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- W351642134 abstract "We study the performance of Empirical Risk Minimization in both noisy and noiseless phase retrieval problems, indexed by subsets of $mathbb{R}^n$ and relative to subgaussian sampling; that is, when the given data is $y_i=left a_i,x_0right^2+w_i$ for a subgaussian random vector $a$, independent noise $w$ and a fixed but unknown $x_0$ that belongs to a given subset of $mathbb{R}^n$. We show that ERM produces $hat{x}$ whose Euclidean distance to either $x_0$ or $-x_0$ depends on the gaussian mean-width of the indexing set and on the signal-to-noise ratio of the problem. The bound coincides with the one for linear regression when $|x_0|_2$ is of the order of a constant. In addition, we obtain a minimax lower bound for the problem and identify sets for which ERM is a minimax procedure. As examples, we study the class of $d$-sparse vectors in $mathbb{R}^n$ and the unit ball in $ell_1^n$." @default.
- W351642134 created "2016-06-24" @default.
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- W351642134 date "2015-01-01" @default.
- W351642134 modified "2023-09-27" @default.
- W351642134 title "Minimax rate of convergence and the performance of empirical risk minimization in phase recovery" @default.
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- W351642134 doi "https://doi.org/10.1214/ejp.v20-3525" @default.
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