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On Coresets for Logistic Regression
Alexander Munteanu · Chris Schwiegelshohn · Christian Sohler · David Woodruff

Wed Dec 05 02:00 PM -- 04:00 PM (PST) @ Room 210 #77
Coresets are one of the central methods to facilitate the analysis of large data. We continue a recent line of research applying the theory of coresets to logistic regression. First, we show the negative result that no strongly sublinear sized coresets exist for logistic regression. To deal with intractable worst-case instances we introduce a complexity measure $\mu(X)$, which quantifies the hardness of compressing a data set for logistic regression. $\mu(X)$ has an intuitive statistical interpretation that may be of independent interest. For data sets with bounded $\mu(X)$-complexity, we show that a novel sensitivity sampling scheme produces the first provably sublinear $(1\pm\eps)$-coreset. We illustrate the performance of our method by comparing to uniform sampling as well as to state of the art methods in the area. The experiments are conducted on real world benchmark data for logistic regression.

Author Information

Alexander Munteanu (TU Dortmund)
Chris Schwiegelshohn (Sapienza, University of Rome)
Christian Sohler (TU Dortmund)
David Woodruff (Carnegie Mellon University)

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