Local Rademacher Complexity for Multi-label Learning
This work addresses multi-label learning, a domain-specific problem, with incremental improvements in algorithm design and theoretical guarantees.
The paper tackles the problem of multi-label learning by proposing a new algorithm that minimizes the tail sum of singular values instead of using trace norm regularization, resulting in a sharper generalization error bound and faster convergence rate. Empirical studies on real-world datasets validate these improvements.
We analyze the local Rademacher complexity of empirical risk minimization (ERM)-based multi-label learning algorithms, and in doing so propose a new algorithm for multi-label learning. Rather than using the trace norm to regularize the multi-label predictor, we instead minimize the tail sum of the singular values of the predictor in multi-label learning. Benefiting from the use of the local Rademacher complexity, our algorithm, therefore, has a sharper generalization error bound and a faster convergence rate. Compared to methods that minimize over all singular values, concentrating on the tail singular values results in better recovery of the low-rank structure of the multi-label predictor, which plays an import role in exploiting label correlations. We propose a new conditional singular value thresholding algorithm to solve the resulting objective function. Empirical studies on real-world datasets validate our theoretical results and demonstrate the effectiveness of the proposed algorithm.