Probability Bracket Notation, Term Vector Space, Concept Fock Space and Induced Probabilistic IR Models

Abstract

After a brief introduction to Probability Bracket Notation (PBN) for discrete random variables in time-independent probability spaces, we apply both PBN and Dirac notation to investigate probabilistic modeling for information retrieval (IR). We derive the expressions of relevance of document to query (RDQ) for various probabilistic models, induced by Term Vector Space (TVS) and by Concept Fock Space (CFS). The inference network model (INM) formula is symmetric and can be used to evaluate relevance of document to document (RDD); the CFS-induced models contain ingredients of all three classical IR models. The relevance formulas are tested and compared on different scenarios against a famous textbook example.