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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence

Asymptotic Risk of Bézier Simplex Fitting

February 1, 2023

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Authors

Akinori Tanaka

RIKEN AIP


Akiyoshi Sannai

RIKEN AIP


Ken Kobayashi

Fujitsu Laboratories


Naoki Hamada

Fujitsu Laboratories


DOI:

10.1609/aaai.v34i03.5622


Abstract:

The B'ezier simplex fitting is a novel data modeling technique which utilizes geometric structures of data to approximate the Pareto set of multi-objective optimization problems. There are two fitting methods based on different sampling strategies. The inductive skeleton fitting employs a stratified subsampling from skeletons of a simplex, whereas the all-at-once fitting uses a non-stratified sampling which treats a simplex as a single object. In this paper, we analyze the asymptotic risks of those B'ezier simplex fitting methods and derive the optimal subsample ratio for the inductive skeleton fitting. It is shown that the inductive skeleton fitting with the optimal ratio has a smaller risk when the degree of a B'ezier simplex is less than three. Those results are verified numerically under small to moderate sample sizes. In addition, we provide two complementary applications of our theory: a generalized location problem and a multi-objective hyper-parameter tuning of the group lasso. The former can be represented by a B'ezier simplex of degree two where the inductive skeleton fitting outperforms. The latter can be represented by a B'ezier simplex of degree three where the all-at-once fitting gets an advantage.

Topics: AAAI

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HOW TO CITE:

Akinori Tanaka||Akiyoshi Sannai||Ken Kobayashi||Naoki Hamada Asymptotic Risk of Bézier Simplex Fitting Proceedings of the AAAI Conference on Artificial Intelligence (2020) 2416-2424.

Akinori Tanaka||Akiyoshi Sannai||Ken Kobayashi||Naoki Hamada Asymptotic Risk of Bézier Simplex Fitting AAAI 2020, 2416-2424.

Akinori Tanaka||Akiyoshi Sannai||Ken Kobayashi||Naoki Hamada (2020). Asymptotic Risk of Bézier Simplex Fitting. Proceedings of the AAAI Conference on Artificial Intelligence, 2416-2424.

Akinori Tanaka||Akiyoshi Sannai||Ken Kobayashi||Naoki Hamada. Asymptotic Risk of Bézier Simplex Fitting. Proceedings of the AAAI Conference on Artificial Intelligence 2020 p.2416-2424.

Akinori Tanaka||Akiyoshi Sannai||Ken Kobayashi||Naoki Hamada. 2020. Asymptotic Risk of Bézier Simplex Fitting. "Proceedings of the AAAI Conference on Artificial Intelligence". 2416-2424.

Akinori Tanaka||Akiyoshi Sannai||Ken Kobayashi||Naoki Hamada. (2020) "Asymptotic Risk of Bézier Simplex Fitting", Proceedings of the AAAI Conference on Artificial Intelligence, p.2416-2424

Akinori Tanaka||Akiyoshi Sannai||Ken Kobayashi||Naoki Hamada, "Asymptotic Risk of Bézier Simplex Fitting", AAAI, p.2416-2424, 2020.

Akinori Tanaka||Akiyoshi Sannai||Ken Kobayashi||Naoki Hamada. "Asymptotic Risk of Bézier Simplex Fitting". Proceedings of the AAAI Conference on Artificial Intelligence, 2020, p.2416-2424.

Akinori Tanaka||Akiyoshi Sannai||Ken Kobayashi||Naoki Hamada. "Asymptotic Risk of Bézier Simplex Fitting". Proceedings of the AAAI Conference on Artificial Intelligence, (2020): 2416-2424.

Akinori Tanaka||Akiyoshi Sannai||Ken Kobayashi||Naoki Hamada. Asymptotic Risk of Bézier Simplex Fitting. AAAI[Internet]. 2020[cited 2023]; 2416-2424.


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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