Embedding Probabilities in Predication Space with Hermitian Holographic Reduced Representations

Predication-based Semantic Indexing (PSI) is an approach to generating high-dimensional vector representations of concept-relation-concept triplets. In this paper, we develop a variant of PSI that accommodates estimation of the probability of encountering a particular predication (such as fluoxetine TREATS major depressive disorder) in a collection of predications concerning a concept of interest (such as major depressive disorder). PSI leverages reversible vector transformations provided by representational approaches known as Vector Symbolic Architectures (VSA). To embed probabilities we develop a novel VSA variant, Hermitian Holographic Reduced Representations, with improvements in predictive modeling experiments. The probabilistic interpretation this facilitates reveals previously unrecognized connections between PSI and quantum theory perhaps most notably that PSI’s estimation of relatedness across multiple reasoning pathways corresponds to the estimation of the probability of traversing indistinguishable pathways in accordance with the rules of quantum probability.