by T. W. Yee, [email protected], 2015-03-06 See http://www.stat.auckland.ac.nz/∼yee/VGAM for the VGAM package and some other documentation. This document is current for version VGAM-0.9-7. The theory1 underlying the software can be found in Yee and Wild (1996), Yee (1998), Yee and Mackenzie (2002), Yee and Hastie (2003), Yee (2004a), Yee (2004b), Yee (2006), Yee and Stephenson (2007), Yee (2...

In this paper, we seek to formulate a geometrically based alternative to nonlinear, nonparametric regression. Hastie and Stuetzle (1989) introduced the ideas of principal curves and surfaces. These were 1and 2-dimensional non-linear regression-type estimators, which were consistent with respect to the mean, i.e. involved conditional expectations. We have developed a similar notion, but with two...

The GLASSO algorithm has been proposed by Friedman, Hastie and Tibshirani in 2008 to solve the `1 regularized inverse covariance matrix estimation problem. The conditional dependency structure which is captured by the inverse of the covariance matrix is of interest in numerous applications and the publication of GLASSO has spurred the development of several other algorithms aimed to solve the s...

One-class support vector machines (1-SVMs) estimate the level set of the underlying density observed data. Aside the kernel selection issue, one difficulty concerns the choice of the ’level’ parameter. In this paper, following the work by Hastie et. al (2004), we derive the entire regularization path for ν-1-SVMs. Since this regularization path is efficient for building different level sets est...

This article describes the asymptotic properties of local polynomial regression estimators for univariate and additive models when observation weights are included. Such weighted additive models are a crucial component of local scoring, the widely used estimation algorithm for generalized additive models described in Hastie and Tibshirani (1990). The statistical properties of the univariate loc...

In this work, I will apply a recently developed automatic reversible jump MCMC algorithm to the problem of fitting a Gaussian mixture model to data. This algorithm, named AutoMix, is due to Hastie [5]. Reversible jump is approriate for this problem, because I will allow the number of mixture components to vary, and will seek to estimate the posterior distribution over both this quantity and the...

This paper describes the use of the GAM procedure for fitting generalized additive models (Hastie and Tibshirani, 1990). PROC GAM, production in Release 8.2, provides an array of powerful tools for data analysis, incorporating nonparametric regression and smoothing techniques as well as generalized distributional modeling. Compared with other regression procedures such as PROC REG and PROC GLM,...

Multiclass SVMs are usually implemented by combining several two-class SVMs. The one-versus-all method using winner-takes-all strategy and the one-versus-one method implemented by max-wins voting are popularly used for this purpose. In this paper we give empirical evidence to show that these methods are inferior to another one-versusone method: one that uses Platt’s posterior probabilities toge...

An algorithm for fitting the entire regularization path of the support vector machine (SVM) was recently proposed by Hastie et al. (2004). It allows effective computation of solutions and greatly facilitates the choice of the regularization parameter that balances a trade-off between complexity of a solution and its fit to data. Extending the idea to more general setting of the multiclass case,...