  Approximate Bayesian computation is an established and popular method for
likelihood-free inference with applications in many disciplines. The
effectiveness of the method depends critically on the availability of well
performing summary statistics. Summary statistic selection relies heavily on
domain knowledge and carefully engineered features, and can be a laborious time
consuming process. Since the method is sensitive to data dimensionality, the
process of selecting summary statistics must balance the need to include
informative statistics and the dimensionality of the feature vector. This paper
proposes to treat the problem of dynamically selecting an appropriate summary
statistic from a given pool of candidate summary statistics as a multi-armed
bandit problem. This allows approximate Bayesian computation rejection sampling
to dynamically focus on a distribution over well performing summary statistics
as opposed to a fixed set of statistics. The proposed method is unique in that
it does not require any pre-processing and is scalable to a large number of
candidate statistics. This enables efficient use of a large library of possible
time series summary statistics without prior feature engineering. The proposed
approach is compared to state-of-the-art methods for summary statistics
selection using a challenging test problem from the systems biology literature.
