Multi-Task Learning using Generalized t Process

Yu Zhang, Dit–Yan Yeung
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:964-971, 2010.

Abstract

Multi-task learning seeks to improve the generalization performance of a learning task with the help of other related learning tasks. Among the multi-task learning methods proposed thus far, Bonilla et al.’s method provides a novel multi-task extension of Gaussian process (GP) by using a task covariance matrix to model the relationships between tasks. However, learning the task covariance matrix directly has both computational and representational drawbacks. In this paper, we propose a Bayesian extension by modeling the task covariance matrix as a random matrix with an inverse-Wishart prior and integrating it out to achieve Bayesian model averaging. To make the computation feasible, we first give an alternative weight-space view of Bonilla et al.’s multi-task GP model and then integrate out the task covariance matrix in the model, leading to a multi-task generalized t process (MTGTP). For the likelihood, we use a generalized t noise model which, together with the generalized t process prior, brings about the robustness advantage as well as an analytical form for the marginal likelihood. In order to specify the inverse-Wishart prior, we use the maximum mean discrepancy (MMD) statistic to estimate the parameter matrix of the inverse-Wishart prior. Moreover, we investigate some theoretical properties of MTGTP, such as its asymptotic analysis and learning curve. Comparative experimental studies on two common multi-task learning applications show very promising results.

Cite this Paper


BibTeX
@InProceedings{pmlr-v9-zhang10c, title = {Multi-Task Learning using Generalized t Process}, author = {Zhang, Yu and Yeung, Dit–Yan}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {964--971}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/zhang10c/zhang10c.pdf}, url = { http://proceedings.mlr.press/v9/zhang10c.html }, abstract = {Multi-task learning seeks to improve the generalization performance of a learning task with the help of other related learning tasks. Among the multi-task learning methods proposed thus far, Bonilla et al.’s method provides a novel multi-task extension of Gaussian process (GP) by using a task covariance matrix to model the relationships between tasks. However, learning the task covariance matrix directly has both computational and representational drawbacks. In this paper, we propose a Bayesian extension by modeling the task covariance matrix as a random matrix with an inverse-Wishart prior and integrating it out to achieve Bayesian model averaging. To make the computation feasible, we first give an alternative weight-space view of Bonilla et al.’s multi-task GP model and then integrate out the task covariance matrix in the model, leading to a multi-task generalized t process (MTGTP). For the likelihood, we use a generalized t noise model which, together with the generalized t process prior, brings about the robustness advantage as well as an analytical form for the marginal likelihood. In order to specify the inverse-Wishart prior, we use the maximum mean discrepancy (MMD) statistic to estimate the parameter matrix of the inverse-Wishart prior. Moreover, we investigate some theoretical properties of MTGTP, such as its asymptotic analysis and learning curve. Comparative experimental studies on two common multi-task learning applications show very promising results.} }
Endnote
%0 Conference Paper %T Multi-Task Learning using Generalized t Process %A Yu Zhang %A Dit–Yan Yeung %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-zhang10c %I PMLR %P 964--971 %U http://proceedings.mlr.press/v9/zhang10c.html %V 9 %X Multi-task learning seeks to improve the generalization performance of a learning task with the help of other related learning tasks. Among the multi-task learning methods proposed thus far, Bonilla et al.’s method provides a novel multi-task extension of Gaussian process (GP) by using a task covariance matrix to model the relationships between tasks. However, learning the task covariance matrix directly has both computational and representational drawbacks. In this paper, we propose a Bayesian extension by modeling the task covariance matrix as a random matrix with an inverse-Wishart prior and integrating it out to achieve Bayesian model averaging. To make the computation feasible, we first give an alternative weight-space view of Bonilla et al.’s multi-task GP model and then integrate out the task covariance matrix in the model, leading to a multi-task generalized t process (MTGTP). For the likelihood, we use a generalized t noise model which, together with the generalized t process prior, brings about the robustness advantage as well as an analytical form for the marginal likelihood. In order to specify the inverse-Wishart prior, we use the maximum mean discrepancy (MMD) statistic to estimate the parameter matrix of the inverse-Wishart prior. Moreover, we investigate some theoretical properties of MTGTP, such as its asymptotic analysis and learning curve. Comparative experimental studies on two common multi-task learning applications show very promising results.
RIS
TY - CPAPER TI - Multi-Task Learning using Generalized t Process AU - Yu Zhang AU - Dit–Yan Yeung BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-zhang10c PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 964 EP - 971 L1 - http://proceedings.mlr.press/v9/zhang10c/zhang10c.pdf UR - http://proceedings.mlr.press/v9/zhang10c.html AB - Multi-task learning seeks to improve the generalization performance of a learning task with the help of other related learning tasks. Among the multi-task learning methods proposed thus far, Bonilla et al.’s method provides a novel multi-task extension of Gaussian process (GP) by using a task covariance matrix to model the relationships between tasks. However, learning the task covariance matrix directly has both computational and representational drawbacks. In this paper, we propose a Bayesian extension by modeling the task covariance matrix as a random matrix with an inverse-Wishart prior and integrating it out to achieve Bayesian model averaging. To make the computation feasible, we first give an alternative weight-space view of Bonilla et al.’s multi-task GP model and then integrate out the task covariance matrix in the model, leading to a multi-task generalized t process (MTGTP). For the likelihood, we use a generalized t noise model which, together with the generalized t process prior, brings about the robustness advantage as well as an analytical form for the marginal likelihood. In order to specify the inverse-Wishart prior, we use the maximum mean discrepancy (MMD) statistic to estimate the parameter matrix of the inverse-Wishart prior. Moreover, we investigate some theoretical properties of MTGTP, such as its asymptotic analysis and learning curve. Comparative experimental studies on two common multi-task learning applications show very promising results. ER -
APA
Zhang, Y. & Yeung, D.. (2010). Multi-Task Learning using Generalized t Process. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:964-971 Available from http://proceedings.mlr.press/v9/zhang10c.html .

Related Material