A generative flow for conditional sampling via optimal transport
Jason Alfonso Ricardo Baptista Anupam Bhakta Noam Gal Alfin Hou Isa Lyubimova Daniel Pocklington Josef Sajonz Giulio Trigila Ryan Tsai
Sampling conditional distributions is a fundamental task for Bayesian
inference and density estimation. Generative models, such as normalizing flows
and generative adversarial networks, characterize conditional distributions by
learning a transport map that pushes forward a simple reference (e.g., a
standard Gaussian) to a target distribution. While these approaches
successfully describe many non-Gaussian problems, their performance is often
limited by parametric bias and the reliability of gradient-based (adversarial)
optimizers to learn these transformations. This work proposes a non-parametric
generative model that iteratively maps reference samples to the target. The
model uses block-triangular transport maps, whose components are shown to
characterize conditionals of the target distribution. These maps arise from
solving an optimal transport problem with a weighted $L^2$ cost function,
thereby extending the data-driven approach in [Trigila and Tabak, 2016] for
conditional sampling. The proposed approach is demonstrated on a two
dimensional example and on a parameter inference problem involving nonlinear
ODEs.