  This work introduces Dirichlet Active Learning (DiAL), a Bayesian-inspired
approach to the design of active learning algorithms. Our framework models
feature-conditional class probabilities as a Dirichlet random field and lends
observational strength between similar features in order to calibrate the
random field. This random field can then be utilized in learning tasks: in
particular, we can use current estimates of mean and variance to conduct
classification and active learning in the context where labeled data is scarce.
We demonstrate the applicability of this model to low-label rate graph learning
by constructing ``propagation operators'' based upon the graph Laplacian, and
offer computational studies demonstrating the method's competitiveness with the
state of the art. Finally, we provide rigorous guarantees regarding the ability
of this approach to ensure both exploration and exploitation, expressed
respectively in terms of cluster exploration and increased attention to
decision boundaries.
