发表机构
Arizona State University（亚利桑那州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出更紧的转导局部复杂度（STLC）方法，通过 Bernstein 型不等式和剥离论证获得与归纳 Rademacher 复杂度相同的超额风险界，在可实现学习和核学习中匹配或改进现有转导结果。
AI 中文摘要
我们引入了更紧的转导局部复杂度（STLC），这是一种在无放回均匀采样下用于转导学习的局部化复杂度方法。该构造始于对测试-训练经验过程上确界的 Bernstein 型浓度不等式。其证明使用了交换游走的修正对数 Sobolev 不等式和双参数熵闭包。结合带有替代局部化泛函的剥离论证，我们得到了超额风险界，其不动点和置信项与经典归纳局部 Rademacher 复杂度界相同，且没有早期转导结果中额外的对数置信因子。对于 VC 维为 $\dVC$ 的二元类别上的可实现学习，当训练规模为 $m$、测试规模为 $u$ 且 $u\ge m\ge\dVC$ 时，STLC 给出 $\cO\{\dVC\log(me/\dVC)/m\}$。这与标准归纳速率匹配，并且当 $m\ge9$ 时，与阶为 $\dVC/m$ 的转导极小极大下界仅差一个对数因子。对于转导核学习，STLC 给出了谱自适应的超额风险界，而无需早期局部复杂度界中出现的乘法不平衡因子。
英文摘要
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.
CommentsAccepted by NeurIPS 2026
