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Learning Probability Measures with respect to Optimal Transport Metrics
Guillermo D Canas · Lorenzo Rosasco

Tue Dec 04 07:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor

We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal quantization, and learning theory, we derive new probabilistic bounds for the performance of a classic algorithm in unsupervised learning (k-means), when used to produce a probability measure derived from the data. In the course of the analysis, we arrive at new lower bounds, as well as probabilistic bounds on the convergence rate of the empirical law of large numbers, which, unlike existing bounds, are applicable to a wide class of measures.

Author Information

Guillermo D Canas (Massachusetts Institute of Technology)
Lorenzo Rosasco (University of Genova- MIT - IIT)

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