Cecilia Viscardi

A large deviation approach to approximate Bayesian computation

We consider the problem of sample degeneracy in approximate Bayesian computation (ABC). This problem arises when proposed values of the parameters, once given as input to the generative model, rarely lead to simulations resembling the observed data and are hence discarded. Such ``poor'' parameters' proposals do not contribute to the representation of the parameters' posterior distribution. This state of affairs leads to a large number of required simulations and/or a waste of computational resources and distortions in the computed posterior distribution. To mitigate this problem, we propose a Large Deviation Approximate Bayesian Computation algorithm ( LD-ABC), where the evaluation of the probability of rare events allows avoiding the rejection step altogether. We adopt the information-theoretic “Method of Types” formulation of Large Deviations, thus restricting attention to models for i.i.d. discrete random variables and for finite-state Markov chains. Finally, we experimentally evaluate our methodology through a proof-of-concept implementation.