DOCTORAL ABSTRACT

Document Ranking with Quantum Probabilities
Guido Zuccon
Australian E-Health Research Centre
CSIRO
Herston, QLD 4029
Australia
guido.zuccon@csiro.au2012
Abstract
In this thesis we investigate the use of quantum probability theory for ranking documents.
Quantum probability theory is used to estimate the probability of relevance of a document
given a user’s query. We posit that quantum probability theory can lead to a better estimation of the probability of a document being relevant to a user’s query than the common IR
approach, i. e. the Probability Ranking Principle (PRP), which is based upon Kolmogorovian
probability theory. Following our hypothesis, we formulate an analogy between the document retrieval scenario and a physical scenario, that of the double slit experiment. Throughthe analogy, we propose a novel ranking approach, the quantum probability ranking principle (qPRP). Key to our proposal is the presence of quantum interference. Mathematically,
this is the statistical deviation between empirical observations and expected values predictedby the Kolmogorovian rule of additivity of probabilities of disjoint events in configurations
such that of the double slit experiment. While PRP explicitly assumes that the relevancy
of a document is independent of that of other documents, we suggest that qPRP implicitly
models interdependent document relevance through quantum interference and thus is suited
to those document ranking tasks where the independence assumption fails. Throughout thethesis, we also suggest how quantum interference can be estimated for effective document
ranking.
To validate our proposal and to gain more insights about approaches for document ranking, we (1) analyse PRP, qPRP and other ranking approaches, exposing the assumptions
underlying their ranking criteria and formulating the conditions for the optimality of the tworanking principles, (2) empirically compare three ranking principles (i. e. PRP, interactive
PRP, and qPRP) and two state-of-the-art ranking strategies in two retrieval scenarios, thoseof ad-hoc retrieval and diversity retrieval, (3) analytically contrast the ranking criteria of theexamined approaches, exposing similarities and differences, (4) study the ranking behavioursof approaches alternative to PRP in terms of the kinematics they impose on relevant documents, i. e. by considering the extent and direction of the movements of relevant documents
across the ranking recorded when comparing PRP against its alternatives.

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Our findings show that the effectiveness of the examined ranking approaches strongly
depends upon the evaluation context. In the traditional evaluation context of ad-hoc retrieval, PRP is empirically shown to be better than or comparable to alternative ranking
approaches. However, when evaluation contexts that account for interdependent document
relevance are examined (i. e. when the relevance of a document is assessed also with respect
to other retrieved documents, as it is the case in the diversity retrieval scenario), the useof quantum probability theory and thus of qPRP is shown to improve retrieval and ranking
effectiveness over the traditional PRP and alternative ranking strategies, such as Maximal
Marginal Relevance, Portfolio theory, and Interactive PRP.
This work represents a significant step forward regarding the use of quantum theory ininformation retrieval. It demonstrates that the application of quantum theory to problems
within information retrieval can lead to improvements both in modelling power and retrieval
effectiveness, allowing the constructions of models that capture the complexity of information
retrieval situations.
Furthermore, the thesis opens up a number of lines of future research. These include
investigating estimations and approximations of quantum interference in qPRP, exploiting
complex numbers for the representation of documents and queries, and applying the concepts
underlying qPRP to tasks other than document ranking.
This dissertation was completed at School of Computing Science, University of Glasgow
under the advise of Dr. Leif Azzopardi and Prof. Keith van Rijsbergen. Prof. Norbert Fuhr,Dr. Iadh Ounis, and Dr. John O’Donnell served as dissertation committee members. For
the full dissertation, visit: http://theses.gla.ac.uk/3463/

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