  An explosion of high-throughput DNA sequencing in the past decade has led to
a surge of interest in population-scale inference with whole-genome data.
Recent work in population genetics has centered on designing inference methods
for relatively simple model classes, and few scalable general-purpose inference
techniques exist for more realistic, complex models. To achieve this, two
inferential challenges need to be addressed: (1) population data are
exchangeable, calling for methods that efficiently exploit the symmetries of
the data, and (2) computing likelihoods is intractable as it requires
integrating over a set of correlated, extremely high-dimensional latent
variables. These challenges are traditionally tackled by likelihood-free
methods that use scientific simulators to generate datasets and reduce them to
hand-designed, permutation-invariant summary statistics, often leading to
inaccurate inference. In this work, we develop an exchangeable neural network
that performs summary statistic-free, likelihood-free inference. Our framework
can be applied in a black-box fashion across a variety of simulation-based
tasks, both within and outside biology. We demonstrate the power of our
approach on the recombination hotspot testing problem, outperforming the
state-of-the-art.
