Given a matrix the seriation problem consists in permuting its rows in such\nway that all its columns have the same shape, for example, they are monotone\nincreasing. We propose a statistical approach to this problem where the matrix\nof interest is observed with noise and study the corresponding minimax rate of\nestimation of the matrices. Specifically, when the columns are either unimodal\nor monotone, we show that the least squares estimator is optimal up to\nlogarithmic factors and adapts to matrices with a certain natural structure.\nFinally, we propose a computationally efficient estimator in the monotonic case\nand study its performance both theoretically and experimentally. Our work is at\nthe intersection of shape constrained estimation and recent work that involves\npermutation learning, such as graph denoising and ranking.\n