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Submitted by Assigned_Reviewer_1 Q1 The authors propose a flexible and interpretable kernel (the CSM kernel), building on spectral mixture kernels, for learning relationships between multiple tasks. The starting point is to use Gaussian processes with 1 component spectral mixture kernels as the basis functions in a linear model of coregionalisation (SM-LMC). However, SM-LMC does not contain information about the phases between channels. Thus the authors propose the cross spectral mixture kernel, which mixes phase shifted versions of spectral mixture kernels across channels. The resulting kernel is interpretable and flexible.