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Agnostic Sample Compression for Linear Regression. (arXiv:1810.01864v1 [cs.LG])
来源于:arXiv
We obtain the first positive results for bounded sample compression in the
agnostic regression setting. We show that for p in {1,infinity}, agnostic
linear regression with $\ell_p$ loss admits a bounded sample compression
scheme. Specifically, we exhibit efficient sample compression schemes for
agnostic linear regression in $R^d$ of size $d+1$ under the $\ell_1$ loss and
size $d+2$ under the $\ell_\infty$ loss. We further show that for every other
$\ell_p$ loss (1 < p < infinity), there does not exist an agnostic compression
scheme of bounded size. This refines and generalizes a negative result of
David, Moran, and Yehudayoff (2016) for the $\ell_2$ loss. We close by posing a
general open question: for agnostic regression with $\ell_1$ loss, does every
function class admit a compression scheme of size equal to its
pseudo-dimension? This question generalizes Warmuth's classic sample
compression conjecture for realizable-case classification (Warmuth, 2003). 查看全文>>