  Approximate Bayesian Computation is widely used in systems biology for
inferring parameters in stochastic gene regulatory network models. Its
performance hinges critically on the ability to summarize high-dimensional
system responses such as time series into a few informative, low-dimensional
summary statistics. The quality of those statistics acutely impacts the
accuracy of the inference task. Existing methods to select the best subset out
of a pool of candidate statistics do not scale well with large pools of several
tens to hundreds of candidate statistics. Since high quality statistics are
imperative for good performance, this becomes a serious bottleneck when
performing inference on complex and high-dimensional problems. This paper
proposes a convolutional neural network architecture for automatically learning
informative summary statistics of temporal responses. We show that the proposed
network can effectively circumvent the statistics selection problem of the
preprocessing step for ABC inference. The proposed approach is demonstrated on
two benchmark problem and one challenging inference problem learning parameters
in a high-dimensional stochastic genetic oscillator. We also study the impact
of experimental design on network performance by comparing different data
richness and data acquisition strategies.
