Even the best information retrieval model cannot always identify the most useful answers to a user query. This is in particular the case with web search systems, where it is known that users tend to minimise their effort to access relevant information. It is, however, believed that the interaction between users and a retrieval system, such as a web search engine, can be exploited to provide better answers to users. Interactive Information Retrieval (IR) systems, in which users access information through a series of interactions with the search system, are concerned with building models for IR, where interaction plays a central role. There are many possible interactions between a user and a search system, ranging from query (re)formulation to relevance feedback. However, capturing them within a single framework is difficult and previously proposed approaches have mostly focused on relevance feedback. In this paper, we propose a general framework for interactive IR that is able to capture the full interaction process in a principled way. Our approach relies upon a generalisation of the probability framework of quantum physics, whose strong geometric component can be a key towards a successful interactive IR model.
The most related work in that field is that of Melucci's @cite_19 , which computes the probability of having a given context @math , where @math is the probability distribution generated by the document vector @math , and the subspace @math is equalled to the context and is built through user interaction. More specifically, given a set of documents deemed relevant, either using user feedback or pseudo-relevance feedback, one can compute a subspace @math corresponding to the principal components of a subspace spanned by those documents. A document vector fully included in this space will be fully relevant (probability of 1), an orthogonal one will be fully irrelevant (zero probability). Melucci's approach is dual to ours, in the sense that instead of representing users in an IN space, he considers documents in a contextual space. Our approach, which relies on an IN space, facilitates the possibility of using the different quantum evolution mechanisms to model the interaction between the user and the retrieval system.
@cite_19
2141957180 2133027741 2082729696 2033074184
Given a set @math of @math strings of total length @math , our task is to report the "most relevant"strings for a given query pattern @math . This involves somewhat more advanced query functionality than the usual pattern matching, as some notion of "most relevant" is involved. In information retrieval literature, this task is best achieved by using inverted indexes. However, inverted indexes work only for some predefined set of patterns. In the pattern matching community, the most popular pattern-matching data structures are suffix trees and suffix arrays. However, a typical suffix tree search involves going through all the occurrences of the pattern over the entire string collection, which might be a lot more than the required relevant documents. The first formal framework to study such kind of retrieval problems was given by [Muthukrishnan, 2002]. He considered two metrics for relevance: frequency and proximity. He took a threshold-based approach on these metrics and gave data structures taking @math words of space. We study this problem in a slightly different framework of reporting the top @math most relevant documents (in sorted order) under similar and more general relevance metrics. Our framework gives linear space data structure with optimal query times for arbitrary score functions. As a corollary, it improves the space utilization for the problems in [Muthukrishnan, 2002] while maintaining optimal query performance. We also develop compressed variants of these data structures for several specific relevance metrics. These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental in the quantification of uncertainty within applications in volving the blending of mathematical models with data. The finite dimensional situation is described first, along with some motivational examples. Then the development of probability measures on separable Banach space is undertaken, using a random series over an infinite set of functions to construct draws; these probability measures are used as priors in the Bayesian approach to inverse problems. Regularity of draws from the priors is studied in the natural Sobolev or Besov spaces implied by the choice of functions in the random series construction, and the Kolmogorov continuity theorem is used to extend regularity considerations to the space of Holder continuous functions. Bayes’ theorem is de rived in this prior setting, and here interpreted as finding conditions under which the posterior is absolutely continuous with respect to the prior, and determining a formula for the Radon-Nikodym derivative in terms of the likelihood of the data. Having established the form of the posterior, we then describe various properties common to it in the infinite dimensional setting. These properties include well-posedness, approximation theory, and the existence of maximum a posteriori estimators. We then describe measure-preserving dynamics, again on the infinite dimensional space, including Markov chain-Monte C arlo and sequential Monte Carlo methods, and measure-preserving reversible stochastic differential equations. By formulating the theory and algorithms on the underlying infinite dimensional space, we obtain a framework suitable for rigorous analysis of the accuracy of reconstructions, of computational complexity, as well as naturally constructing algorithms which perform well under mesh refinement, since they are inherently well-defined in infinite dimensions. This paper reports on a novel technique for literature indexing and searching in a mechanized library system. The notion of relevance is taken as the key concept in the theory of information retrieval and a comparative concept of relevance is explicated in terms of the theory of probability. The resulting technique called “Probabilistic Indexing,” allows a computing machine, given a request for information, to make a statistical inference and derive a number (called the “relevance number”) for each document, which is a measure of the probability that the document will satisfy the given request. The result of a search is an ordered list of those documents which satisfy the request ranked according to their probable relevance. The paper goes on to show that whereas in a conventional library system the cross-referencing (“see” and “see also”) is based solely on the “semantical closeness” between index terms, statistical measures of closeness between index terms can be defined and computed. Thus, given an arbitrary request consisting of one (or many) index term(s), a machine can elaborate on it to increase the probability of selecting relevant documents that would not otherwise have been selected. Finally, the paper suggests an interpretation of the whole library problem as one where the request is considered as a clue on the basis of which the library system makes a concatenated statistical inference in order to provide as an output an ordered list of those documents which most probably satisfy the information needs of the user. The extraction of relevant and meaningful information from multivariate or high-dimensional data is a challenging problem. One reason for this is that the number of possible representations, which might contain relevant information, grows exponentially with the amount of data dimensions. Also, not all views from a possibly large view space, are potentially relevant to a given analysis task or user. Focus+Context or Semantic Zoom Interfaces can help to some extent to efficiently search for interesting views or data segments, yet they show scalability problems for very large data sets. Accordingly, users are confronted with the problem of identifying interesting views, yet the manual exploration of the entire view space becomes ineffective or even infeasible. While certain quality metrics have been proposed recently to identify potentially interesting views, these often are defined in a heuristic way and do not take into account the application or user context. We introduce a framework for a feedback-driven view exploration, inspired by relevance feedback approaches used in Information Retrieval. Our basic idea is that users iteratively express their notion of interestingness when presented with candidate views. From that expression, a model representing the user's preferences, is trained and used to recommend further interesting view candidates. A decision support system monitors the exploration process and assesses the relevance-driven search process for convergence and stability. We present an instantiation of our framework for exploration of Scatter Plot Spaces based on visual features. We demonstrate the effectiveness of this implementation by a case study on two real-world datasets. We also discuss our framework in light of design alternatives and point out its usefulness for development of user- and context-dependent visual exploration systems.