bgam - Boosted Generalized Additive Models package
Implements boosting for the Generalized Additive and Linear Models (GAM and GLM).
Extensible, fully documented. Implements linear and stub learners,
The generalized linear model (GLM) is a flexible generalization of ordinary
least squares regression. The GLM generalizes linear regression by allowing
the linear model to be related to the response variable via a link function
and by allowing the magnitude of the variance of each measurement to be a
function of its predicted value. (Wikipedia)
A common example of a GLM is binomial-logistic distribution/inverse link
GLM (aka logistic regression), where:
eta = X*w, y ~ Binomial( logistic (eta ))
This GLM allows one to tackle classification problems (where the output is 0 or 1)
in a quasi-linear way.
The generalized additive model (GAM) is a generalization of the GLM where the internal
dynamics are nonlinear, but nevertheless additive:
eta_i = f_1(X^(i,1)) + f_2(X^(i,2)) + ...
f_i are known as smoothers or (in the context of boosting) as learners. Boosting is
a method of fitting GAMs and by extension GLMs by building up a model (eta) iteratively,
by, at every iteration, adding to the model the learner most similar to the gradient
of the likelihood with respect to eta. Regularization is usually done by early-stopping
where the optimal number of iterations is determined through validation.
bgam is a well-documented package that implements boosting with GAMs.
It currently implements linear learners and stubs (depth-1 trees). Implemented distro-link
combos include Gaussian/identity, Binomial/Logistic, Poisson/exponential. The package is
object-oriented and new distro-link combos and learners can be implemented and used
with ease. The package includes facilities for cross-validation, including a parallel implementation through the parallel computing toolbox. It also allows a subset
of the data to be used at any boosting iteration (stochastic gradient boosting).
Open up TestBgam.m in the editor for several usage examples.
Contributions and requests for new features are welcome.
Author: Patrick Mineault (patrick DOT mineault AT gmail DOT com)
Friedman, Hastie and Tibshirani. Additive logistic regression: a
statistical view of boosting. Ann. Statist. Volume 28, Number 2 (2000),
Bühlmann and Hothorn. Boosting Algorithms: Regularization, Prediction
and Model Fitting. Statist. Sci. Volume 22, Number 4 (2007), 477-505.
Wood. Generalized Additive Models: an introduction with R. CRC Press,
Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive
Models. Chapman & Hall/CRC.
Patrick Mineault (2022). Boosted Generalized Additive Models (bgam) package (https://www.mathworks.com/matlabcentral/fileexchange/30145-boosted-generalized-additive-models-bgam-package), MATLAB Central File Exchange. Retrieved .
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