TY - GEN
T1 - Probability Distribution on Rooted Trees
AU - Nakahara, Yuta
AU - Saito, Shota
AU - Kamatsuka, Akira
AU - Matsushima, Toshiyasu
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Numbers JP17K06446, JP19K04914, and JP19K14989.
Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical expressive capability causes a problem in tree selection to avoid overfitting. One unified approach to solve this is a Bayesian approach, on which the rooted tree is regarded as a random variable and a direct loss function can be assumed on the selected model or the predicted value for a new data point. However, all the previous studies on this approach are based on the probability distribution on full trees, to the best of our knowledge. In this paper, we propose a generalized probability distribution for any rooted trees in which only the maximum number of child nodes and the maximum depth are fixed. Furthermore, we derive recursive methods to evaluate the characteristics of the probability distribution without any approximations.
AB - The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical expressive capability causes a problem in tree selection to avoid overfitting. One unified approach to solve this is a Bayesian approach, on which the rooted tree is regarded as a random variable and a direct loss function can be assumed on the selected model or the predicted value for a new data point. However, all the previous studies on this approach are based on the probability distribution on full trees, to the best of our knowledge. In this paper, we propose a generalized probability distribution for any rooted trees in which only the maximum number of child nodes and the maximum depth are fixed. Furthermore, we derive recursive methods to evaluate the characteristics of the probability distribution without any approximations.
KW - Bayes decision theory
KW - Bayes statistics
KW - recursive algorithm
KW - rooted trees
UR - http://www.scopus.com/inward/record.url?scp=85136244421&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85136244421&partnerID=8YFLogxK
U2 - 10.1109/ISIT50566.2022.9834481
DO - 10.1109/ISIT50566.2022.9834481
M3 - Conference contribution
AN - SCOPUS:85136244421
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 174
EP - 179
BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022
Y2 - 26 June 2022 through 1 July 2022
ER -