Alexander Aushev

Alexander Aushev, Aini Putkonen, Gregoire Clarte et al.

The problem of model selection with a limited number of experimental trials has received considerable attention in cognitive science, where the role of experiments is to discriminate between theories expressed as computational models. Research on this subject has mostly been restricted to optimal experiment design with analytically tractable models. However, cognitive models of increasing complexity, with intractable likelihoods, are becoming more commonplace. In this paper, we propose BOSMOS: an approach to experimental design that can select between computational models without tractable likelihoods. It does so in a data-efficient manner, by sequentially and adaptively generating informative experiments. In contrast to previous approaches, we introduce a novel simulator-based utility objective for design selection, and a new approximation of the model likelihood for model selection. In simulated experiments, we demonstrate that the proposed BOSMOS technique can accurately select models in up to 2 orders of magnitude less time than existing LFI alternatives for three cognitive science tasks: memory retention, sequential signal detection and risky choice.

Alexander Aushev, Thong Tran, Henri Pesonen et al.

Likelihood-free inference (LFI) has been successfully applied to state-space models, where the likelihood of observations is not available but synthetic observations generated by a black-box simulator can be used for inference instead. However, much of the research up to now have been restricted to cases, in which a model of state transition dynamics can be formulated in advance and the simulation budget is unrestricted. These methods fail to address the problem of state inference when simulations are computationally expensive and the Markovian state transition dynamics are undefined. The approach proposed in this manuscript enables LFI of states with a limited number of simulations by estimating the transition dynamics, and using state predictions as proposals for simulations. In the experiments with non-stationary user models, the proposed method demonstrates significant improvement in accuracy for both state inference and prediction, where a multi-output Gaussian process is used for LFI of states, and a Bayesian Neural Network as a surrogate model of transition dynamics.

Alexander Aushev, Henri Pesonen, Markus Heinonen et al.

In recent years, surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations. The current state-of-the-art performance for this task has been achieved by Bayesian Optimization with Gaussian Processes (GPs). While this combination works well for unimodal target distributions, it is restricting the flexibility and applicability of Bayesian Optimization for accelerating likelihood-free inference more generally. We address this problem by proposing a Deep Gaussian Process (DGP) surrogate model that can handle more irregularly behaved target distributions. Our experiments show how DGPs can outperform GPs on objective functions with multimodal distributions and maintain a comparable performance in unimodal cases. This confirms that DGPs as surrogate models can extend the applicability of Bayesian Optimization for likelihood-free inference (BOLFI), while adding computational overhead that remains negligible for computationally intensive simulators.