We compute the fat-shattering function and the level fat-shattering function for important classes of affine functions. We observe that the level fat-shattering function and the fat-shattering function are identical for these classes. In addition we observe that the notion that adding the constant term to linear functions increases the dimension by at most 1 is incorrect for fat-shattering and level fat-shattering.
D. Hush and C. Scovel, Fat-shattering of affine functions. Combinatorics Probability and Computing, Vol. 13, No. 3, pp. 353-360, 2004. Los Alamos National Laboratory Technical Report LA-UR-03-0937. [ Abstract | PostScript (160 KB) | PDF (160 KB) ]
