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.

An analysis of ranking principles and retrieval strategies

The assumptions underlying the Probability Ranking Principle (PRP) have led to a number of alternative approaches that cater or compensate for the PRP’s limitations. All alternatives deviate from the PRP by incorporating dependencies. This results in a re-ranking that promotes or demotes documents depending upon their relationship with the documents that have been already ranked. In this paper, we compare and contrast the behaviour of state-of-the-art ranking strategies and principles. To do so, we tease out analytical relationships between the ranking approaches and we investigate the document kinematics to visualise the effects of the different approaches on document ranking.

When two is better than one : a study of ranking paradigms and their integrations for subtopic retrieval

In this paper, we consider the problem of document ranking in a non-traditional retrieval task, called subtopic retrieval. This task involves promoting relevant documents that cover many subtopics of a query at early ranks, providing thus diversity within the ranking. In the past years, several approaches have been proposed to diversify retrieval results. These approaches can be classified into two main paradigms, depending upon how the ranks of documents are revised for promoting diversity. In the first approach subtopic diversification is achieved implicitly, by choosing documents that are different from each other, while in the second approach this is done explicitly, by estimating the subtopics covered by documents. Within this context, we compare methods belonging to the two paradigms. Furthermore, we investigate possible strategies for integrating the two paradigms with the aim of formulating a new ranking method for subtopic retrieval. We conduct a number of experiments to empirically validate and contrast the state-of-the-art approaches as well as instantiations of our integration approach. The results show that the integration approach outperforms state-of-the-art strategies with respect to a number of measures.

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’ relevance.

Stochastic ranking method for thermostatically controllable appliances to provide regulation services

Demand response can be used for providing regulation services in the electricity markets. The retailers can bid in a day-ahead market and respond to real-time regulation signal by load control. This paper proposes a new stochastic ranking method to provide regulation services via demand response. A pool of thermostatically controllable appliances (TCAs) such as air conditioners and water heaters are adjusted using direct load control method. The selection of appliances is based on a probabilistic ranking technique utilizing attributes such as temperature variation and statuses of TCAs. These attributes are stochastically forecasted for the next time step using day-ahead information. System performance is analyzed with a sample regulation signal. Network capability to provide regulation services under various seasons is analyzed. The effect of network size on the regulation services is also investigated.

Do-Rank: DCG optimization for learning-to-rank in tag-based item recommendation systems

Discounted Cumulative Gain (DCG) is a well-known ranking evaluation measure for models built with multiple relevance graded data. By handling tagging data used in recommendation systems as an ordinal relevance set of {negative,null,positive}, we propose to build a DCG based recommendation model. We present an efficient and novel learning-to-rank method by optimizing DCG for a recommendation model using the tagging data interpretation scheme. Evaluating the proposed method on real-world datasets, we demonstrate that the method is scalable and outperforms the benchmarking methods by generating a quality top-N item recommendation list.

Relative ranking: A biased rating

Reviewers' ratings have become one of the most influential parameters when making a decision to purchase or rent the products or services from the online vendors. Star Rating system is the de-facto standard for rating a product. It is regarded as one of the most visually appealing rating systems that directly interact with the consumers; helping them find products they will like to purchase as well as register their views on the product. It offers visual advantage to pick the popular or most rated product. Any system that is not as appealing as star system will have a chance of rejection by online business community. This paper argues that, the visual advantage is not enough to declare star rating system as a triumphant, the success of a ranking system should be measured by how effectively the system helps customers make decisions that they, retrospectively, consider correct. This paper argues and suggests a novel approach of Relative Ranking within the boundaries of star rating system to overcome a few inherent disadvantages the former system comes with. © Springer Science+Business Media B.V. 2010.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.