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| Presentation | 2016-11-17 14:00 Minimax optimal estimator for additively decomposable scalar functionals of discrete distributions Kazuto Fukuchi, Jun Sakuma (Univ. of Tsukuba)  IBISML2016-82 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | We deal with a problem of estimating additively decomposable scalar functionals from a set of $n$ iid samples drawn from a discrete distribution $P=(p_1,...,p_k)$ of $k$ alphabets. The additively decomposable scalar functional of a single function $phi$ is formed as $theta(P)=sum_{i=1}^kphi(p_i)$, and by a choice of $phi$, it becomes entropy-like criteria including $f$-entropy, Shannon entropy, and R'enyi entropy. Estimation of these criteria is an important component for machine learning algorithms such as decision-tree learning and feature selection. More precise estimation of the functionals is thus expected to improve the performance of these algorithms. In our previous study, we introduced a minimax optimal estimator with rate $frac{k^2}{(nln n)^{2-2alpha}}+frac{k^{2alpha}}{n}$, where $alpha$ is a parameter of the bound on the fifth derivative of $phi$. However, the coverage of the assumption in the estimation problems of additively decomposable scalar functionals is not clear. In this paper, we reveal the conditions of $phi$ that the estimation problem of additively decomposable scalar functional of $phi$ has no consistent estimator. These conditions clarify the coverage of the assumption of the introduced minimax optimal estimator. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | cosistent estimator / minimax optimality / functional estimation / approximation theory / algebraic polynomial approximation / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 116, no. 300, IBISML2016-82, pp. 259-265, Nov. 2016. | |
| Paper # | IBISML2016-82 | |
| Date of Issue | 2016-11-09 (IBISML) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | IBISML2016-82 |
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| Conference Information | |
| Committee | IBISML |
| Conference Date | 2016-11-16 - 2016-11-18 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Kyoto Univ. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Information-Based Induction Science Workshop (IBIS2016) |
| Paper Information | |
| Registration To | IBISML |
| Conference Code | 2016-11-IBISML |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Minimax optimal estimator for additively decomposable scalar functionals of discrete distributions |
| Sub Title (in English) | |
| Keyword(1) | cosistent estimator |
| Keyword(2) | minimax optimality |
| Keyword(3) | functional estimation |
| Keyword(4) | approximation theory |
| Keyword(5) | algebraic polynomial approximation |
| Keyword(6) | |
| Keyword(7) | |
| Keyword(8) | |
| 1st Author's Name | Kazuto Fukuchi |
| 1st Author's Affiliation | University of Tsukuba (Univ. of Tsukuba) |
| 2nd Author's Name | Jun Sakuma |
| 2nd Author's Affiliation | University of Tsukuba (Univ. of Tsukuba) |
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| Speaker | Author-1 |
| Date Time | 2016-11-17 14:00:00 |
| Presentation Time | 180 minutes |
| Registration for | IBISML |
| Paper # | IBISML2016-82 |
| Volume (vol) | vol.116 |
| Number (no) | no.300 |
| Page | pp.259-265 |
| #Pages | 7 |
| Date of Issue | 2016-11-09 (IBISML) |
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