Generalized Spectral Mixture Kernels for Multi-Task Gaussian Processes

Multi-Task Gaussian processes (MTGPs) have shown a significant progress both in expressiveness and interpretation of the relatedness between different tasks: from linear combinations of independent single-output Gaussian processes (GPs), through the direct modeling of the cross-covariances such as spectral mixture kernels with phase shift, to the design of multivariate covariance functions based on spectral mixture kernels which model delays among tasks in addition to phase differences, and which provide a parametric interpretation of the relatedness across tasks. In this paper we further extend expressiveness and interpretability of MTGPs models and introduce a new family of kernels capable to model nonlinear correlations between tasks as well as dependencies between spectral mixtures, including time and phase delay. Specifically, we use generalized convolution spectral mixture kernels for modeling dependencies at spectral mixture level, and coupling coregionalization for discovering task level correlations. The proposed kernels for MTGP are validated on artificial data and compared with existing MTGPs methods on three real-world experiments. Results indicate the benefits of our more expressive representation with respect to performance and interpretability.