59c33016884a62116be975a9bb8257e3-Reviews.html

It is assumed that all the training outputs are observed at all inputs, which leads to a Kronecker product covariance. Noisy observations are modeled via a structured process and this is the main contribution of the paper. While previous work on multi-task GP approaches with Kronecker covariances has considered iid noise in order to carry out efficient computations, this paper shows that it is possible to consider a noise process with Kronecker structure, while maintaining efficient computations. In other words, as in the iid noise case, one never has to compute a Kronecker product and hence computations are O(N 3 T 3) instead of O(N 3T 3). This is achieved by whitening the noise process and projecting the (noiseless) covariance of the system into the eigen-basis of the noise covariance (scaled by the eigenvalues). Their experiments show that the proposed structured-noise multi-task GP approach outperforms the baseline iid-noise multi-task GP method and independent GPs on synthetic data and real applications.