arXiv subjects

Yoshihiro Hirose

Publications and source records attributed to Yoshihiro Hirose.

3 recordsLinked to original sources

arXiv2020

Regularization Methods Based on the $L_q$-Likelihood for Linear Models with Heavy-Tailed Errors

We propose regularization methods for linear models based on the $L_q$-likelihood, which is a generalization of the log-likelihood using a power function. Some heavy-tailed distributions are known as $q$-normal distributions. We find that the proposed methods for linear models with $q$-normal errors coincide with the regularization methods that are applied to the normal linear model. The proposed methods work well and efficiently, and can be computed using existing packages. We examine the proposed methods using numerical experiments, showing that the methods perform well, even when the error is heavy-tailed.

stat.ME↗

arXiv2020

Least Angle Regression in Tangent Space and LASSO for Generalized Linear Models

This study proposes sparse estimation methods for the generalized linear models, which run one of least angle regression (LARS) and least absolute shrinkage and selection operator (LASSO) in the tangent space of the manifold of the statistical model. This study approximates the statistical model and subsequently uses exact calculations. LARS was proposed as an efficient algorithm for parameter estimation and variable selection for the normal linear model. The LARS algorithm is described in terms of Euclidean geometry regarding the correlation as the metric of the parameter space. Since the LARS algorithm only works in Euclidean space, we transform a manifold of the statistical model into the tangent space at the origin. In the generalized linear regression, this transformation allows us to run the original LARS algorithm for the generalized linear models. The proposed methods are efficient and perform well. Real-data analysis indicates that the proposed methods output similar results to that of the $l_1$-regularized maximum likelihood estimation for the aforementioned models. Numerical experiments reveal that our methods work well and they may be better than the $l_1$-regularization in generalization, parameter estimation, and model selection.

stat.ML↗

arXiv2018

Holonomic extended least angle regression

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 R, and was tested with real and simulated datasets.

stat.CO↗