Adaptive multi-task sparse learning with an application to fMRI study

Xi Chen, Jinghui He, Rick Lawrence, Jaime G. Carbonell

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

In this paper, we consider the multi-task sparse learning problem under the assumption that the dimensionality diverges with the sample size. The traditional l1/l2 multi-task lasso does not enjoy the oracle property unless a rather strong condition is enforced. Inspired by adaptive lasso, we propose a multi-stage procedure, adaptive multi-task lasso, to simultaneously conduct model estimation and variable selection across different tasks. Motivated by adaptive elastic-net, we further propose the adaptive multi-task elastic-net by adding another quadratic penalty to address the problem of collinearity. When the number of tasks is fixed, under weak assumptions, we establish the asymptotic oracle property for the proposed adaptive multi-task sparse learning methods including both adaptive multitask lasso and elastic-net. In addition to the desirable asymptotic property, we show by simulations that adaptive sparse learning methods also achieve much improved finite sample performance. As a case study, we apply adaptive multi-task elastic-net to a cognitive science problem, where one wants to discover a compact semantic basis for predicting fMRI images. We show that adaptive multi-task sparse learning methods achieve superior performance and provide some insights into how the brain represents meanings of words.

Original languageEnglish (US)
Title of host publicationProceedings of the 12th SIAM International Conference on Data Mining, SDM 2012
PublisherSociety for Industrial and Applied Mathematics Publications
Pages212-223
Number of pages12
ISBN (Print)9781611972320
DOIs
StatePublished - Jan 1 2012
Event12th SIAM International Conference on Data Mining, SDM 2012 - Anaheim, CA, United States
Duration: Apr 26 2012Apr 28 2012

Publication series

NameProceedings of the 12th SIAM International Conference on Data Mining, SDM 2012

Other

Other12th SIAM International Conference on Data Mining, SDM 2012
CountryUnited States
CityAnaheim, CA
Period4/26/124/28/12

ASJC Scopus subject areas

  • Computer Science Applications

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  • Cite this

    Chen, X., He, J., Lawrence, R., & Carbonell, J. G. (2012). Adaptive multi-task sparse learning with an application to fMRI study. In Proceedings of the 12th SIAM International Conference on Data Mining, SDM 2012 (pp. 212-223). (Proceedings of the 12th SIAM International Conference on Data Mining, SDM 2012). Society for Industrial and Applied Mathematics Publications. https://doi.org/10.1137/1.9781611972825.19