  The iterative selection of examples for labeling in active machine learning
is conceptually similar to feedback channel coding in information theory: in
both tasks, the objective is to seek a minimal sequence of actions to encode
information in the presence of noise. While this high-level overlap has been
previously noted, there remain open questions on how to best formulate active
learning as a communications system to leverage existing analysis and
algorithms in feedback coding. In this work, we formally identify and leverage
the structural commonalities between the two problems, including the
characterization of encoder and noisy channel components, to design a new
algorithm. Specifically, we develop an optimal transport-based feedback coding
scheme called Approximate Posterior Matching (APM) for the task of active
example selection and explore its application to Bayesian logistic regression,
a popular model in active learning. We evaluate APM on a variety of datasets
and demonstrate learning performance comparable to existing active learning
methods, at a reduced computational cost. These results demonstrate the
potential of directly deploying concepts from feedback channel coding to design
efficient active learning strategies.
