A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks
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Inference for population genetics models is hindered by computationally intractable likelihoods. While this issue is tackled by likelihood-free methods, these approaches typically rely on hand-crafted summary statistics of the data. In complex settings, designing and selecting suitable summary statistics is problematic and results are very sensitive to such choices. In this paper, we learn the first exchangeable feature representation for population genetic data to work directly with genotype data. This is achieved by means of a novel Bayesian likelihood-free inference framework, where a permutation-invariant convolutional neural network learns the inverse functional relationship from the data to the posterior. We leverage access to scientific simulators to learn such likelihood-free function mappings, and establish a general framework for inference in a variety of simulation-based tasks. We demonstrate the power of our method on the recombination hotspot testing problem, outperforming the state-of-the-art.
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