## Precise Error Analysis of Regularized $M$ -Estimators in High Dimensions

- Christos Thrampoulidis, Ehsan Abbasi, Babak Hassibi
- IEEE Transactions on Information Theory
- 2018

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@article{Oymak2015UniversalityLF, title={Universality laws for randomized dimension reduction, with applications}, author={Samet Oymak and Joel A. Tropp}, journal={CoRR}, year={2015}, volume={abs/1511.09433} }

- Published 2015 in ArXiv

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. This dimension reduction procedure succeeds when it preserves certain geometric features of the set. The question is how large the embedding dimension must be to ensure that randomized dimension reduction succeeds with high probability. This paper… CONTINUE READING

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