In:
Proceedings of the AAAI Conference on Artificial Intelligence, Association for the Advancement of Artificial Intelligence (AAAI), Vol. 35, No. 12 ( 2021-05-18), p. 10338-10346
Abstract:
Many fundamental machine learning tasks can be formulated as a problem of learning with vector-valued functions, where we learn multiple scalar-valued functions together. Although there is some generalization analysis on different specific algorithms under the empirical risk minimization principle, a unifying analysis of vector-valued learning under a regularization framework is still lacking. In this paper, we initiate the generalization analysis of regularized vector-valued learning algorithms by presenting bounds with a mild dependency on the output dimension and a fast rate on the sample size. Our discussions relax the existing assumptions on the restrictive constraint of hypothesis spaces, smoothness of loss functions and low-noise condition. To understand the interaction between optimization and learning, we further use our results to derive the first generalization bounds for stochastic gradient descent with vector-valued functions. We apply our general results to multi-class classification and multi-label classification, which yield the first bounds with a logarithmic dependency on the output dimension for extreme multi-label classification with the Frobenius regularization. As a byproduct, we derive a Rademacher complexity bound for loss function classes defined in terms of a general strongly convex function.
Type of Medium:
Online Resource
ISSN:
2374-3468
,
2159-5399
DOI:
10.1609/aaai.v35i12.17238
Language:
Unknown
Publisher:
Association for the Advancement of Artificial Intelligence (AAAI)
Publication Date:
2021
