  Risk-based active learning is an approach to developing statistical
classifiers for online decision-support. In this approach, data-label querying
is guided according to the expected value of perfect information for incipient
data points. For SHM applications, the value of information is evaluated with
respect to a maintenance decision process, and the data-label querying
corresponds to the inspection of a structure to determine its health state.
Sampling bias is a known issue within active-learning paradigms; this occurs
when an active learning process over- or undersamples specific regions of a
feature-space, thereby resulting in a training set that is not representative
of the underlying distribution. This bias ultimately degrades decision-making
performance, and as a consequence, results in unnecessary costs incurred. The
current paper outlines a risk-based approach to active learning that utilises a
semi-supervised Gaussian mixture model. The semi-supervised approach
counteracts sampling bias by incorporating pseudo-labels for unlabelled data
via an EM algorithm. The approach is demonstrated on a numerical example
representative of the decision processes found in SHM.
