# Self-measuring Similarity for Multi-task Gaussian Process

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Kohei Hayashi,
Takashi Takenouchi,
Ryota Tomioka,
Hisashi Kashima
;

Proceedings of ICML Workshop on Unsupervised and Transfer Learning, PMLR 27:145-153, 2012.

#### Abstract

Multi-task learning aims at transferring knowledge between similar tasks. The multi-task Gaussian process framework of Bonilla *et al.* models (incomplete) responses of $C$ data points for $R$ tasks (e.g., the responses are given by an $R \times C$ matrix) by using a Gaussian process; the covariance function takes its form as the product of a covariance function defined on input-specific features and an inter-task covariance matrix (which is empirically estimated as a model parameter). We extend this framework by incorporating a novel similarity measurement, which allows for the representation of much more complex data structures. The proposed framework also enables us to exploit additional information (e.g., the input-specific features) when constructing the covariance matrices by combining additional information with the covariance function. We also derive an efficient learning algorithm which uses an iterative method to make predictions. Finally, we apply our model to a real data set of recommender systems and show that the proposed method achieves the best prediction accuracy on the data set.

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