  Seasonal influenza infects between 10 and 50 million people in the United
States every year, overburdening hospitals during weeks of peak incidence.
Named by the CDC as an important tool to fight the damaging effects of these
epidemics, accurate forecasts of influenza and influenza-like illness (ILI)
forewarn public health officials about when, and where, seasonal influenza
outbreaks will hit hardest. Multi-model ensemble forecasts---weighted
combinations of component models---have shown positive results in forecasting.
Ensemble forecasts of influenza outbreaks have been static, training on all
past ILI data at the beginning of a season, generating a set of optimal weights
for each model in the ensemble, and keeping the weights constant. We propose an
adaptive ensemble forecast that (i) changes model weights week-by-week
throughout the influenza season, (ii) only needs the current influenza season's
data to make predictions, and (iii) by introducing a prior distribution,
shrinks weights toward the reference equal weighting approach and adjusts for
observed ILI percentages that are subject to future revisions. We investigate
the prior's ability to impact adaptive ensemble performance and, after finding
an optimal prior via a cross-validation approach, compare our adaptive
ensemble's performance to equal-weighted and static ensembles. Applied to
forecasts of short-term ILI incidence at the regional and national level in the
US, our adaptive model outperforms a naive equal-weighted ensemble, and has
similar or better performance to the static ensemble, which requires multiple
years of training data. Adaptive ensembles are able to quickly train and
forecast during epidemics, and provide a practical tool to public health
officials looking for forecasts that can conform to unique features of a
specific season.
