  Meta-learning has proven to be successful for few-shot learning across the
regression, classification, and reinforcement learning paradigms. Recent
approaches have adopted Bayesian interpretations to improve gradient-based
meta-learners by quantifying the uncertainty of the post-adaptation estimates.
Most of these works almost completely ignore the latent relationship between
the covariate distribution $(p(x))$ of a task and the corresponding conditional
distribution $p(y|x)$. In this paper, we identify the need to explicitly model
the meta-distribution over the task covariates in a hierarchical Bayesian
framework. We begin by introducing a graphical model that leverages the samples
from the marginal $p(x)$ to better infer the posterior over the optimal
parameters of the conditional distribution $(p(y|x))$ for each task. Based on
this model we propose a computationally feasible meta-learning algorithm by
introducing meaningful relaxations in our final objective. We demonstrate the
gains of our algorithm over initialization based meta-learning baselines on
popular classification benchmarks. Finally, to understand the potential benefit
of modeling task covariates we further evaluate our method on a synthetic
regression dataset.
