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.
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.
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-inspired algorithms represent an important direction in modern software information technologies that use heuristic methods and approaches of quantum science. This work presents a quantum approach for document search, retrieval, and ranking based on the Bell-like test, which is well-known in quantum physics. We propose quantum probability theory in the hyperspace analog to language (HAL) framework exploiting a Hilbert space for word and document vector specification. The quantum approach allows for accounting for specific user preferences in different contexts. To verify the algorithm proposed, we use a dataset of synthetic advertising text documents from travel agencies generated by the OpenAI GPT-4 model. We show that the "entanglement" in two-word document search and retrieval can be recognized as the frequent occurrence of two words in incompatible query contexts. We have found that the user preferences and word ordering in the query play a significant role in relatively small sizes of the HAL window. The comparison with the cosine similarity metrics demonstrates the key advantages of our approach based on the user-enforced contextual and semantic relationships between words and not just their superficial occurrence in texts. Our approach to retrieving and ranking documents allows for the creation of new information search engines that require no resource-intensive deep machine learning 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.
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.
Tests are essential in Information Retrieval and Data Mining in order to evaluate the effectiveness of a query. An automatic measure tool intended to exhibit the meaning of words in context has been developed and linked with Quantum Theory, particularly entanglement. "Quantum like" experiments were undertaken on semantic space based on the Hyperspace Analogue Language (HAL) method. A quantum HAL model was implemented using state vectors issued from the HAL matrix and query observables, testing a wide range of windows sizes. The Bell parameter S, associating measures on two words in a document, was derived showing peaks for specific window sizes. The peaks show maximum quantum violation of the Bell inequalities and are document dependent. This new correlation measure inspired by Quantum Theory could be promising for measuring query relevance.
The subject of study. The paper focuses on the extraction of semantics from texts in Arabic. In particular, the applicability of the Bell test to word pairs is investigated as a measure of the semantic words relatedness in a context. The study applies the quantum formalism to the task of information retrieval in Arabic texts and presents the results of this work. The authors also examine the influence of the context width on the effectiveness of information retrieval. Method. The research is based on the vector representation of the context. It uses the well-known approach based on the HAL (Hyperspace Analogue to Language) matrix and Bell test. The HAL matrix allows taking into account both the frequency of the words occurrence in the context and the distance to the target word. Quantum theory operates with probability density matrices. Quantum theory allows describing probabilities in the vector space in a more natural way i.e., words can be represented as vectors. Main results. The results demonstrate that using the Bell’s test for texts in Arabic provides a better ranking of search results compared to the results of search services. Practical significance. The research results can be used in the development of the information retrieval systems, as well as for the further development of methods based on the distributive hypothesis.