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- W2509930680 abstract "We study high-dimensional signal recovery from non-linear measurements with design vectors having elliptically symmetric distribution. Special attention is devoted to the situation when the unknown signal belongs to a set of low statistical complexity, while both the measurements and the design vectors are heavy-tailed. We propose and analyze a new estimator that adapts to the structure of the problem, while being robust both to the possible model misspecification characterized by arbitrary non-linearity of the measurements as well as to data corruption modeled by the heavy-tailed distributions. Moreover, this estimator has low computational complexity. Our results are expressed in the form of exponential concentration inequalities for the error of the proposed estimator. On the technical side, our proofs rely on the generic chaining methods, and illustrate the power of this approach for statistical applications. Theory is supported by numerical experiments demonstrating that our estimator outperforms existing alternatives when data is heavy-tailed." @default.
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- W2509930680 date "2016-09-04" @default.
- W2509930680 modified "2023-10-11" @default.
- W2509930680 title "Structured signal recovery from non-linear and heavy-tailed measurements" @default.
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- W2509930680 doi "https://doi.org/10.48550/arxiv.1609.01025" @default.
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