  Accurate and trustworthy epidemic forecasting is an important problem that
has impact on public health planning and disease mitigation. Most existing
epidemic forecasting models disregard uncertainty quantification, resulting in
mis-calibrated predictions. Recent works in deep neural models for
uncertainty-aware time-series forecasting also have several limitations; e.g.
it is difficult to specify meaningful priors in Bayesian NNs, while methods
like deep ensembling are computationally expensive in practice. In this paper,
we fill this important gap. We model the forecasting task as a probabilistic
generative process and propose a functional neural process model called EPIFNP,
which directly models the probability density of the forecast value. EPIFNP
leverages a dynamic stochastic correlation graph to model the correlations
between sequences in a non-parametric way, and designs different stochastic
latent variables to capture functional uncertainty from different perspectives.
Our extensive experiments in a real-time flu forecasting setting show that
EPIFNP significantly outperforms previous state-of-the-art models in both
accuracy and calibration metrics, up to 2.5x in accuracy and 2.4x in
calibration. Additionally, due to properties of its generative process,EPIFNP
learns the relations between the current season and similar patterns of
historical seasons,enabling interpretable forecasts. Beyond epidemic
forecasting, the EPIFNP can be of independent interest for advancing principled
uncertainty quantification in deep sequential models for predictive analytics
