  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.
