Proximal Multitask Learning Over Networks With Sparsity-Inducing Coregularization
In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number of similar entries. We propose a fully distributed algorithm...
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| Published in | IEEE transactions on signal processing Vol. 64; no. 23; pp. 6329 - 6344 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
IEEE
01.12.2016
Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1053-587X 1941-0476 1941-0476 |
| DOI | 10.1109/TSP.2016.2601282 |
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| Abstract | In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number of similar entries. We propose a fully distributed algorithm for solving this problem. The approach relies on minimizing a global mean-square error criterion regularized by nondifferentiable terms to promote cooperation among neighboring clusters. A general diffusion forward-backward splitting strategy is introduced. Then, it is specialized to the case of sparsity promoting regularizers. A closed-form expression for the proximal operator of a weighted sum of ℓ 1 -norms is derived to achieve higher efficiency. We also provide conditions on the step-sizes that ensure convergence of the algorithm in the mean and mean-square error sense. Simulations are conducted to illustrate the effectiveness of the strategy. |
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| AbstractList | In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number of similar entries. We propose a fully distributed algorithm for solving this problem. The approach relies on minimizing a global mean-square error criterion regularized by nondifferentiable terms to promote cooperation among neighboring clusters. A general diffusion forward-backward splitting strategy is introduced. Then, it is specialized to the case of sparsity promoting regularizers. A closed-form expression for the proximal operator of a weighted sum of ℓ 1 -norms is derived to achieve higher efficiency. We also provide conditions on the step-sizes that ensure convergence of the algorithm in the mean and mean-square error sense. Simulations are conducted to illustrate the effectiveness of the strategy. In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number of similar entries. We propose a fully distributed algorithm for solving this problem. The approach relies on minimizing a global mean-square error criterion regularized by non-differentiable terms to promote cooperation among neighboring clusters. A general diffusion forward-backward splitting strategy is introduced. Then, it is specialized to the case of sparsity promoting regularizers. A closed-form expression for the proximal operator of a weighted sum of ℓ1-norms is derived to achieve higher efficiency. We also provide conditions on the step-sizes that ensure convergence of the algorithm in the mean and mean-square error sense. Simulations are conducted to illustrate the effectiveness of the strategy. |
| Author | Richard, Cedric Ferrari, Andre Nassif, Roula Sayed, Ali H. |
| Author_xml | – sequence: 1 givenname: Roula surname: Nassif fullname: Nassif, Roula email: roula.nassif@oca.eu organization: OCA, Univ. Cote d'Azur, Nice, France – sequence: 2 givenname: Cedric surname: Richard fullname: Richard, Cedric email: cedric.richard@unice.fr organization: OCA, Univ. Cote d'Azur, Nice, France – sequence: 3 givenname: Andre surname: Ferrari fullname: Ferrari, Andre email: andre.ferrari@unice.fr organization: OCA, Univ. Cote d'Azur, Nice, France – sequence: 4 givenname: Ali H. surname: Sayed fullname: Sayed, Ali H. email: sayed@ee.ucla.edu organization: Dept. of Electr. Eng., Univ. of California, Los Angeles, Los Angeles, CA, USA |
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| SubjectTerms | adaptive regularization factors Adaptive systems Closed-form solutions Computer Science Convergence diffusion LMS Distributed algorithms Distributed processing Estimation forward-backward splitting approach Machine Learning Mean square error methods Multiagent Systems multitask networks Signal processing algorithms sparsity-inducing coregularizers Systems and Control |
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| Title | Proximal Multitask Learning Over Networks With Sparsity-Inducing Coregularization |
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