Learning bounded subsets of $L_p$
This work offers a theoretical advancement in statistical learning theory for heavy-tailed data, but it is incremental as it builds on existing boundedness assumptions.
The paper addresses the problem of learning bounded subsets in L_p spaces for p > 4, providing a sharp sample complexity estimate that extends previous results limited to p = ∞, and introduces a learning procedure designed for heavy-tailed problems.
We study learning problems in which the underlying class is a bounded subset of $L_p$ and the target $Y$ belongs to $L_p$. Previously, minimax sample complexity estimates were known under such boundedness assumptions only when $p=\infty$. We present a sharp sample complexity estimate that holds for any $p > 4$. It is based on a learning procedure that is suited for heavy-tailed problems.