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.
@cite_30: We extend Support Vector Machines to input spaces that are sets by ensuring that the classifier is invariant to permutations of sub-elements within each input. Such permutations include reordering of scalars in an input vector, re-orderings of tuples in an input matrix or re-orderings of general objects (in Hilbert spaces) within a set as well. This approach induces permutational invariance in the classifier which can then be directly applied to unusual set-based representations of data. The permutation invariant Support Vector Machine alternates the Hungarian method for maximum weight matching within the maximum margin learning procedure. We effectively estimate and apply permutations to the input data points to maximize classification margin while minimizing data radius. This procedure has a strong theoretical justification via well established error probability bounds. Experiments are shown on character recognition, 3D object recognition and various UCI datasets.
The inferential accuracy and scalability of these methods can be improved by exploiting symmetries in the input data. Permutation-invariant models have been previously studied in machine learning for SVMs @cite_30 and, recently, gained a surge of interest in the deep learning literature. Recent work on designing architectures for exchangeable data include , , and , which exploit parameter sharing to encode invariances. To our knowledge, no prior work has been done on learning feature representations for exchangeable population genetic data.