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Award ID contains: 1712596

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  1. ; (, Information and Inference: A Journal of the IMA)
    Abstract Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown non-decreasing regression function $$f$$ from independent pairs $$(x_i, y_i)$$ where $${\mathbb{E}}[y_i]=f(x_i), i=1, \ldots n$$. While this problem is well understood both statistically and computationally, much less is known about its uncoupled counterpart, where one is given only the unordered sets $$\{x_1, \ldots , x_n\}$$ 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 $$y_i$$ and to give an efficient algorithm achieving optimal rates. Both upper and lower bounds employ moment-matching arguments that are also pertinent to learning mixtures of distributions and deconvolution. 
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  2. ; (, Foundations of Computational Mathematics)
    Full Text Available 
  3. ; (, The Annals of Statistics)
    Full Text Available 
  4. ; ; (, Proceedings of Machine Learning Research)
    Banerjee, Arindam; Fukumizu, Kenji (Ed.)
    Accepted Manuscript Full Text Available
  5. (, Proceedings of Thirty Fourth Conference on Learning Theory)
    Accepted Manuscript Full Text Available
  6. ; ; (, Proceedings of Machine Learning Research)
    null (Ed.)
    Accepted Manuscript Full Text Available
  7. (, Proceedings of The 24th International Conference on Artificial Intelligence and Statistics)
    Accepted Manuscript Full Text Available
  8. ; ; ; ; ; (, Proceedings of Machine Learning Research)
    null (Ed.)
    Accepted Manuscript Full Text Available
  9. (, Proceedings of The 24th International Conference on Artificial Intelligence and Statistics)
    Accepted Manuscript Full Text Available
  10. ; ; ; (, Bernoulli)
    Full Text Available