Classification and Bayesian Optimization for Likelihood-Free Inference
This work provides a solution for researchers in statistics and machine learning dealing with models where likelihood functions are intractable, though it appears incremental as it builds on existing classification and optimization techniques.
The paper addresses the challenges of likelihood-free inference by tackling the choice of discrepancy measure and efficient parameter space exploration, using classification and Bayesian optimization methods.
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by finding the values which yield simulated data that resemble the observed data. This approach faces at least two major difficulties: The first difficulty is the choice of the discrepancy measure which is used to judge whether the simulated data resemble the observed data. The second difficulty is the computationally efficient identification of regions in the parameter space where the discrepancy is low. We give here an introduction to our recent work where we tackle the two difficulties through classification and Bayesian optimization.