Likelihood-free inference with deep Gaussian processes

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. This problem is addressed by proposing a Deep Gaussian Process (DGP) surrogate model that can handle more irregularly behaved target distributions. The experiments show how DGPs can outperform GPs on objective functions with multimodal distributions and maintain a comparable performance in unimodal cases. At the same time, DGPs generally require much fewer data to achieve the same level of performance as neural density and kernel mean embedding alternatives. This confirms that DGPs as surrogate models can extend the applicability of Bayesian Optimization for likelihood-free inference (BOLFI), while only adding computational overhead that remains negligible for computationally intensive simulators.