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We develop two methods for the following fundamental statistical task: given an $\epsilon$-corrupted set of $n$ samples from a $d$-dimensional sub-Gaussian distribution, return an approximate top eigenvector of the covariance matrix.
Robust estimation of a location parameter
Peter J Huber · 1964
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Mathematics and the picturing of data
John W Tukey · 1975
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Interior-Point Polynomial Algorithms in Convex Programming
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An elementary proof of a theorem of johnson and lindenstrauss
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Randomized PCA algorithms with regret bounds that are logarithmic in the dimension
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Using optimization to obtain a width-independent, parallel, simpler, and faster positive SDP solver
Zeyuan Allen Zhu, Yin Tat Lee, and Lorenzo Orecchia · 2016
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Agnostic estimation of mean and covariance
Kevin A Lai, Anup B Rao, and Santosh Vempala · 2016
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Approximating the solution to mixed packing and covering lps in parallel o~(epsilonˆ{-3}) time
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Robust moment estimation and improved clustering via sum of squares
Pravesh K Kothari, Jacob Steinhardt, and David Steurer · 2018
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Principled approaches to robust machine learning and beyond
Jerry Zheng Li · 2018
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Robust Learning: Information Theory and Algorithms
Jacob Steinhardt · 2018
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High-dimensional robust mean estimation in nearly-linear time
Yu Cheng, Ilias Diakonikolas, and Rong Ge · 2019
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Faster algorithms for high-dimensional robust covariance estimation
Yu Cheng, Ilias Diakonikolas, Rong Ge, and David Woodruff · 2019
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A rank-1 sketch for matrix multiplicative weights
Yair Carmon, John C. Duchi, Aaron Sidford, and Kevin Tian · 2019
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Ilias Diakonikolas, Gautam Kamath, Daniel M Kane, Jerry Li, Ankur Moitra, and Alistair Stewart · 2017
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Yu Cheng and Rong Ge · 2018
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Jelena Diakonikolas, Maryam Fazel, and Lorenzo Orecchia · 2018
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Ilias Diakonikolas, Gautam Kamath, Daniel M Kane, Jerry Li, Ankur Moitra, and Alistair Stewart · 2018
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Yeshwanth Cherapanamjeri, Sidhanth Mohanty, and Morris Yau · 2020
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