Sample-efficient inference for agent-based cognitive models and other computationally intensive simulators

Abstract

In recent years, simulator models have become increasingly popular in many scientific domains, such as epidemiology, cosmology, and behavioural sciences. Since simulators often do not have tractable likelihoods, which are either too costly to evaluate or not available, the field needs to resort to likelihood-free inference (LFI), which uses forward simulations instead. With the development of more complex simulators, traditional LFI methods become unfeasible as the cost of simulations significantly increases. This thesis deals with three challenges that arise in the context of computationally heavy simulators and for which the existing LFI methods, such as approximate Bayesian computation, synthetic likelihood, or neural density estimation approaches, are inadequate since they require a large number of simulations.

The first challenge is modelling complex simulator noise, which influences the accuracy of LFI methods and becomes problematic when simulations are computationally costly. The existing methods either oversimplify the noise (e.g., by assuming it to be Gaussian) or require an infeasible number of simulations to accurately model it. We show how to handle multimodal, non-stationary, and heteroscedastic noise distributions in LFI while also assuming a small simulation budget. For this, we adopt deep Gaussian process surrogates in Bayesian Optimisation (BO), along with novel quantile-based multimodal-capable modifications for the acquisition function and posterior extraction procedures.

Another challenge for modern LFI approaches occurs when they are applied to time-series settings, as these methods either need an accurate model of transition dynamics available or always assume it to be linear. We propose a way of estimating the unknown transition dynamics for state predictions in simulator-based dynamical systems, which greatly reduces the required simulation budget and also enables time-series prediction. Our proposed approach uses a multi-objective surrogate for LFI and a semi-parametric model for the transition dynamics.

Finally, we significantly reduce the time required to select agent-based cognitive models with limited experimental designs. The previous methods have primarily focused on either model selection or parameter estimation, while we achieve both in a fraction of the time. This is accomplished through a novel simulator-based utility objective for selecting designs in BO and a LFI approximation of model marginal likelihood for model selection. This new method is needed for developing and verifying computational cognitive theories, which often lack tractable likelihoods.