Even Sharper Bounds for Transductive Learning and Its Applications

TL;DR

The paper introduces STLC, a new method for analyzing transductive learning that achieves tighter excess-risk bounds by leveraging a Bernstein-type inequality and a modified log-Sobolev inequality for the swap walk. It matches inductive learning rates for realizable binary classification and removes logarithmic confidence factors present in prior transductive bounds. The approach adapts to kernel learning spectra without imbalance penalties.

Why It Matters

STLC provides sharper theoretical guarantees for transductive learning, enabling more accurate risk estimation in scenarios with limited labeled data. This improves performance in practical applications like semi-supervised learning and active learning where test and training sets are fixed and sampled without replacement.

Key Findings

• For realizable binary classification with VC dimension dVC, STLC delivers a rate of O(dVC log(me/dVC)/m), matching the inductive rate and approaching the transductive minimax lower bound.
• In transductive kernel learning, STLC produces spectrum-adaptive bounds that avoid multiplicative imbalance terms seen in earlier local-complexity approaches.