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Probability Distribution on Full Rooted Trees

The recursive and hierarchical structure of full rooted trees is applicable to statistical models in various fields, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is not a random variable; as such, model selection to avoid overfitting...

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Autores principales: Nakahara, Yuta, Saito, Shota, Kamatsuka, Akira, Matsushima, Toshiyasu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8947532/
https://www.ncbi.nlm.nih.gov/pubmed/35327839
http://dx.doi.org/10.3390/e24030328
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author Nakahara, Yuta
Saito, Shota
Kamatsuka, Akira
Matsushima, Toshiyasu
author_facet Nakahara, Yuta
Saito, Shota
Kamatsuka, Akira
Matsushima, Toshiyasu
author_sort Nakahara, Yuta
collection PubMed
description The recursive and hierarchical structure of full rooted trees is applicable to statistical models in various fields, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is not a random variable; as such, model selection to avoid overfitting is problematic. One method to solve this problem is to assume a prior distribution on the full rooted trees. This enables the optimal model selection based on Bayes decision theory. For example, by assigning a low prior probability to a complex model, the maximum a posteriori estimator prevents the selection of the complex one. Furthermore, we can average all the models weighted by their posteriors. In this paper, we propose a probability distribution on a set of full rooted trees. Its parametric representation is suitable for calculating the properties of our distribution using recursive functions, such as the mode, expectation, and posterior distribution. Although such distributions have been proposed in previous studies, they are only applicable to specific applications. Therefore, we extract their mathematically essential components and derive new generalized methods to calculate the expectation, posterior distribution, etc.
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spelling pubmed-89475322022-03-25 Probability Distribution on Full Rooted Trees Nakahara, Yuta Saito, Shota Kamatsuka, Akira Matsushima, Toshiyasu Entropy (Basel) Article The recursive and hierarchical structure of full rooted trees is applicable to statistical models in various fields, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is not a random variable; as such, model selection to avoid overfitting is problematic. One method to solve this problem is to assume a prior distribution on the full rooted trees. This enables the optimal model selection based on Bayes decision theory. For example, by assigning a low prior probability to a complex model, the maximum a posteriori estimator prevents the selection of the complex one. Furthermore, we can average all the models weighted by their posteriors. In this paper, we propose a probability distribution on a set of full rooted trees. Its parametric representation is suitable for calculating the properties of our distribution using recursive functions, such as the mode, expectation, and posterior distribution. Although such distributions have been proposed in previous studies, they are only applicable to specific applications. Therefore, we extract their mathematically essential components and derive new generalized methods to calculate the expectation, posterior distribution, etc. MDPI 2022-02-24 /pmc/articles/PMC8947532/ /pubmed/35327839 http://dx.doi.org/10.3390/e24030328 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Nakahara, Yuta
Saito, Shota
Kamatsuka, Akira
Matsushima, Toshiyasu
Probability Distribution on Full Rooted Trees
title Probability Distribution on Full Rooted Trees
title_full Probability Distribution on Full Rooted Trees
title_fullStr Probability Distribution on Full Rooted Trees
title_full_unstemmed Probability Distribution on Full Rooted Trees
title_short Probability Distribution on Full Rooted Trees
title_sort probability distribution on full rooted trees
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8947532/
https://www.ncbi.nlm.nih.gov/pubmed/35327839
http://dx.doi.org/10.3390/e24030328
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