Linear Algebraic proofs of VC-Dimension based inequalities
We apply linear algebra(polynomial) techniques to various VC-Dimension based inequalities. We explore connections between the sample compression and this technique for so called maximum classes and prove that maximum classes are connected subgraphs of a Boolean cube.We provide a fast (linear in the cardinality of the class for the fixed VC-dimension) interpolational algorithm for maximum classes.A new method to bound a pseudo-dimension for a class of cell-wise constant functions is proposed.
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