Probabilistic models require the notion of event space for defining a probability measure. An event space has a probability measure which ensues the Kolmogorov axioms. However, the probabilities observed from distinct sources, such as that of relevance of documents, may not admit a single event space thus causing some issues. In this article, some results are introduced for ensuring whether the observed prob- abilities of relevance of documents admit a single event space. More- over, an alternative framework of probability is introduced, thus chal- lenging the use of classical probability for ranking documents. Some reflections on the convenience of extending the classical probabilis- tic retrieval toward a more general framework which encompasses the issues are made.
Probabilistic models require the notion of event space for defining a probability measure. An event space has a probability measure which ensues the Kolmogorov axioms. However, the probabilities observed from distinct sources, such as that of relevance of documents, may not admit a single event space thus causing some issues. In this article, some results are introduced for ensuring whether the observed prob- abilities of relevance of documents admit a single event space. More- over, an alternative framework of probability is introduced, thus chal- lenging the use of classical probability for ranking documents. Some reflections on the convenience of extending the classical probabilis- tic retrieval toward a more general framework which encompasses the issues are made.
According to the probability ranking principle, the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key point of this principle is the separation of the document set into two subsets with a given level of fallout and with the highest recall. If subsets of set measures are replaced by subspaces and space measures, we obtain an alternative theory stemming from Quantum Theory. That theory is named after vector probability because vectors represent event like sets do in classical probability. The paper shows that the separation into vector subspaces is more effective than the separation into subsets with the same available evidence. The result is proved mathematically and verified experimentally. In general, the paper suggests that quantum theory is not only a source of rhetoric inspiration, but is a sufficient condition to improve retrieval effectiveness in a principled way.
The probabilistic formalism of quantum physics is said to provide a sound basis for building a principled information retrieval framework. Such a framework can be based on the notion of information need vector spaces where events, such as document relevance or observed user interactions, correspond to subspaces. As in quantum theory, a probability distribution over these subspaces is defined through weighted sets of state vectors (density operators), and used to represent the current view of the retrieval system on the user information need. Tensor spaces can be used to capture different aspects of information needs. Our evaluation shows that the framework can lead to acceptable performance in an ad-hoc retrieval task. Going beyond this, we discuss the potential of the framework for three active challenges in information retrieval, namely, interaction, novelty and diversity.
Document ranking based on probabilistic evaluations of relevance is known to exhibit non-classical correlations, which may be explained by admitting a complex structure of the event space, namely, by assuming the events to emerge from multiple sample spaces. The structure of event space formed by overlapping sample spaces is known in quantum mechanics, they may exhibit some counter-intuitive features, called quantum contextuality. In this Note I observe that from the structural point of view quantum contextuality looks similar to personalization of information retrieval scenarios. Along these lines, Knowledge Revision is treated as operationalistic measurement and a way to quantify the rate of personalization of Information Retrieval scenarios is suggested.
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.
In the light of Quantum Physics, probabilistic technique is said to support a backbone in the domain of Quantum Information Retrieval (QIR). This well known domain is based on the Quantum Probability Theory, which is used to examine the probability of relevance of a document given a user's query. The Quantum Probability Ranking Principle (QPRP), captures dependencies between documents in absolute way via “quantum interference” by considering a single vector i.e., one-dimension subspace. The HAL semantic space can be used to capture meaning of the document of information needs by representing the document into a high dimensional semantic space. This paper presents an investigation of the Quantum Probability Ranking Principle with the concept of HAL semantic space such that which can act as a bridge the gap between Quantum Probability Theory and HAL semantic space, that can results to agreeable performance in an ad-hoc retrieval task of document ranking.
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.