A study of the kinematics of probabilities in information retrieval

In Information Retrieval (IR), probabilistic modelling is related to the use of a model that ranks documents in decreasing order of their estimated probability of relevance to a user's information need expressed by a query. In an IR system based on a probabilistic model, the user is guided to examine first the documents that are the most likely to be relevant to his need. If the system performed well, these documents should be at the top of the retrieved list. In mathematical terms the problem consists of estimating the probability P(R | q,d), that is the probability of relevance given a query q and a document d. This estimate should be performed for every document in the collection, and documents should then be ranked according to this measure. For this evaluation the system should make use of all the information available in the indexing term space. This thesis contains a study of the kinematics of probabilities in probabilistic IR. The aim is to get a better insight of the behaviour of the probabilistic models of IR currently in use and to propose new and more effective models by exploiting different kinematics of probabilities. The study is performed both from a theoretical and an experimental point of view. Theoretically, the thesis explores the use of the probability of a conditional, namely P(d → q), to estimate the conditional probability P(R | q,d). This is achieved by interpreting the term space in the context of the "possible worlds semantics". Previous approaches in this direction had as their basic assumption the consideration that "a document is a possible world". In this thesis a different approach is adopted, based on the assumption that "a term is a possible world". This approach enables the exploitation of term-term semantic relationships in the term space, estimated using an information theoretic measure. This form of information is rarely used in IR at retrieval time. Two new models of IR are proposed, based on two different way of estimating P(d → q) using a logical technique called Imaging. The first model is called Retrieval by Logical Imaging; the second is called Retrieval by General Logical Imaging, being a generalisation of the first model. The probability kinematics of these two models is compared with that of two other proposed models: the Retrieval by Joint Probability model and the Retrieval by Conditional Probability model. These last two models mimic the probability kinematics of the Vector Space model and of the Probabilistic Retrieval model. Experimentally, the retrieval effectiveness of the above four models is analysed and compared using five test collections of different sizes and characteristics. The results of this experimentation depend heavily on the choice of term weight and term similarity measures adopted. The most important conclusion of this thesis is that theoretically a probability transfer that takes into account the semantic similarity between the probability-donor and the probability-recipient is more effective than a probability transfer that does not take that into account. In the context of IR this is equivalent to saying that models that exploit the semantic similarity between terms in the term space at retrieval time are more effective that models that do not do that. Unfortunately, while the experimental investigation carried out using small test collections provide evidence supporting this conclusion, experiments performed using larger test collections do not provide as much supporting evidence (although they do not provide contrasting evidence either). The peculiar characteristics of the term space of different collections play an important role in shaping the effects that different probability kinematics have on the effectiveness of the retrieval process. The above result suggests the necessity and the usefulness of further investigations into more complex and optimised models of probabilistic IR, where probability kinematics follows non-classical approaches. The models proposed in this thesis are just two such approaches; other ones can be developed using recent results achieved in other fields, such as non-classical logics and belief revision theory