Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, January 20, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Kenneth Clarkson (IBM Research)

A Unified Approach to Robust Regression

We give algorithms for *M-estimators*, that minimize $||Ax - b||_G$ with respect to $x$, where $A$ is an $n$ by $d$ matrix, $b$ is an $n$-vector, and the "norm" $||y||_G$ for $n$-vector $y$ is specified by a cost function $G : R^n \to R^+$, with $||y||_G == \sum_i G(y_i)$.

M-estimators generalize $L_p$ regression, for which $G(x) = |x|^p$. We use the *M-sketch*, a randomized construction of a sketching matrix $S$, so that $||SAx||_G$ is a useful approximation to $||Ax||_G$ for $d$-vector $x$. This yields an algorithm for M-estimators requiring $O(nnz(A)+ poly(d))$ time to find a solution whose residual error is within a constant factor of optimal.

We also show that one of the most popular M-estimators, using the Huber measure, can be computed up to relative error $\epsilon$ in $O(nnz(A) \log n + poly(d/\epsilon))$ time.

Joint work with David Woodruff.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2025  2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login