Fast Factorization of Probability Trees and Its Application to Recursive Trees Learning

2010 ◽  
pp. 65-72
Author(s):  
Andrés Cano ◽  
Manuel Gómez-Olmedo ◽  
Cora B. Pérez-Ariza ◽  
Antonio Salmerón
Keyword(s):  
Recursive Trees ◽  
Probability Trees

scholarly journals Isolating nodes in recursive trees

2008 ◽  
Vol 76 (3) ◽  
pp. 258-280 ◽  
Author(s):  
Markus Kuba ◽  
Alois Panholzer
Keyword(s):  
Recursive Trees

scholarly journals Approximate inference in Bayesian networks using binary probability trees

2011 ◽  
Vol 52 (1) ◽  
pp. 49-62 ◽  
Author(s):  
Andrés Cano ◽  
Manuel Gémez-Olmedo ◽  
Serafén Moral
Keyword(s):  
Bayesian Networks ◽  
Approximate Inference ◽  
Probability Trees

scholarly journals New strategies for finding multiplicative decompositions of probability trees

2013 ◽  
Vol 225 ◽  
pp. 573-589
Author(s):  
Irene Martínez ◽  
Serafín Moral ◽  
Carmelo Rodríguez ◽  
Antonio Salmerón
Keyword(s):  
New Strategies ◽  
Probability Trees

Extended Probability Trees for Probabilistic Graphical Models

2014 ◽  
pp. 113-128
Author(s):  
Andrés Cano ◽  
Manuel Gómez-Olmedo ◽  
Serafín Moral ◽  
Cora B. Pérez-Ariza
Keyword(s):  
Graphical Models ◽  
Probabilistic Graphical Models ◽  
Probability Trees

scholarly journals Labels distance in bucket recursive trees with variable capacities of buckets

2021 ◽  
Vol 13 (2) ◽  
pp. 413-426
Author(s):  
S. Naderi ◽  
R. Kazemi ◽  
M. H. Behzadi
Keyword(s):  
Partial Differential Equations ◽  
Probability Distribution ◽  
Differential Equations ◽  
Generating Function ◽  
Generating Functions ◽  
Function Approach ◽  
Closed Formula ◽  
Tree Model ◽  
Partial Differential ◽  
Recursive Trees

Abstract The bucket recursive tree is a natural multivariate structure. In this paper, we apply a trivariate generating function approach for studying of the depth and distance quantities in this tree model with variable bucket capacities and give a closed formula for the probability distribution, the expectation and the variance. We show as j → ∞, lim-iting distributions are Gaussian. The results are obtained by presenting partial differential equations for moment generating functions and solving them.

scholarly journals On the Distribution of Depths in Increasing Trees

10.37236/409 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Markus Kuba ◽  
Stephan Wagner
Keyword(s):  
Common Ancestor ◽  
Short Note ◽  
Bijective Proof ◽  
Lowest Common Ancestor ◽  
Recursive Trees

By a theorem of Dobrow and Smythe, the depth of the $k$th node in very simple families of increasing trees (which includes, among others, binary increasing trees, recursive trees and plane ordered recursive trees) follows the same distribution as the number of edges of the form $j-(j+1)$ with $j < k$. In this short note, we present a simple bijective proof of this fact, which also shows that the result actually holds within a wider class of increasing trees. We also discuss some related results that follow from the bijection as well as a possible generalization. Finally, we use another similar bijection to determine the distribution of the depth of the lowest common ancestor of two nodes.

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