Iterative Alignment Flows

Zeyu Zhou, Ziyu Gong, Pradeep Ravikumar, David I. Inouye
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:6409-6444, 2022.

Abstract

The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate multiple flows independently, which is equivalent to learning multiple full generative models. Other approaches require adversarial learning, which can be computationally expensive and challenging to optimize. Thus, we aim to jointly align multiple distributions while avoiding adversarial learning. Inspired by efficient alignment algorithms from optimal transport (OT) theory for univariate distributions, we develop a simple iterative method to build deep and expressive flows. Our method decouples each iteration into two subproblems: 1) form a variational approximation of a distribution divergence and 2) minimize this variational approximation via closed-form invertible alignment maps based on known OT results. Our empirical results give evidence that this iterative algorithm achieves competitive distribution alignment at low computational cost while being able to naturally handle more than two distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-zhou22b, title = { Iterative Alignment Flows }, author = {Zhou, Zeyu and Gong, Ziyu and Ravikumar, Pradeep and Inouye, David I.}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {6409--6444}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/zhou22b/zhou22b.pdf}, url = {https://proceedings.mlr.press/v151/zhou22b.html}, abstract = { The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate multiple flows independently, which is equivalent to learning multiple full generative models. Other approaches require adversarial learning, which can be computationally expensive and challenging to optimize. Thus, we aim to jointly align multiple distributions while avoiding adversarial learning. Inspired by efficient alignment algorithms from optimal transport (OT) theory for univariate distributions, we develop a simple iterative method to build deep and expressive flows. Our method decouples each iteration into two subproblems: 1) form a variational approximation of a distribution divergence and 2) minimize this variational approximation via closed-form invertible alignment maps based on known OT results. Our empirical results give evidence that this iterative algorithm achieves competitive distribution alignment at low computational cost while being able to naturally handle more than two distributions. } }
Endnote
%0 Conference Paper %T Iterative Alignment Flows %A Zeyu Zhou %A Ziyu Gong %A Pradeep Ravikumar %A David I. Inouye %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-zhou22b %I PMLR %P 6409--6444 %U https://proceedings.mlr.press/v151/zhou22b.html %V 151 %X The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate multiple flows independently, which is equivalent to learning multiple full generative models. Other approaches require adversarial learning, which can be computationally expensive and challenging to optimize. Thus, we aim to jointly align multiple distributions while avoiding adversarial learning. Inspired by efficient alignment algorithms from optimal transport (OT) theory for univariate distributions, we develop a simple iterative method to build deep and expressive flows. Our method decouples each iteration into two subproblems: 1) form a variational approximation of a distribution divergence and 2) minimize this variational approximation via closed-form invertible alignment maps based on known OT results. Our empirical results give evidence that this iterative algorithm achieves competitive distribution alignment at low computational cost while being able to naturally handle more than two distributions.
APA
Zhou, Z., Gong, Z., Ravikumar, P. & Inouye, D.I.. (2022). Iterative Alignment Flows . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:6409-6444 Available from https://proceedings.mlr.press/v151/zhou22b.html.

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