The statistical analysis of compositional data
The statistical analysis of compositional data
Transformation and weighting in regression
Transformation and weighting in regression
An introduction to variational methods for graphical models
Learning in graphical models
Estimation and variable selection in nonparametric heteroscedastic regression
Statistics and Computing
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
The Journal of Machine Learning Research
On the Consistency of Feature Selection using Greedy Least Squares Regression
The Journal of Machine Learning Research
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
Modern statistical applications involving large data sets have focused attention on statistical methodologies which are both efficient computationally and able to deal with the screening of large numbers of different candidate models. Here we consider computationally efficient variational Bayes approaches to inference in high-dimensional heteroscedastic linear regression, where both the mean and variance are described in terms of linear functions of the predictors and where the number of predictors can be larger than the sample size. We derive a closed form variational lower bound on the log marginal likelihood useful for model selection, and propose a novel fast greedy search algorithm on the model space which makes use of one-step optimization updates to the variational lower bound in the current model for screening large numbers of candidate predictor variables for inclusion/exclusion in a computationally thrifty way. We show that the model search strategy we suggest is related to widely used orthogonal matching pursuit algorithms for model search but yields a framework for potentially extending these algorithms to more complex models. The methodology is applied in simulations and in two real examples involving prediction for food constituents using NIR technology and prediction of disease progression in diabetes.