2013
NeurIPS
NeurIPS 2013
On model selection consistency of penalized M-estimators: a geometric theory
Abstract
Penalized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Often, the penalties are \emph{geometrically decomposable}, \ie\ can be expressed as a sum of (convex) support functions. We generalize the notion of irrepresentable to geometrically decomposable penalties and develop a general framework for establishing consistency and model selection consistency of M-estimators with such penalties. We then use this framework to derive results for some special cases of interest in bioinformatics and statistical learning.
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Interdisciplinary Bridge
- Artificial Intelligence and Interdisciplinary and Mathematics & Optimization
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Trend Setter
- Bioinformatics
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Hot Topic Early Bird
- high-dimensional regression
Authors
Topics
Machine Learning > Optimization & Theory > Learning Theory
Machine Learning > Optimization & Theory > Statistical Learning
Machine Learning > Optimization & Theory > Theory
Mathematics & Optimization > Mathematics > Statistics
Machine Learning > Core Methods > Feature Selection
Mathematics & Optimization > Statistics
Machine Learning > Optimization & Theory > Sparse Optimization
Interdisciplinary > Science > Bioinformatics
Machine Learning > Optimization & Theory > Convex Optimization
Keywords
statistical learning
learning theory
model selection
variable selection
high-dimensional statistics
high-dimensional regression
sparse optimization
m-estimators
model selection consistency
geometric decomposability
penalized m-estimators
geometric decomposition
penalized estimator
high-dimensional model
irrepresentable condition
geometrically decomposable penalties
support function