IEICE Technical Committee Submission System
Conference Paper's Information
Online Proceedings
[Sign in]
Tech. Rep. Archives
 Go Top Page Go Previous   [Japanese] / [English] 

Paper Abstract and Keywords
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
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
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

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  
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)
3rd Author's Name  
3rd Author's Affiliation ()
4th Author's Name  
4th Author's Affiliation ()
5th Author's Name  
5th Author's Affiliation ()
6th Author's Name  
6th Author's Affiliation ()
7th Author's Name  
7th Author's Affiliation ()
8th Author's Name  
8th Author's Affiliation ()
9th Author's Name  
9th Author's Affiliation ()
10th Author's Name  
10th Author's Affiliation ()
11th Author's Name  
11th Author's Affiliation ()
12th Author's Name  
12th Author's Affiliation ()
13th Author's Name  
13th Author's Affiliation ()
14th Author's Name  
14th Author's Affiliation ()
15th Author's Name  
15th Author's Affiliation ()
16th Author's Name  
16th Author's Affiliation ()
17th Author's Name  
17th Author's Affiliation ()
18th Author's Name  
18th Author's Affiliation ()
19th Author's Name  
19th Author's Affiliation ()
20th Author's Name  
20th Author's Affiliation ()
Date Time 2016-11-17 14:00:00 
Presentation Time 180 
Registration for IBISML 
Paper # IBISML2016-82 
Volume (vol) 116 
Number (no) no.300 
Page pp.259-265 
Date of Issue 2016-11-09 (IBISML) 

[Return to Top Page]

[Return to IEICE Web Page]

The Institute of Electronics, Information and Communication Engineers (IEICE), Japan