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SUMMARY:Uncoupled isotonic regression via minimum Wasserstein deconvolutio
 n - Philippe Rigollet (Massachusetts Institute of Technology)
DTSTART:20180625T104500Z
DTEND:20180625T113000Z
UID:TALK107362@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Isotonic regression is a standard problem in shape constrained
  estimation where the goal is to estimate an unknown nondecreasing regress
 ion 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 statistic
 ally and computationally\, much less is known about its uncoupled counterp
 art where one is given uncoupled $\\{x_1\, \\ldots\, x_n\\}$ and $\\{y_1\,
  \\ldots\, y_n\\}$. In this work\, we leverage tools from optimal transpor
 t theory to derive minimax rates under weak moments conditions on $y_i$ to
 gether with an efficient algorithm. Both upper and lower bounds are articu
 lated around moment-matching arguments that are also pertinent to learning
  mixtures of distributions and deconvolution. [Joint work with Jonathan We
 ed (MIT)]
LOCATION:Seminar Room 1\, Newton Institute
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