Generalized Belief Transport

Junqi Wang, PEI WANG, Patrick Shafto

Abstract: Human learners have ability to adopt appropriate learning approaches depending on constraints such as prior on the hypothesis and urgency of decision. However, existing learning models are typically considered individually rather than in relation to one and other. To build agents that have the ability to move between different modes of learning over time, it is important to understand how learning models are related as points in a broader space of possibilities. We introduce a mathematical framework, Generalized Belief Transport (GBT), that unifies and generalizes prior models, including Bayesian inference, cooperative communication and classification, as parameterizations of three learning constraints within Unbalanced Optimal Transport (UOT). We visualize the space of learning models encoded by GBT as a cube which includes classic learning models as special points. We derive critical properties of this parameterized space including proving continuity and differentiability which is the basis for model interpolation, and study limiting behavior of the parameters, which allows attaching learning models on the boundaries. Moreover, we investigate the long-run behavior of GBT, explore convergence properties of models in GBT mathematical and computationally, and formulate conjectures about general behavior. We conclude with open questions and implications for more unified models of learning.

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