"Fusion-based inference from heterogeneous data " chair

Our contributions lie at the synergistic intersection of two popular tools in the machine learning community: normalizing flows (NF) and optimal transport (OT). First, we address the problem of transporting a finite set of samples associated with a first underlying unknown distribution towards another finite set of samples drawn from another unknown distribution. When trained appropriately, we show that a NF can be used to approximate the solution of this OT problem between a pair of empirical distributions [1]. Then we propose to hybridize the conventional objective function generally designed to train NF by resorting to an OT metric, namely a sliced Wasserstein distance. We show that this hybrid training cost function leads to NFs with better generative abilities [2].


[1] F. Coeurdoux, N. Dobigeon and P. Chainais, “Learning optimal transport between two empirical distributions with normalizing flows,” in Proc. European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML-PKDD), Grenoble, France, Sept. 2022.

[2] F. Coeurdoux, N. Dobigeon and P. Chainais, “Sliced-Wasserstein normalizing flows: beyond maximum likelihood learning,” in Proc. European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN), Bruges, Belgium, Oct. 2022

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