TY - JOUR

T1 - Cluster’s Number Free Bayes Prediction of General Framework on Mixture of Regression Models

AU - Murayama, Haruka

AU - Saito, Shota

AU - Iikubo, Yuji

AU - Nakahara, Yuta

AU - Matsushima, Toshiyasu

N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Numbers JP17K06446, JP18K11585, JP19K04914, JP19K14989.
Publisher Copyright:
© 2021, The Author(s).

PY - 2021/9

Y1 - 2021/9

N2 - 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.

AB - 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.

KW - Bayes criterion

KW - Clustering

KW - Linear regression

KW - Variational Bayes algorithm

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U2 - 10.1007/s44199-021-00001-5

DO - 10.1007/s44199-021-00001-5

M3 - Article

AN - SCOPUS:85116062869

SN - 1538-7887

VL - 20

SP - 425

EP - 449

JO - Journal of Statistical Theory and Applications

JF - Journal of Statistical Theory and Applications

IS - 3

ER -