Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, October 28, 2014, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Hemant Tyagi

Efficient sampling for learning SPAMs in high dimensions

We consider the problem of learning Sparse Additive Models (SPAMs), i.e. functions of the form: $f(x_1,...,x_d) = \sum_{l \in S} \phi_{l}(x_l)$; $S \subset {1,\dots,d}$, from point queries of $f$. Here $\phi_l$ and $S$ are unknown and $|S| = k \ll d$. Such models have been studied extensively in statistics, in the context of non-parametric regression. However in that setting, one typically does not have control over the points, at which the value of $f$ is observed.

Assuming $\phi_l$'s to be smooth, we propose a set of points at which to query $f$ and an efficient randomized algorithm that recovers: (i) $S$ exactly and, (ii) a uniform approximation to each $\phi_l$; for all $l \in S$. In contrast, the existing results in statistics provide error bounds for recovering $f$ in the weaker mean square sense.

If the point queries are noiseless, we show that $O(k \log d)$ queries suffice while if the point queries are corrupted with (i.i.d) Gaussian noise, we show that $O(k^3 (\log d)^2)$ queries suffice.

Joint work with Bernd Gärtner and Andreas Krause.

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

Previous talks by year:   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