On extensions of LARS by information geometry: Convex objectives and ̀p-norm

Masahiro Yukawa; Shun Ichi Amari

On extensions of LARS by information geometry: Convex objectives and ̀p-norm

Research output: Contribution to conference › Paper › peer-review

Abstract

This paper addresses extensions of the Least Angle Regression (LARS) algorithm from two different aspects: (i) from quadratic to more general objectives, and (ii) from ̀1-norm to ̀p-norm for p < 1. The equiangular vector, which is the key of LARS, is reproduced in connection with the Riemannian metric induced by the objective function, thereby making the extensions feasible. It is shown, in the case of p < 1, that two types of trajectory . the c-trajectory and the λ-trajectory . need to be distinguished by revealing the discontinuity of the λ-trajectory.

Original language	English
Pages	326-331
Number of pages	6
Publication status	Published - 2011 Dec 1
Externally published	Yes
Event	Asia-Pacific Signal and Information Processing Association Annual Summit and Conference 2011, APSIPA ASC 2011 - Xi'an, China Duration: 2011 Oct 18 → 2011 Oct 21

Other

Other	Asia-Pacific Signal and Information Processing Association Annual Summit and Conference 2011, APSIPA ASC 2011
Country/Territory	China
City	Xi'an
Period	11/10/18 → 11/10/21

ASJC Scopus subject areas

Information Systems
Signal Processing

Cite this

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title = "On extensions of LARS by information geometry: Convex objectives and{\` }p-norm",

abstract = "This paper addresses extensions of the Least Angle Regression (LARS) algorithm from two different aspects: (i) from quadratic to more general objectives, and (ii) from{\` }1-norm to{\` }p-norm for p < 1. The equiangular vector, which is the key of LARS, is reproduced in connection with the Riemannian metric induced by the objective function, thereby making the extensions feasible. It is shown, in the case of p < 1, that two types of trajectory . the c-trajectory and the λ-trajectory . need to be distinguished by revealing the discontinuity of the λ-trajectory.",

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AB - This paper addresses extensions of the Least Angle Regression (LARS) algorithm from two different aspects: (i) from quadratic to more general objectives, and (ii) from ̀1-norm to ̀p-norm for p < 1. The equiangular vector, which is the key of LARS, is reproduced in connection with the Riemannian metric induced by the objective function, thereby making the extensions feasible. It is shown, in the case of p < 1, that two types of trajectory . the c-trajectory and the λ-trajectory . need to be distinguished by revealing the discontinuity of the λ-trajectory.

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Y2 - 18 October 2011 through 21 October 2011

ER -

On extensions of LARS by information geometry: Convex objectives and ̀p-norm

Abstract

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ASJC Scopus subject areas

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