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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 35 / No. 12: AAAI-21 Technical Tracks 12

Fine-grained Generalization Analysis of Vector-Valued Learning

February 1, 2023

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Authors

Liang Wu

Southwestern University of Finance and Economics


Antoine Ledent

TU Kaiserslautern


Yunwen Lei

University of Birmingham TU Kaiserslautern


Marius Kloft

TU Kaiserslautern


DOI:

10.1609/aaai.v35i12.17238


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.

Topics: AAAI

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HOW TO CITE:

Liang Wu||Antoine Ledent||Yunwen Lei||Marius Kloft Fine-grained Generalization Analysis of Vector-Valued Learning Proceedings of the AAAI Conference on Artificial Intelligence (2021) 10338-10346.

Liang Wu||Antoine Ledent||Yunwen Lei||Marius Kloft Fine-grained Generalization Analysis of Vector-Valued Learning AAAI 2021, 10338-10346.

Liang Wu||Antoine Ledent||Yunwen Lei||Marius Kloft (2021). Fine-grained Generalization Analysis of Vector-Valued Learning. Proceedings of the AAAI Conference on Artificial Intelligence, 10338-10346.

Liang Wu||Antoine Ledent||Yunwen Lei||Marius Kloft. Fine-grained Generalization Analysis of Vector-Valued Learning. Proceedings of the AAAI Conference on Artificial Intelligence 2021 p.10338-10346.

Liang Wu||Antoine Ledent||Yunwen Lei||Marius Kloft. 2021. Fine-grained Generalization Analysis of Vector-Valued Learning. "Proceedings of the AAAI Conference on Artificial Intelligence". 10338-10346.

Liang Wu||Antoine Ledent||Yunwen Lei||Marius Kloft. (2021) "Fine-grained Generalization Analysis of Vector-Valued Learning", Proceedings of the AAAI Conference on Artificial Intelligence, p.10338-10346

Liang Wu||Antoine Ledent||Yunwen Lei||Marius Kloft, "Fine-grained Generalization Analysis of Vector-Valued Learning", AAAI, p.10338-10346, 2021.

Liang Wu||Antoine Ledent||Yunwen Lei||Marius Kloft. "Fine-grained Generalization Analysis of Vector-Valued Learning". Proceedings of the AAAI Conference on Artificial Intelligence, 2021, p.10338-10346.

Liang Wu||Antoine Ledent||Yunwen Lei||Marius Kloft. "Fine-grained Generalization Analysis of Vector-Valued Learning". Proceedings of the AAAI Conference on Artificial Intelligence, (2021): 10338-10346.

Liang Wu||Antoine Ledent||Yunwen Lei||Marius Kloft. Fine-grained Generalization Analysis of Vector-Valued Learning. AAAI[Internet]. 2021[cited 2023]; 10338-10346.


ISSN: 2374-3468


Published by AAAI Press, Palo Alto, California USA
Copyright 2022, Association for the Advancement of
Artificial Intelligence 1900 Embarcadero Road, Suite
101, Palo Alto, California 94303 All Rights Reserved

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