statistics and Probability
- Gilles Louppe
- George Papamakarios
- Iain Murray
- Marcel Nonnenmacher
- David S. Greenberg
- Jakob H. Macke
- Joeri Hermans
- Jukka Corander
In Probabilistic & Bayesian Methods
- Gilles Louppe
- George Papamakarios
- Iain Murray
- Jakob H. Macke
- Marcel Nonnenmacher
- David S. Greenberg
- Michael U Gutmann
- Joeri Hermans
Citations in the corpus
- Sequential Neural Methods for Likelihood-free Inference (2018, unknown): “[10], given by θ = argmaxθ Vφ[qφ(x0 |θ)p(θ)].”
- Automatic Posterior Transformation for Likelihood-Free Inference (2019, background): “Atomic proposals also greatly enhance flexibility when generating new simulations: they can emphasize the posterior’s peaks or tails, or use active learning schemes (Lueckmann et al., 2018; Järvenpää et al., 2018) incompatible with previous SNPE approaches.”
- Flexible statistical inference for mechanistic models of neural dynamics (2017, methodology): “method could be extended by alternative approaches to designing proposal priors [48, 49], e.”
- Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows (2018, methodology): “An active-learning-style approach is to use the Bayesian uncertainty in the posterior estimate to choose what simulation to run next [34, 44]; in this scheme, the next simulation is chosen to maximally reduce the Bayesian uncertainty.”
- Likelihood-Free Inference by Ratio Estimation (2016, methodology): “There are several ways to reduce the inference cost: First, Bayesian optimisation can be used to intelligently decide where to evaluate the posterior as previously done for the synthetic likelihood, thus reducing unnecessary computations (Gutmann and Corander, 2016; Järvenpää et al., 2018).”
- Likelihood-free inference with emulator networks (2018, methodology): “We refer to this rule as the MaxVar rule (Järvenpää et al., 2017).”