Meta-tree random forest: Probabilistic data-generative model and bayes optimal prediction

Nao Dobashi, Shota Saito, Yuta Nakahara, Toshiyasu Matsushima

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This paper deals with a prediction problem of a new targeting variable corresponding to a new explanatory variable given a training dataset. To predict the targeting variable, we consider a model tree, which is used to represent a conditional probabilistic structure of a targeting variable given an explanatory variable, and discuss statistical optimality for prediction based on the Bayes decision theory. The optimal prediction based on the Bayes decision theory is given by weighting all the model trees in the model tree candidate set, where the model tree candidate set is a set of model trees in which the true model tree is assumed to be included. Because the number of all the model trees in the model tree candidate set increases exponentially according to the maximum depth of model trees, the computational complexity of weighting them increases exponentially according to the maximum depth of model trees. To solve this issue, we introduce a notion of meta-tree and propose an algorithm called MTRF (Meta-Tree Random Forest) by using multiple meta-trees. Theoretical and experimental analyses of the MTRF show the superiority of the MTRF to previous decision tree-based algorithms.

Original languageEnglish
Article number768
JournalEntropy
Volume23
Issue number6
DOIs
Publication statusPublished - 2021 Jun

Keywords

  • Bayes decision theory
  • Data-generative model
  • Meta-tree
  • Prediction
  • Random forest

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering

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