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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
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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  
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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
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 
#Pages
Date of Issue 2016-11-09 (IBISML) 


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