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The Linear Model of Co-regionalization (LMC) is a very general model ofmultitask gaussian process for regression or classification. While itsexpressivity and conceptual simplicity are appealing, naive implementationshave cubic complexity in the number of datapoints and number of tasks, makingapproximations mandatory for most applications. However, recent work has shownthat under some conditions the latent processes of the model can be decoupled,leading to a complexity that is only linear in the number of said processes. Wehere extend these results, showing from the most general assumptions that theonly condition necessary to an efficient exact computation of the LMC is a mildhypothesis on the noise model. We introduce a full parametrization of theresulting \emph{projected LMC} model, and an expression of the marginallikelihood enabling efficient optimization. We perform a parametric study onsynthetic data to show the excellent performance of our approach, compared toan unrestricted exact LMC and approximations of the latter. Overall, theprojected LMC appears as a credible and simpler alternative to state-of-the artmodels, which greatly facilitates some computations such as leave-one-outcross-validation and fantasization.

Exact and efficient solutions of the LMC Multitask Gaussian Process model