Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Chemical Society (ACS)  

DOI： 10.1021/acs.jpca.2c02354

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Language：Japanese   Publishing type：Research paper (scientific journal)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

Abstract

One of the main problems studied in statistics is the fitting of models. Ideally, we would like to explain a large dataset with as few parameters as possible. There have been numerous attempts at automatizing this process. Most notably, the Least Angle Regression algorithm, or LARS, is a computationally efficient algorithm that ranks the covariates of a linear model. The algorithm is further extended to a class of distributions in the generalized linear model by using properties of the manifold of exponential families as dually flat manifolds. However this extension assumes that the normalizing constant of the joint distribution of observations is easy to compute. This is often not the case, for example the normalizing constant may contain a complicated integral. We circumvent this issue if the normalizing constant satisfies a holonomic system, a system of linear partial differential equations with a finite-dimensional space of solutions. In this paper we present a modification of the holonomic gradient method and add it to the extended LARS algorithm. We call this the holonomic extended least angle regression algorithm, or HELARS. The algorithm was implemented using the statistical software , and was tested with real and simulated datasets.

DOI： 10.1007/s41884-020-00035-1

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Other Link： https://link.springer.com/article/10.1007/s41884-020-00035-1/fulltext.html

Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：MDPI AG  

We propose regularization methods for linear models based on the Lq-likelihood, which is a generalization of the log-likelihood using a power function. Regularization methods are popular for the estimation in the normal linear model. However, heavy-tailed errors are also important in statistics and machine learning. We assume q-normal distributions as the errors in linear models. A q-normal distribution is heavy-tailed, which is defined using a power function, not the exponential function. We find that the proposed methods for linear models with q-normal errors coincide with the ordinary regularization methods that are applied to the normal linear model. The proposed methods can be computed using existing packages because they are penalized least squares methods. We examine the proposed methods using numerical experiments, showing that the methods perform well, even when the error is heavy-tailed. The numerical experiments also illustrate that our methods work well in model selection and generalization, especially when the error is slightly heavy-tailed.

DOI： 10.3390/e22091036

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Authorship：Corresponding author   Publishing type：Research paper (scientific journal)  

DOI： 10.1007/s00362-018-1001-5

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Internal/External technical report, pre-print, etc.  

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Authorship：Corresponding author   Publishing type：Internal/External technical report, pre-print, etc.  

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Language：Japanese  

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Language：Japanese  

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