Abstract
We focus on an optimization algorithm for a normal-likelihood-based group Lasso in multivariate linear regression. A negative multivariate normal log-likelihood function with a block-norm penalty is used as the objective function. A solution for the minimization problem of a quadratic form with a norm penalty is given without using the Karush–Kuhn–Tucker condition. In special cases, the minimization problem can be solved without solving simultaneous equations of the first derivatives. We derive update equations of a coordinate descent algorithm for minimizing the objective function. Further, by using the result of the special case, we also derive update equations of an iterative thresholding algorithm for minimizing the objective function.
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Acknowledgements
The authors wish to thank two reviewers for their helpful comments. This work was financially supported by JSPS KAKENHI (grant numbers JP16H03606, JP18K03415, and JP20H04151 to Hirokazu Yanagihara; JP19K21672, JP20K14363, and JP20H04151 to Ryoya Oda).
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Yanagihara, H., Oda, R. (2021). Coordinate Descent Algorithm for Normal-Likelihood-Based Group Lasso in Multivariate Linear Regression. In: Czarnowski, I., Howlett, R.J., Jain, L.C. (eds) Intelligent Decision Technologies. Smart Innovation, Systems and Technologies, vol 238. Springer, Singapore. https://doi.org/10.1007/978-981-16-2765-1_36
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DOI: https://doi.org/10.1007/978-981-16-2765-1_36
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