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Smoothing spline ANOVA models for large data sets with Bernoulli observations and the randomized GACV
 Ann. Statist
"... (ranGACV) method for choosing multiple smoothing parameters in penalized likelihood estimates for Bernoulli data. The method is intended for application with penalized likelihood smoothing spline ANOVA models. In addition we propose a class of approximate numerical methods for solving the penalized ..."
Abstract

Cited by 49 (22 self)
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(ranGACV) method for choosing multiple smoothing parameters in penalized likelihood estimates for Bernoulli data. The method is intended for application with penalized likelihood smoothing spline ANOVA models. In addition we propose a class of approximate numerical methods for solving the penalized likelihood variational problem which, in conjunction with the ranGACV method allows the application of smoothing spline ANOVA models with Bernoulli data to much larger data sets than previously possible. These methods are based on choosing an approximating subset of the natural (representer) basis functions for the variational problem. Simulation studies with synthetic data, including synthetic data mimicking demographic risk factor data sets is used to examine the properties of the method and to compare the approach with the GRKPACK code of Wang (1997c). Bayesian “confidence intervals ” are obtained for the fits and are shown in the simulation studies to have the “across the function ” property usually claimed for these confidence intervals. Finally the method is applied
LASSOPatternsearch Algorithm with Application to Ophthalmology and Genomic Data
, 2008
"... The LASSOPatternsearch algorithm is proposed to efficiently identify patterns of multiple dichotomous risk factors for outcomes of interest in demographic and genomic studies. The patterns considered are those that arise naturally from the log linear expansion of the multivariate Bernoulli density. ..."
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Cited by 33 (24 self)
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The LASSOPatternsearch algorithm is proposed to efficiently identify patterns of multiple dichotomous risk factors for outcomes of interest in demographic and genomic studies. The patterns considered are those that arise naturally from the log linear expansion of the multivariate Bernoulli density. The method is designed for the case where there is a possibly very large number of candidate patterns but it is believed that only a relatively small number are important. A LASSO is used to greatly reduce the number of candidate patterns, using a novel computational algorithm that can handle an extremely large number of unknowns simultaneously. The patterns surviving the LASSO are further pruned in the framework of (parametric) generalized linear models. A novel tuning procedure based on the GACV for Bernoulli outcomes, modified to act
Reproducing Kernel Hilbert Spaces  Two Brief Reviews
, 2003
"... This TR contains two brief reviews which will appear in the Proceedings of the 13th IFAC Symposium on System Identification (SYSID 2003), Rotterdam, August 2003. They are ..."
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Cited by 1 (0 self)
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This TR contains two brief reviews which will appear in the Proceedings of the 13th IFAC Symposium on System Identification (SYSID 2003), Rotterdam, August 2003. They are
Reproducing Kernel Hilbert Spaces  Two Brief Reviews
, 2003
"... This TR contains two brief reviews which will appear in the Proceedings of the ..."
Abstract
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This TR contains two brief reviews which will appear in the Proceedings of the
An Introduction to (Smoothing Spline) ANOVA Models in RKHS, With Examples in Geographical Data, Medicine, Atmospheric Science and Machine Learning.
, 2004
"... ..."
Investigator AwardsLASSOPatternsearch Algorithm with Application to Ophthalmology Data
, 2008
"... The LASSOPatternsearch is proposed, as a twostage procedure to identify clusters of multiple risk factors for outcomes of interest in large demographic studies, when the predictor variables are dichotomous or take on values in a small finite set. Many diseases are suspected of having multiple inte ..."
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The LASSOPatternsearch is proposed, as a twostage procedure to identify clusters of multiple risk factors for outcomes of interest in large demographic studies, when the predictor variables are dichotomous or take on values in a small finite set. Many diseases are suspected of having multiple interacting risk factors acting in concert, and it is of much interest to uncover higher order interactions when they exist. The method is related to Zhang et al(2004) except that variable flexibility is sacrificed to allow entertaining models with high as well as low order interactions among multiple predictors. A LASSO is used to select important patterns, being applied conservatively to have a high rate of retention of true patterns, while allowing some noise. Then the patterns selected by the LASSO are tested in the framework of (parametric) generalized linear models to reduce the noise. Notably, the patterns are those that arise naturally from the log linear expansion of the multivariate Bernoulli density. Separate tuning procedures are proposed for the LASSO step and then the parametric step and a novel