Sharp oracle bounds for monotone and convex regression through aggregation

@article{Bellec2015SharpOB,
  title={Sharp oracle bounds for monotone and convex regression through aggregation},
  author={Pierre C. Bellec and Alexandre B. Tsybakov},
  journal={Journal of Machine Learning Research},
  year={2015},
  volume={16},
  pages={1879-1892}
}
We derive oracle inequalities for the problems of isotonic and convex regression using the combination of Q-aggregation procedure and sparsity pattern aggregation. This improves upon the previous results including the oracle inequalities for the constrained least squares estimator. One of the improvements is that our oracle inequalities are sharp, i.e., with leading constant 1. It allows us to obtain bounds for the minimax regret thus accounting for model misspecification, which was not… CONTINUE READING

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