Agnostic Sample Compression Schemes for Regression

We obtain the first positive results for bounded sample compression in the agnostic regression setting with the $\ell_p$ loss, where $p\in [1,\infty]$. We construct a generic approximate sample compression scheme for real-valued function classes exhibiting exponential size in the fat-shattering dimension but independent of the sample size. Notably, for linear regression, an approximate compression of size linear in the dimension is constructed. Moreover, for $\ell_1$ and $\ell_\infty$ losses, we can even exhibit an efficient exact sample compression scheme of size …

compression construct cs.it cs.lg function independent linear linear regression loss math.it math.st positive regression sample stat.ml stat.th