  Seasonal influenza causes on average 425,000 hospitalizations and 32,000
deaths per year in the United States. Forecasts of influenza-like illness (ILI)
-- a surrogate for the proportion of patients infected with influenza --
support public health decision making. The goal of an ensemble forecast of ILI
is to increase accuracy and calibration compared to individual forecasts and to
provide a single, cohesive prediction of future influenza. However, an ensemble
may be composed of models that produce similar forecasts, causing issues with
ensemble forecast performance and non-identifiability. To improve upon the
above issues we propose a novel Cluster-Aggregate-Pool or `CAP' ensemble
algorithm that first clusters together individual forecasts, aggregates
individual models that belong to the same cluster into a single forecast
(called a cluster forecast), and then pools together cluster forecasts via a
linear pool. When compared to a non-CAP approach, we find that a CAP ensemble
improves calibration by approximately 10% while maintaining similar accuracy to
non-CAP alternatives. In addition, our CAP algorithm (i) generalizes past
ensemble work associated with influenza forecasting and introduces a framework
for future ensemble work, (ii) automatically accounts for missing forecasts
from individual models, (iii) allows public health officials to participate in
the ensemble by assigning individual models to clusters, and (iv) provide an
additional signal about when peak influenza may be near.
