Document ranking with quantum probabilities

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 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. We propose an interpretation of quantum interference in the document ranking scenario, and examine how quantum interference can be effectively estimated for document retrieval. 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 or comparable to alternative ranking approaches. However, when we turn to examine evaluation contexts that account for interdependent document relevance (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) then 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 in fact 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 for future research. These include (1) investigating estimations and approximations of quantum interference in qPRP, (2) exploiting complex numbers for the representation of documents and queries, and (3) applying the concepts underlying qPRP to tasks other than document ranking

Using the quantum probability ranking principle to rank interdependent documents

A known limitation of the Probability Ranking Principle (PRP) is that it does not cater for dependence between documents. Recently, the Quantum Probability Ranking Principle (QPRP) has been proposed, which implicitly captures dependencies between documents through “quantum interference”. This paper explores whether this new ranking principle leads to improved performance for subtopic retrieval, where novelty and diversity is required. In a thorough empirical investigation, models based on the PRP, as well as other recently proposed ranking strategies for subtopic retrieval (i.e. Maximal Marginal Relevance (MMR) and Portfolio Theory(PT)), are compared against the QPRP. On the given task, it is shown that the QPRP outperforms these other ranking strategies. And unlike MMR and PT, one of the main advantages of the QPRP is that no parameter estimation/tuning is required; making the QPRP both simple and effective. This research demonstrates that the application of quantum theory to problems within information retrieval can lead to significant improvements

The quantum probability ranking principle for information retrieval

While the Probability Ranking Principle for Information Retrieval provides the basis for formal models, it makes a very strong assumption regarding the dependence between documents. However, it has been observed that in real situations this assumption does not always hold. In this paper we propose a reformulation of the Probability Ranking Principle based on quantum theory. Quantum probability theory naturally includes interference effects between events. We posit that this interference captures the dependency between the judgement of document relevance. The outcome is a more sophisticated principle, the Quantum Probability Ranking Principle, that provides a more sensitive ranking which caters for interference/dependence between documents’ relevanc

Looking at Vector Space and Language Models for IR using Density Matrices

In this work, we conduct a joint analysis of both Vector Space and Language Models for IR using the mathematical framework of Quantum Theory. We shed light on how both models allocate the space of density matrices. A density matrix is shown to be a general representational tool capable of leveraging capabilities of both VSM and LM representations thus paving the way for a new generation of retrieval models. We analyze the possible implications suggested by our findings.Comment: In Proceedings of Quantum Interaction 201

The University of Glasgow at ImageClefPhoto 2009

In this paper we describe the approaches adopted to generate the five runs submitted to ImageClefPhoto 2009 by the University of Glasgow. The aim of our methods is to exploit document diversity in the rankings. All our runs used text statistics extracted from the captions associated to each image in the collection, except one run which combines the textual statistics with visual features extracted from the provided images. The results suggest that our methods based on text captions significantly improve the performance of the respective baselines, while the approach that combines visual features with text statistics shows lower levels of improvements

A Quantum Many-body Wave Function Inspired Language Modeling Approach

The recently proposed quantum language model (QLM) aimed at a principled approach to modeling term dependency by applying the quantum probability theory. The latest development for a more effective QLM has adopted word embeddings as a kind of global dependency information and integrated the quantum-inspired idea in a neural network architecture. While these quantum-inspired LMs are theoretically more general and also practically effective, they have two major limitations. First, they have not taken into account the interaction among words with multiple meanings, which is common and important in understanding natural language text. Second, the integration of the quantum-inspired LM with the neural network was mainly for effective training of parameters, yet lacking a theoretical foundation accounting for such integration. To address these two issues, in this paper, we propose a Quantum Many-body Wave Function (QMWF) inspired language modeling approach. The QMWF inspired LM can adopt the tensor product to model the aforesaid interaction among words. It also enables us to reveal the inherent necessity of using Convolutional Neural Network (CNN) in QMWF language modeling. Furthermore, our approach delivers a simple algorithm to represent and match text/sentence pairs. Systematic evaluation shows the effectiveness of the proposed QMWF-LM algorithm, in comparison with the state of the art quantum-inspired LMs and a couple of CNN-based methods, on three typical Question Answering (QA) datasets.Comment: 10 pages,4 figures,CIK

On the probabilistic logical modelling of quantum and geometrically-inspired IR

Information Retrieval approaches can mostly be classed into probabilistic, geometric or logic-based. Recently, a new unifying framework for IR has emerged that integrates a probabilistic description within a geometric framework, namely vectors in Hilbert spaces. The geometric model leads naturally to a predicate logic over linear subspaces, also known as quantum logic. In this paper we show the relation between this model and classic concepts such as the Generalised Vector Space Model, highlighting similarities and differences. We also show how some fundamental components of quantum-based IR can be modelled in a descriptive way using a well-established tool, i.e. Probabilistic Datalog