Deep Moment Matching Kernel for Multi-source Gaussian Processes

Chi-Ken Lu, Patrick Shafto

Human learners have the ability to solve new tasks efficiently if previous knowledge is relevant, which has motivated research into few-shot learning and transfer learning. We formalize the integration of relevant knowledge as multi-source regression in which the target function is inferred using Gaussian Process (GP) with the deep moment matching (DMM) kernel. We obtain a non-stationary DMM kernel from prior relevant data by analytically calculating the covariance of the target function. We interpret the data-informed DMM kernel, which serves as prior for target function, as: (1) a refined similarity determined by squared distance in the latent space and (2) as propagating uncertainty measured in RKHS defined by the posterior covariance from the prior learning. In comparison with the autoregressive models, variational DGP models and others, results show GP regression with the DMM kernels is effective when applying to the standard synthetic and real-world multi-fidelity data sets.

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