  Meta-Learning is a family of methods that use a set of interrelated tasks to
learn a model that can quickly learn a new query task from a possibly small
contextual dataset. In this study, we use a probabilistic framework to
formalize what it means for two tasks to be related and reframe the
meta-learning problem into the problem of Bayesian risk minimization (BRM). In
our formulation, the BRM optimal solution is given by the predictive
distribution computed from the posterior distribution of the task-specific
latent variable conditioned on the contextual dataset, and this justifies the
philosophy of Neural Process. However, the posterior distribution in Neural
Process violates the way the posterior distribution changes with the contextual
dataset. To address this problem, we present a novel Gaussian approximation for
the posterior distribution that generalizes the posterior of the linear
Gaussian model. Unlike that of the Neural Process, our approximation of the
posterior distributions converges to the maximum likelihood estimate with the
same rate as the true posterior distribution. We also demonstrate the
competitiveness of our approach on benchmark datasets.
