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arXiv Machine Learning By J\'er\'emie Bigot, Cl\'ement Bonet

Lifting PCA in the Wasserstein Space

Read the original on arXiv Machine Learning →

The paper introduces Lifted PCA, a canonical extension of Euclidean PCA to the Wasserstein space of probability measures. By lifting variational formulations on the Stiefel and Grassmann manifolds, the authors derive equivalent minimization problems over probability measures that correspond to Wasserstein barycenters with generalized costs. The work establishes dual formulations, optimality conditions, connections to multimarginal optimal transport, statistical consistency, and computational algorithms, and demonstrates practical performance on distributional datasets.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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