Even Sharper Bounds for Transductive Learning and Its Applications

Abstract:We introduce Sharper Transductive Local Complexity (STLC), a localized complexity method for transductive learning under uniform sampling without replacement. The construction starts from a Bernstein-type concentration inequality for the supremum of the test--train empirical process. Its proof uses the modified log-Sobolev inequality for the swap walk and a two-parameter entropy closure. A peeling argument with a surrogate localization functional then gives excess-risk bounds with the same fixed-point and confidence terms as the classical inductive local Rademacher-complexity bounds, without the additional logarithmic confidence factor in earlier transductive results. For realizable learning over a binary class of VC dimension $\dVC$, with training size $m$, test size $u$, and $u\ge m\ge\dVC$, STLC yields $\cO\{\dVC\log(me/\dVC)/m\}$. This matches the standard inductive rate and, when $m\ge9$, is within a logarithmic factor of the transductive minimax lower bound of order $\dVC/m$. For transductive kernel learning, STLC gives a spectrum-adaptive excess-risk bound without the multiplicative imbalance factors appearing in the earlier local-complexity bound.

Machine Learning (cs.LG); Information Theory (cs.IT); Statistics Theory (math.ST)

arXiv:2609.28459 [cs.LG]

(or arXiv:2609.28459v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.28459 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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