In the last years several works have investigated a formal model for Information Retrieval (IR) based on the mathematical formalism underlying quantum theory [1, 2, 3, 4, 5]. These works have mainly exploited geometric and logical–algebraic features of the quantum formalism, for example entanglement, superposition of states, collapse into basis states, lattice relationships. In this poster I present an analogy between a typical IR scenario and the double slit experiment. This experiment exhibits the presence of interference phenomena between events in a quantum system, causing the Kolmogorovian law of total probability to fail. The analogy allows to put forward the routes for the application of quantum probability theory in IR. However, several questions need still to be addressed; they will be the subject of my PhD research.
In the last years several works have investigated a formal model for Information Retrieval (IR) based on the mathematical formalism underlying quantum theory [1, 2, 3, 4, 5]. These works have mainly exploited geometric and logical–algebraic features of the quantum formalism, for example entanglement, superposition of states, collapse into basis states, lattice relationships. In this poster I present an analogy between a typical IR scenario and the double slit experiment. This experiment exhibits the presence of interference phenomena between events in a quantum system, causing the Kolmogorovian law of total probability to fail. The analogy allows to put forward the routes for the application of quantum probability theory in IR. However, several questions need still to be addressed; they will be the subject of my PhD research.
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. Through the 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 predicted by 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 the thesis, 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 two ranking 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, those of ad-hoc retrieval and diversity retrieval, (3) analytically contrast the ranking criteria of the examined approaches, exposing similarities and differences, (4) study the ranking behaviours of 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. 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 use of 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 in information 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.
Quantum theory has been applied in a number of fields outside physics, e.g., cognitive science and information retrieval (IR). Recently, it has been shown that quantum theory can subsume various key IR models into a single mathematical formalism of Hilbert vector spaces. While a series of quantum-inspired IR models has been proposed, limited effort has been devoted to verify the existence of the quantum-like phenomenon in real users’ information retrieval processes, from a real user study perspective. In this paper, we aim to explore and model the quantum interference in users’ relevance judgement about documents, caused by the presentation order of documents. A user study in the context of IR tasks have been carried out. The existence of the quantum interference is tested by the violation of the law of total probability and the validity of the order effect. Our main findings are: (1) there is an apparent judging discrepancy across different users and document presentation orders, and empirical data have violated the law of total probability; (2) most search trials recorded in the user study show the existence of the order effect, and the incompatible decision perspectives in the quantum question (QQ) model are valid in some trials. We further explain the judgement discrepancy in more depth, in terms of four effects (comparison, unfamiliarity, attraction and repulsion) and also analyse the dynamics of document relevance judgement in terms of the evolution of the information need subspace.
This thesis is fundamentally about using conceptual and mathematical constructs from the area of Quantum Theory in Information Retrieval (IR). The need and motivation for this is two-fold – firstly, it has been increasingly shown in decision sciences that human decision-making does not always conform to the norms of traditional probability and logic framework. The quantum framework offers a generalised probability and logic framework which can model decisions or judgements under dynamic context and ambiguity. Secondly, there is a need in IR for theories and models which improve our understanding of user behaviour. Hence it is worth exploring the combination of the quantum framework and IR, especially focused on the user aspects of IR. The overarching research question is whether there is evidence of user behaviour in IR scenarios which warrants the need for a quantum based approach by way of showing the limitations of the traditional (classical) approach. The methodology involves analysing data to detect quantum-like phenomena of interference, contextuality, incompatibility, etc. from two common data sources in IR–standard datasets like query log data, and through crowdsourced user studies designed similar to some quantum physics or cognitive science experiments. While the evidence of quantum-like phenomena from standard datasets is not convincing, we find that some of the user studies reveal the quantum-like structure of document judgements. One of the key findings which has implication for IR is the dynamic interactions between the different dimensions of relevance. For example, a user’s judgement of reliability of a document depends significantly on whether they found it understandable or not. Thus, the consideration of one relevance dimension or document feature can provide a context for another dimension, contrary to the current IR models which consider these features to be independent of each other and an objective property of the document. The quantum framework has been especially designed to deal with such scenarios where properties of systems or objects do not exist independent of measurement context. The thesis concludes with suggestions about incorporating quantum mathematical constructs into state-of-art IR algorithms.
In this work, we summarise the development of a ranking principle based on quantum probability theory, called the Quantum Probability Ranking Principle (QPRP), and we also provide an overview of the initial experiments performed employing the QPRP. The main difference between the QPRP and the classic Probability Ranking Principle, is that the QPRP implicitly captures the dependencies between documents by means of quantum interference". Subsequently, the optimal ranking of documents is not based solely on documents' probability of relevance but also on the interference with the previously ranked documents. Our research shows that the application of quantum theory to problems within information retrieval can lead to consistently better retrieval effectiveness, while still being simple, elegant and tractable.
Recently, Quantum Theory (QT) has been employed to advance the theory of Information Retrieval (IR). Various analogies between QT and IR have been established. Among them, a typical one is applying the idea of photon polarization in IR tasks, e.g., for document ranking and query expansion. In this paper, we aim to further extend this work by constructing a new superposed state of each document in the information need space, based on which we can incorporate the quantum interference idea in query expansion. We then apply the new quantum query expansion model to session search, which is a typical Web search task. Empirical evaluation on the large-scale Clueweb12 dataset has shown that the proposed model is effective in the session search tasks, demonstrating the potential of developing novel and effective IR models based on intuitions and formalisms of QT.
Indexing is a core process of an information retrieval (IR) system (IRS). As indexing can neither be exhaustive nor precise, the decision taken by an IRS about the relevance of the content of a document to an information need is subject to uncertainty. It is our hypothesis that one of the reasons that IRSs are unable to optimally respond to every query is that the document collections and the posting lists are modeled as sets of documents. In contrast, if vector spaces replace sets along the way given by quantum mechanics, it is possible to define a quantum information retrieval basis (QIRB) that at least in principle yields more effective document ranking than the ranking yielded by the current principles, with effectiveness being measured in terms of recall at every level of fallout. To this end, we show that the probability ranking principle and the Neyman–Pearson Lemma (NPL) are equivalent. The rest of the article follows from this result. In particular, we introduce the QIRB, link it to a generalization of the NPL and demonstrate its superiority through a concise mathematical analysis and an empirical study. The challenges posed by this basis and the research directions that would be opened are also discussed.