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Uncoupled isotonic regression via minimum Wasserstein deconvolution

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STSW04 - Future challenges in statistical scalability

Isotonic regression is a standard problem in shape constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i,y_i)$ where $\E[y_i]=f(x_i), i=1, \ldots n$. While this problem is well understood both statistically and computationally, much less is known about its uncoupled counterpart where one is given uncoupled $\{x_1, \ldots, x_n\}$ and $\{y_1, \ldots, y_n\}$. In this work, we leverage tools from optimal transport theory to derive minimax rates under weak moments conditions on $y_i$ together with an efficient algorithm. Both upper and lower bounds are articulated around moment-matching arguments that are also pertinent to learning mixtures of distributions and deconvolution. [Joint work with Jonathan Weed (MIT)]

This talk is part of the Isaac Newton Institute Seminar Series series.

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