Optimizing Likelihood-free Inference using Self-supervised Neural
  Symmetry Embeddings
Deep Chatterjee Philip C. Harris Maanas Goel Malina Desai Michael W. Coughlin Erik Katsavounidis
Likelihood-free inference is quickly emerging as a powerful tool to perform
fast/effective parameter estimation. We demonstrate a technique of optimizing
likelihood-free inference to make it even faster by marginalizing symmetries in
a physical problem. In this approach, physical symmetries, for example,
time-translation are learned using joint-embedding via self-supervised learning
with symmetry data augmentations. Subsequently, parameter inference is
performed using a normalizing flow where the embedding network is used to
summarize the data before conditioning the parameters. We present this approach
on two simple physical problems and we show faster convergence in a smaller
number of parameters compared to a normalizing flow that does not use a
pre-trained symmetry-informed representation.