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Activity Number:
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245
- SLDS CSpeed 4
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Type:
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Contributed
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Date/Time:
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Wednesday, August 11, 2021 : 10:00 AM to 11:50 AM
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Sponsor:
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Section on Statistical Learning and Data Science
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Abstract #319026
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Title:
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Statistical Convergence Rates for Knothe-Rosenblatt Coupling Estimators
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Author(s):
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Nicholas Irons* and Zaid Harchaoui and Soumik Pal and Meyer Scetbon
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Companies:
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University of Washington and University of Washington and University of Washington and CREST, ENSAE
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Keywords:
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optimal transport;
empirical processes;
density estimation;
generative models;
coupling;
convergence rate
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Abstract:
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Let $\mu$ and $\nu$ be probability measures on $\mathbb{R}^d$. The Knothe-Rosenblatt rearrangement $T$ is the unique transport map between $\mu$ and $\nu$ that satisfies a certain monotonicity property. There has been a renewed interest in the Knothe-Rosenblatt rearrangement in relation to optimal transport and statistical learning. We establish convergence rates for the statistical estimator of the Knothe-Rosenblatt of Spantini et al. (2018), which minimizes the sample average approximation of the Kullback-Leibler divergence between $S_\#\mu$ and $\nu$, where $S$ lies in the cone of monotone triangular maps on $\mathbb{R}^d$. The proof techniques involve tools from empirical process and optimal transport.
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Authors who are presenting talks have a * after their name.
