On model selection consistency of M-estimators with geometrically decomposable penalties

Jason D. Lee; Yuekai Sun; Jonathan E. Taylor

On model selection consistency of M-estimators with geometrically decomposable penalties

Jason D. Lee, Yuekai Sun, Jonathan E. Taylor

Research output: Contribution to journal › Conference article › peer-review

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 geometrically decomposable, i.e. can be expressed as a sum of support functions over convex sets. 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.

Original language	English (US)
Journal	Advances in Neural Information Processing Systems
State	Published - 2013
Externally published	Yes
Event	27th Annual Conference on Neural Information Processing Systems, NIPS 2013 - Lake Tahoe, NV, United States Duration: Dec 5 2013 → Dec 10 2013

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Information Systems
Signal Processing

Cite this

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title = "On model selection consistency of M-estimators with geometrically decomposable penalties",

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 geometrically decomposable, i.e. can be expressed as a sum of support functions over convex sets. 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.",

author = "Lee, {Jason D.} and Yuekai Sun and Taylor, {Jonathan E.}",

year = "2013",

language = "English (US)",

journal = "Advances in Neural Information Processing Systems",

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publisher = "Neural information processing systems foundation",

note = "27th Annual Conference on Neural Information Processing Systems, NIPS 2013 ; Conference date: 05-12-2013 Through 10-12-2013",

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TY - JOUR

T1 - On model selection consistency of M-estimators with geometrically decomposable penalties

AU - Lee, Jason D.

AU - Sun, Yuekai

AU - Taylor, Jonathan E.

PY - 2013

Y1 - 2013

N2 - 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 geometrically decomposable, i.e. can be expressed as a sum of support functions over convex sets. 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.

AB - 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 geometrically decomposable, i.e. can be expressed as a sum of support functions over convex sets. 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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UR - http://www.scopus.com/inward/citedby.url?scp=84898967566&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:84898967566

SN - 1049-5258

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

T2 - 27th Annual Conference on Neural Information Processing Systems, NIPS 2013

Y2 - 5 December 2013 through 10 December 2013

ER -

On model selection consistency of M-estimators with geometrically decomposable penalties

Abstract

All Science Journal Classification (ASJC) codes

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