Bayesian Inference for Mixture of Sparse Linear Regression Model

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Abstract

This paper proposes a Bayesian Inference for mixture of sparse linear regression models with the exchange Monte Carlo method. Mixture of linear regression model is a hybrid machine learning model that simultaneously performs clustering and linear regression. Mixture of sparse linear regression model imposes sparsity on the regression parameters and is expected to be applied to the analysis of real data in the field of materials science. The proposed method calculates the mixture ratio of each cluster, the label of each data point, and the posterior distribution of the sparse regression parameters by Bayesian inference using the exchange Monte Carlo method. Model selection based on the Bayesian free energy determines the appropriate number of mixtures of clusters. Experiments on artificial data confirmed that we obtained an appropriate posterior distribution of the parameters and showed appropriate model selection results. We applied our method to the data on aluminum alloys in materials science, and model selection and parameter estimation were performed by Bayesian inference.

This paper proposes a Bayesian Inference for mixture of sparse linear regression models with the exchange Monte Carlo method. Mixture of linear regression model is a hybrid machine learning model that simultaneously performs clustering and linear regression. Mixture of sparse linear regression model imposes sparsity on the regression parameters and is expected to be applied to the analysis of real data in the field of materials science. The proposed method calculates the mixture ratio of each cluster, the label of each data point, and the posterior distribution of the sparse regression parameters by Bayesian inference using the exchange Monte Carlo method. Model selection based on the Bayesian free energy determines the appropriate number of mixtures of clusters. Experiments on artificial data confirmed that we obtained an appropriate posterior distribution of the parameters and showed appropriate model selection results. We applied our method to the data on aluminum alloys in materials science, and model selection and parameter estimation were performed by Bayesian inference.

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