Fast $ε$-free Inference of Simulation Models with Bayesian Conditional Density Estimation
This addresses the computational bottleneck in likelihood-free inference for researchers in statistics and machine learning, offering a more efficient alternative to existing methods.
The paper tackles the problem of slow and approximate inference in simulation models with intractable likelihoods by proposing a Bayesian conditional density estimation approach that guides simulations based on preliminary inferences, achieving accurate posterior representation with fewer simulations than traditional ABC methods.
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior over parameters by conditioning on data being inside an $ε$-ball around the observed data, which is only correct in the limit $ε\!\rightarrow\!0$. Monte Carlo methods can then draw samples from the approximate posterior to approximate predictions or error bars on parameters. These algorithms critically slow down as $ε\!\rightarrow\!0$, and in practice draw samples from a broader distribution than the posterior. We propose a new approach to likelihood-free inference based on Bayesian conditional density estimation. Preliminary inferences based on limited simulation data are used to guide later simulations. In some cases, learning an accurate parametric representation of the entire true posterior distribution requires fewer model simulations than Monte Carlo ABC methods need to produce a single sample from an approximate posterior.