hal-00610534, version 1

Multi-task Regression using Minimal Penalties

Matthieu Solnon () ^1, 2, Sylvain Arlot () ^1, 2, Francis Bach () ^1, 2

(2011-07-22)

• 1:  Laboratoire d'informatique de l'école normale supérieure (LIENS)
• http://www.di.ens.fr
  CNRS : UMR8548 – Ecole normale supérieure de Paris - ENS Paris 45 Rue d'Ulm 75230 PARIS CEDEX 05 France
• 2:  SIERRA (INRIA Paris - Rocquencourt)
• 
  INRIA : PARIS - ROCQUENCOURT – Ecole normale supérieure de Paris - ENS Paris – CNRS : UMR8548 INRIA 23 avenue d'Italie 75013 Paris France

Bibliographic reference

• Type of document: Documents without publication reference (Preprint)
• Subject:

  Mathematics/Statistics

  Statistics/Statistics Theory

  Statistics/Machine Learning

• Title: Multi-task Regression using Minimal Penalties
• Abstract: In this paper we study the kernel multiple ridge regression framework, which we refer to as multi-task regression, using penalization techniques. The theoretical analysis of this problem shows that the key element appearing for an optimal calibration is the covariance matrix of the noise between the different tasks. We present a new algorithm to estimate this covariance matrix, based on the concept of minimal penalty, which was previously used in the single-task regression framework to estimate the variance of the noise. We show, in a non-asymptotic setting and under mild assumptions on the target function, that this estimator converges towards the covariance matrix. Then plugging this estimator into the corresponding ideal penalty leads to an oracle inequality. We illustrate the behavior of our algorithm on synthetic examples.
• Fulltext language: English
• Production date: 2011-07-22
• Keyword(s): multi-task – oracle inequalities – machine learning
• Comment: 33 pages
• ANR Project: 9776
• European project:

  Cordis number	239993
  Acronyme	SIERRA
  Title	Sparse Structured Methods for Machine Learning
  Funded by	ERC
  Start date	2009-12-01
  End date	2014-11-30
  Call identifier	ERC-2009-StG

Attached file list to this document: 

TEX

biblio_en.bib(22.8 KB)

jmlr2e.sty(12.7 KB)

multi-task_regression_solnon_arlot_bach_2011.tex(84.2 KB)

variation_n_1.eps(11.9 KB)

variation_n_2.eps(14.5 KB)

variation_n_3.eps(14.3 KB)

variation_p_1.eps(12 KB)

variation_p_2.eps(15 KB)

variation_p_3.eps(14.9 KB)

variation_sigma_1.eps(15.2 KB)

variation_sigma_2.eps(20.5 KB)

PDF

multi-task_regression_solnon_arlot_bach_2011.pdf(407.7 KB)

PS

multi-task_regression_solnon_arlot_bach_2011.ps(958.7 KB)

• hal-00610534, version 1
• http://hal.archives-ouvertes.fr/hal-00610534
• oai:hal.archives-ouvertes.fr:hal-00610534
• From: Matthieu Solnon <>
• Submitted on: Friday, 22 July 2011 13:27:32
• Updated on: Monday, 25 July 2011 11:33:13