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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Uncoupled isotonic regression via minimum Wasserstein deconvolution

## Uncoupled isotonic regression via minimum Wasserstein deconvolutionAdd to your list(s) Download to your calendar using vCal - Philippe Rigollet (Massachusetts Institute of Technology)
- Monday 25 June 2018, 11:45-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact INI IT. 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. ## This talk is included in these lists:- All CMS events
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