Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance

@article{Boissard2011SimpleBF,
  title={Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance},
  author={Emmanuel Boissard},
  journal={Electronic Journal of Probability},
  year={2011},
  volume={16},
  pages={2296-2333}
}
  • Emmanuel Boissard
  • Published 2011
  • Mathematics
  • Electronic Journal of Probability
  • We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the reference measure satisfies a transport-entropy inequality. We extend some results of F. Bolley, A. Guillin and C. Villani with simple proofs. Our methods are based on concentration inequalities and extend to the general setting of measures on a Polish space. Deviation bounds for the occupation measure of a contracting… CONTINUE READING
    50 Citations
    On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
    • 54
    • PDF
    Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
    • 165
    • PDF
    Wasserstein Convergence Rate for Empirical Measures of Markov Chains
    • PDF
    Learning Probability Measures with respect to Optimal Transport Metrics
    • 57
    • PDF
    A non-exponential extension of Sanov’s theorem via convex duality
    • 6
    • PDF
    Deviation inequalities for separately Lipschitz functionals of iterated random functions
    • 16
    • Highly Influenced
    • PDF

    References

    SHOWING 1-10 OF 40 REFERENCES
    On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
    • 54
    • PDF
    Sanov’s theorem in the Wasserstein distance: A necessary and sufficient condition
    • 29
    • Highly Influential
    • PDF
    Ricci curvature of Markov chains on metric spaces
    • 443
    • PDF
    CURVATURE, CONCENTRATION AND ERROR ESTIMATES FOR MARKOV CHAIN MONTE CARLO
    • 115
    • PDF
    Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces
    • 185
    • Highly Influential
    • PDF
    Functional Quantization and Small Ball Probabilities for Gaussian Processes
    • S. Graf, H. Luschgy
    • Mathematics, Computer Science
    • Universität Trier, Mathematik/Informatik, Forschungsbericht
    • 2002
    • 37
    Bounding $\bar{d}$-distance by informational divergence: a method to prove measure concentration
    • 221
    • Highly Influential