Bayesian Perspectives on Sparse Empirical Bayes Analysis (SEBA)

Natalia Bochkina; Ya'acov Ritov

doi:10.1007/978-3-642-19989-9_5

Bayesian Perspectives on Sparse Empirical Bayes Analysis (SEBA)

Natalia Bochkina, Ya'acov Ritov

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed)

Abstract

We consider a joint processing of n independent similar sparse regression
problems. Each is based on a sample (y_{i1}, x_{i1}) . . . , (y_{im}, x_{im})
of m i.i.d. observations from y_{ik} = x^T_{ik}β_i + ε_{ik}, y_{ik} ∈ R, x_{ik} ∈ R^p,
and ε_{ik} ∼ N(0, σ), say. The dimension p is large enough so that the
empirical risk minimizer is not feasible. We consider, from a Bayesian
point of view, three possible extensions of the lasso. Each of the three
estimators, the lassoes, the group lasso, and the RING lasso, utilizes
different assumptions on the relation between the n vectors β_1, . . . , β_n.

Original language	English
Title of host publication	Inverse Problems and High-Dimensional estimation
Subtitle of host publication	Stats in the Château Summer School, August 31 - September 4, 2009
Editors	Pierre Alquier, Eric Gautier, Gilles Stoltz
Publisher	Springer
Pages	171-189
Number of pages	19
Volume	203
Edition	1
ISBN (Print)	978-3-642-19988-2
DOIs	https://doi.org/10.1007/978-3-642-19989-9_5
Publication status	Published - 2011

Publication series

Name	Lecture Notes in Statistics
Publisher	Springer Berlin Heidelberg
ISSN (Print)	0930-0325

Keywords / Materials (for Non-textual outputs)

sparse regression
LASSO
Bayesian inference
compound decision

Access to Document

10.1007/978-3-642-19989-9_5

http://pluto.huji.ac.il/~yaacov/BayesianSEBA.pdf

Cite this

Bochkina, N., & Ritov, Y. (2011). Bayesian Perspectives on Sparse Empirical Bayes Analysis (SEBA). In P. Alquier, E. Gautier, & G. Stoltz (Eds.), Inverse Problems and High-Dimensional estimation: Stats in the Château Summer School, August 31 - September 4, 2009 (1 ed., Vol. 203, pp. 171-189). (Lecture Notes in Statistics). Springer. https://doi.org/10.1007/978-3-642-19989-9_5

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abstract = "We consider a joint processing of n independent similar sparse regression problems. Each is based on a sample (y_{i1}, x_{i1}) . . . , (y_{im}, x_{im}) of m i.i.d. observations from y_{ik} = x^T_{ik}β_i + ε_{ik}, y_{ik} ∈ R, x_{ik} ∈ R^p, and ε_{ik} ∼ N(0, σ), say. The dimension p is large enough so that the empirical risk minimizer is not feasible. We consider, from a Bayesian point of view, three possible extensions of the lasso. Each of the three estimators, the lassoes, the group lasso, and the RING lasso, utilizes different assumptions on the relation between the n vectors β_1, . . . , β_n.",

keywords = "sparse regression, LASSO, Bayesian inference, compound decision",

author = "Natalia Bochkina and Ya'acov Ritov",

year = "2011",

doi = "10.1007/978-3-642-19989-9_5",

language = "English",

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volume = "203",

series = "Lecture Notes in Statistics",

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editor = "Pierre Alquier and Eric Gautier and Gilles Stoltz",

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Bayesian Perspectives on Sparse Empirical Bayes Analysis (SEBA). / Bochkina, Natalia; Ritov, Ya'acov.
Inverse Problems and High-Dimensional estimation: Stats in the Château Summer School, August 31 - September 4, 2009. ed. / Pierre Alquier; Eric Gautier; Gilles Stoltz. Vol. 203 1. ed. Springer, 2011. p. 171-189 (Lecture Notes in Statistics).

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed)

TY - CHAP

T1 - Bayesian Perspectives on Sparse Empirical Bayes Analysis (SEBA)

AU - Bochkina, Natalia

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AB - We consider a joint processing of n independent similar sparse regression problems. Each is based on a sample (y_{i1}, x_{i1}) . . . , (y_{im}, x_{im}) of m i.i.d. observations from y_{ik} = x^T_{ik}β_i + ε_{ik}, y_{ik} ∈ R, x_{ik} ∈ R^p, and ε_{ik} ∼ N(0, σ), say. The dimension p is large enough so that the empirical risk minimizer is not feasible. We consider, from a Bayesian point of view, three possible extensions of the lasso. Each of the three estimators, the lassoes, the group lasso, and the RING lasso, utilizes different assumptions on the relation between the n vectors β_1, . . . , β_n.

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KW - Bayesian inference

KW - compound decision

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A2 - Alquier, Pierre

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PB - Springer

ER -

Bayesian Perspectives on Sparse Empirical Bayes Analysis (SEBA)

Abstract

Publication series

Keywords / Materials (for Non-textual outputs)

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Cite this