Efficient Robust Proper Learning of Log-concave Distributions

@article{Diakonikolas2016EfficientRP,
  title={Efficient Robust Proper Learning of Log-concave Distributions},
  author={Ilias Diakonikolas and Daniel M. Kane and Alistair Stewart},
  journal={CoRR},
  year={2016},
  volume={abs/1606.03077}
}
We study the robust proper learning of univariate log-concave distributions (over continuous and discrete domains). Given a set of samples drawn from an unknown target distribution, we want to compute a log-concave hypothesis distribution that is as close as possible to the target, in total variation distance. In this work, we give the first computationally efficient algorithm for this learning problem. Our algorithm achieves the information-theoretically optimal sample size (up to a constant… CONTINUE READING
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