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

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 Lowlands team at TRECVID 2008

In this paper we describe our experiments performed for TRECVID 2008. We participated in the High Level Feature extraction and the Search task. For the High Level Feature extraction task we mainly installed our detection environment. In the Search task we applied our new PRFUBE ranking model together with an estimation method which estimates a vital parameter of the model, the probability of a concept occurring in relevant shots. The PRFUBE model has similarities to the well known Probabilistic Text Information Retrieval methodology and follows the Probability Ranking Principle

Convergence of Learning Dynamics in Information Retrieval Games

We consider a game-theoretic model of information retrieval with strategic authors. We examine two different utility schemes: authors who aim at maximizing exposure and authors who want to maximize active selection of their content (i.e. the number of clicks). We introduce the study of author learning dynamics in such contexts. We prove that under the probability ranking principle (PRP), which forms the basis of the current state of the art ranking methods, any better-response learning dynamics converges to a pure Nash equilibrium. We also show that other ranking methods induce a strategic environment under which such a convergence may not occur

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

Maximum Likelihood Approach to Vote Aggregation with Variable Probabilities

Condorcet (1785) initiated the statistical approach to vote aggregation. Two centuries later, Young (1988) showed that a correct application of the maximum likelihood principle leads to the selection of rankings called Kemeny orders, which have the minimal total number of disagreements with those of the voters. The Condorcet-Kemeny-Yoiung approach is based on the assumption that the voters have the same probability of comparing correctly two alternatives and that this probability is the same for any pair of alternatives. We relax the second part of this assumption by letting the probability of comparing correctly two alternatives be increasing with the distance between two alternatives in the allegedly true ranking. This leads to a rule in which the majority in favor of one alternative against another one is given a larger weight the larger the distance between the two alternatives in the true ranking, i.e. the larger the probability that the voters compare them correctly. This rule is not Condorcet consistent. Thus, it may be different from the Kemeny rule. Yet, it is anonymous, neutral, and paretian. However, contrary to the Kemeny rule, it does not satisfy Young and Levenglick (1978)'s local independence of irrelevant alternatives. Condorcet also hinted that the Condorcet winner or the top alternative in the Condorcet ranking is not necessarily most likely to be the best. Young confirms that indeed with a constant probability close to 1/2, this alternative is the Borda winner while it is the alternative whose smallest majority is the largest when the probability is close to 1. We extend his analysis to the case of variable probabilities. Young's result implies that the Kemeny rule does not necessarily select the alternative most likely to be the best. A natural question that comes to mind is whether the rule obtained with variable probabilities does better than the Kemeny rule in this respect. It appears that this performance imporves with the rate at which the probability increases.Vote Aggregation, Kemeny Rule, Maximum Likelihood, Variable Probabilities

Ranking heterogeneous search result pages using the interactive Probability Ranking Principle

The Probability Ranking Principle (PRP) ranks search results based on their expected utility derived solely from document contents, often overlooking the nuances of presentation and user interaction. However, with the evolution of Search Engine Result Pages (SERPs), now comprising a variety of result cards, the manner in which these results are presented is pivotal in influencing user engagement and satisfaction. This shift prompts the question: How does the PRP and its user-centric counterpart, the Interactive Probability Ranking Principle (iPRP), compare in the context of these heterogeneous SERPs? Our study draws a comparison between the PRP and the iPRP, revealing significant differences in their output. The iPRP, accounting for item-specific costs and interaction probabilities to determine the ``Expected Perceived Utility" (EPU), yields different result orderings compared to the PRP. We evaluate the effect of the EPU on the ordering of results by observing changes in the ranking within a heterogeneous SERP compared to the traditional ``ten blue links''. We find that changing the presentation affects the ranking of items according to the (iPRP) by up to 48\% (with respect to DCG, TBG and RBO) in ad-hoc search tasks on the TREC WaPo Collection. This work suggests that the iPRP should be employed when ranking heterogeneous SERPs to provide a user-centric ranking that adapts the ordering based on the presentation and user engagement