Robust Training in High Dimensions via Block Coordinate Geometric Median Descent
Geometric median (\textsc{Gm}) is a classical method in statistics for achieving a robust estimation of the uncorrupted data; under gross corruption, it achieves the optimal breakdown point of 0.5. However, its computational complexity makes it infeasible for robustifying stochastic gradient descent...
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| creator | Acharya, Anish Hashemi, Abolfazl Jain, Prateek Sanghavi, Sujay Dhillon, Inderjit S Topcu, Ufuk |
| description | Geometric median (\textsc{Gm}) is a classical method in statistics for
achieving a robust estimation of the uncorrupted data; under gross corruption,
it achieves the optimal breakdown point of 0.5. However, its computational
complexity makes it infeasible for robustifying stochastic gradient descent
(SGD) for high-dimensional optimization problems. In this paper, we show that
by applying \textsc{Gm} to only a judiciously chosen block of coordinates at a
time and using a memory mechanism, one can retain the breakdown point of 0.5
for smooth non-convex problems, with non-asymptotic convergence rates
comparable to the SGD with \textsc{Gm}. |
| doi_str_mv | 10.48550/arxiv.2106.08882 |
| format | Article |
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achieving a robust estimation of the uncorrupted data; under gross corruption,
it achieves the optimal breakdown point of 0.5. However, its computational
complexity makes it infeasible for robustifying stochastic gradient descent
(SGD) for high-dimensional optimization problems. In this paper, we show that
by applying \textsc{Gm} to only a judiciously chosen block of coordinates at a
time and using a memory mechanism, one can retain the breakdown point of 0.5
for smooth non-convex problems, with non-asymptotic convergence rates
comparable to the SGD with \textsc{Gm}.</description><identifier>DOI: 10.48550/arxiv.2106.08882</identifier><language>eng</language><subject>Computer Science - Distributed, Parallel, and Cluster Computing ; Computer Science - Learning ; Mathematics - Optimization and Control ; Statistics - Machine Learning</subject><creationdate>2021-06</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2106.08882$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2106.08882$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Acharya, Anish</creatorcontrib><creatorcontrib>Hashemi, Abolfazl</creatorcontrib><creatorcontrib>Jain, Prateek</creatorcontrib><creatorcontrib>Sanghavi, Sujay</creatorcontrib><creatorcontrib>Dhillon, Inderjit S</creatorcontrib><creatorcontrib>Topcu, Ufuk</creatorcontrib><title>Robust Training in High Dimensions via Block Coordinate Geometric Median Descent</title><description>Geometric median (\textsc{Gm}) is a classical method in statistics for
achieving a robust estimation of the uncorrupted data; under gross corruption,
it achieves the optimal breakdown point of 0.5. However, its computational
complexity makes it infeasible for robustifying stochastic gradient descent
(SGD) for high-dimensional optimization problems. In this paper, we show that
by applying \textsc{Gm} to only a judiciously chosen block of coordinates at a
time and using a memory mechanism, one can retain the breakdown point of 0.5
for smooth non-convex problems, with non-asymptotic convergence rates
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achieving a robust estimation of the uncorrupted data; under gross corruption,
it achieves the optimal breakdown point of 0.5. However, its computational
complexity makes it infeasible for robustifying stochastic gradient descent
(SGD) for high-dimensional optimization problems. In this paper, we show that
by applying \textsc{Gm} to only a judiciously chosen block of coordinates at a
time and using a memory mechanism, one can retain the breakdown point of 0.5
for smooth non-convex problems, with non-asymptotic convergence rates
comparable to the SGD with \textsc{Gm}.</abstract><doi>10.48550/arxiv.2106.08882</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Distributed, Parallel, and Cluster Computing Computer Science - Learning Mathematics - Optimization and Control Statistics - Machine Learning |
| title | Robust Training in High Dimensions via Block Coordinate Geometric Median Descent |
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