Probability Distribution on Full Rooted Trees
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, 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 becomes problematic. A method to solve this problem is to assume a prior distribution on the full rooted trees. This enables the optimal model selection based on the 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.
Code (0)
등록된 구현이 없습니다.
Tasks
Data CompressionModel SelectionSimilar Papers 제목 키워드 기반
Probability Distribution on Rooted Trees
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, su…
Data CompressionTwo Results about the Sackin and Colless Indices for Phylogenetic Trees and Their Shapes
The Sackin and Colless indices are two widely-used metrics for measuring the balance of trees and for testing evolutionary models in phylogenetics. This short paper contributes two results about the Sackin and Colless in…
Anomaly zones for uniformly sampled gene trees under the gene duplication and loss model
Recently, there has been interest in extending long-known results about the multispecies coalescent tree to other models of gene trees. Results about the gene duplication and loss (GDL) tree have mathematical proofs, inc…
Mathematical ProofsA partial order and cluster-similarity metric on rooted phylogenetic trees
Metrics on rooted phylogenetic trees are integral to a number of areas of phylogenetic analysis. Cluster-similarity metrics have recently been introduced in order to limit skew in the distribution of distances, and to en…
Random graph matching at Otter's threshold via counting chandeliers
We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erd\H{o}s-R\'enyi graphs $\mathcal{G}(n,q)$ whos…
Graph Matching