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Efficient Sampling for Learning Sparse Additive Models in High Dimensions
Hemant Tyagi · Bernd Gärtner · Andreas Krause

Wed Dec 10 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D
We consider the problem of learning sparse additive models, i.e., functions of the form: $f(\vecx) = \sum_{l \in S} \phi_{l}(x_l)$, $\vecx \in \matR^d$ from point queries of $f$. Here $S$ is an unknown subset of coordinate variables with $\abs{S} = k \ll d$. Assuming $\phi_l$'s to be smooth, we propose a set of points at which to sample $f$ and an efficient randomized algorithm that recovers a \textit{uniform approximation} to each unknown $\phi_l$. We provide a rigorous theoretical analysis of our scheme along with sample complexity bounds. Our algorithm utilizes recent results from compressive sensing theory along with a novel convex quadratic program for recovering robust uniform approximations to univariate functions, from point queries corrupted with arbitrary bounded noise. Lastly we theoretically analyze the impact of noise -- either arbitrary but bounded, or stochastic -- on the performance of our algorithm.

Author Information

Hemant Tyagi (ETH Zurich)
Bernd Gärtner (ETH Zurich)
Andreas Krause (ETH Zurich)

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