An Extension of Least Angle Regression Based on the Information Geometry of Dually Flat Spaces

作者：Hirose Yoshihiro^*; Komaki Fumiyasu

来源：Journal of Computational and Graphical Statistics, 2010, 19(4): 1007-1023.

DOI：10.1198/jcgs.2010.09064

• Bisector
• Divergence
• Exponential family
• Generalized linear regression
• Iterative algorithm
• Variable selection

We extend the least angle regression algorithm using the information geometry of dually flat spaces. The extended least angle regression algorithm is used for estimating parameters in generalized linear regression, and it can be also used for selecting explanatory variables. We use the fact that a model manifold of an exponential family is a dually flat space. In estimating parameters, curves corresponding to bisectors in the Euclidean space play an important role. Originally, the least angle regression algorithm is used for estimating parameters and selecting explanatory variables in linear regression. It is an efficient algorithm in the sense that the number of iterations is the same as the number of explanatory variables. We extend the algorithm while keeping this efficiency. However, the extended least angle regression algorithm differs significantly from the original algorithm. The extended least angle regression algorithm reduces one explanatory variable in each iteration while the original algorithm increases one explanatory variable in each iteration. We show results of the extended least angle regression algorithm for two types of datasets. The behavior of the extended least angle regression algorithm is shown. Especially, estimates of parameters become smaller and smaller, and vanish in turn.

• 出版日期2010-12