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Kevin O'Connor

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JMLR Journal 2022 Journal Article

Optimal Transport for Stationary Markov Chains via Policy Iteration

  • Kevin O'Connor
  • Kevin McGoff
  • Andrew B. Nobel

We study the optimal transport problem for pairs of stationary finite-state Markov chains, with an emphasis on the computation of optimal transition couplings. Transition couplings are a constrained family of transport plans that capture the dynamics of Markov chains. Solutions of the optimal transition coupling (OTC) problem correspond to alignments of the two chains that minimize long-term average cost. We establish a connection between the OTC problem and Markov decision processes, and show that solutions of the OTC problem can be obtained via an adaptation of policy iteration. For settings with large state spaces, we develop a fast approximate algorithm based on an entropy-regularized version of the OTC problem, and provide bounds on its per-iteration complexity. We establish a stability result for both the regularized and unregularized algorithms, from which a statistical consistency result follows as a corollary. We validate our theoretical results empirically through a simulation study, demonstrating that the approximate algorithm exhibits faster overall runtime with low error. Finally, we extend the setting and application of our methods to hidden Markov models, and illustrate the potential use of the proposed algorithms in practice with an application to computer-generated music. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2022. ( edit, beta )

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AAAI Conference 2020 Conference Paper

Exchangeable Generative Models with Flow Scans

  • Christopher Bender
  • Kevin O'Connor
  • Yang Li
  • Juan Garcia
  • Junier Oliva
  • Manzil Zaheer

In this work, we develop a new approach to generative density estimation for exchangeable, non-i. i. d. data. The proposed framework, FlowScan, combines invertible flow transformations with a sorted scan to flexibly model the data while preserving exchangeability. Unlike most existing methods, FlowScan exploits the intradependencies within sets to learn both global and local structure. FlowScan represents the first approach that is able to apply sequential methods to exchangeable density estimation without resorting to averaging over all possible permutations. We achieve new state-of-the-art performance on point cloud and image set modeling.

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v2026.09.13