Cluster’s Number Free Bayes Prediction of General Framework on Mixture of Regression Models

Haruka Murayama*, Shota Saito, Yuji Iikubo, Yuta Nakahara, Toshiyasu Matsushima

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Prediction based on a single linear regression model is one of the most common way in various field of studies. It enables us to understand the structure of data, but might not be suitable to express the data whose structure is complex. To express the structure of data more accurately, we make assumption that the data can be divided in clusters, and has a linear regression model in each cluster. In this case, we can assume that each explanatory variable has their own role; explaining the assignment to the clusters, explaining the regression to the target variable, or being both of them. Introducing probabilistic structure to the data generating process, we derive the optimal prediction under Bayes criterion and the algorithm which calculates it sub-optimally with variational inference method. One of the advantages of our algorithm is that it automatically weights the probabilities of being each number of clusters in the process of the algorithm, therefore it solves the concern about selection of the number of clusters. Some experiments are performed on both synthetic and real data to demonstrate the above advantages and to discover some behaviors and tendencies of the algorithm.

Original languageEnglish
Pages (from-to)425-449
Number of pages25
JournalJournal of Statistical Theory and Applications
Volume20
Issue number3
DOIs
Publication statusPublished - 2021 Sep

Keywords

  • Bayes criterion
  • Clustering
  • Linear regression
  • Variational Bayes algorithm

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics
  • Computer Science Applications

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