  The Conditional Neural Process (CNP) family of models offer a promising
direction to tackle few-shot problems by achieving better scalability and
competitive predictive performance. However, the current CNP models only
capture the overall uncertainty for the prediction made on a target data point.
They lack a systematic fine-grained quantification on the distinct sources of
uncertainty that are essential for model training and decision-making under the
few-shot setting. We propose Evidential Conditional Neural Processes (ECNP),
which replace the standard Gaussian distribution used by CNP with a much richer
hierarchical Bayesian structure through evidential learning to achieve
epistemic-aleatoric uncertainty decomposition. The evidential hierarchical
structure also leads to a theoretically justified robustness over noisy
training tasks. Theoretical analysis on the proposed ECNP establishes the
relationship with CNP while offering deeper insights on the roles of the
evidential parameters. Extensive experiments conducted on both synthetic and
real-world data demonstrate the effectiveness of our proposed model in various
few-shot settings.
