Optimal Rates of Statistical Seriation

@article{Flammarion2016OptimalRO,
  title={Optimal Rates of Statistical Seriation},
  author={Nicolas Flammarion and Cheng Mao and P. Rigollet},
  journal={arXiv: Statistics Theory},
  year={2016}
}
Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of interest is observed with noise and study the corresponding minimax rate of estimation of the matrices. Specifically, when the columns are either unimodal or monotone, we show that the least squares estimator is optimal up to logarithmic factors and adapts to… Expand
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