Principal Observable Analysis defines stable mean and covariance statistics for metric measure spaces using 1-Lipschitz functions and proves Wasserstein and Kantorovich-Sturm stability bounds for them.
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Observable Covariance and Principal Observable Analysis for Data on Metric Spaces
Principal Observable Analysis defines stable mean and covariance statistics for metric measure spaces using 1-Lipschitz functions and proves Wasserstein and Kantorovich-Sturm stability bounds for them.