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
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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. This paper considers recovering @math -dimensional vectors @math , and @math from their circular convolutions @math . The vector @math is assumed to be @math -sparse in a known basis that is spread out in the Fourier domain, and each input @math is a member of a known @math -dimensional random subspace. We prove that whenever @math , the problem can be solved effectively by using only the nuclear-norm minimization as the convex relaxation, as long as the inputs are sufficiently diverse and obey @math . By “diverse inputs,” we mean that the @math ’s belong to different, generic subspaces. To the best of our knowledge, this is the first theoretical result on blind deconvolution where the subspace to which @math belongs is not fixed but needs to be determined. We discuss the result in the context of multipath channel estimation in wireless communications. Both the fading coefficients and the delays in the channel impulse response @math are unknown. The encoder codes the @math -dimensional message vectors randomly and then transmits coded messages @math ’s over a fixed channel one after the other. The decoder then discovers all of the messages and the channel response when the number of samples taken for each received message are roughly greater than @math , and the number of messages is roughly at least @math . Given a set of objects @math , each with @math numeric attributes, a top- @math preference scores these objects using a linear combination of their attribute values, where the weight on each attribute reflects the interest in this attribute. Given a query preference @math , a top- @math query finds the @math objects in @math with highest scores with respect to @math . Given a query object @math and a set of preferences @math , a reverse top- @math query finds all preferences @math for which @math becomes one of the top @math objects with respect to @math . Previous solutions to these problems are effective only in low dimensions. In this paper, we develop a solution for much higher dimensions (up to high tens), if many preferences exhibit sparsity —i.e., each specifies non-zero weights for only a handful (say @math - @math ) of attributes (though the subsets of such attributes and their weights can vary greatly). Our idea is to select carefully a set of low-dimensional core subspaces to “cover” the sparse preferences in a workload. These subspaces allow us to index them more effectively than the full-dimensional space. Being multi-dimensional, each subspace covers many possible preferences; furthermore, multiple subspaces can jointly cover a preference, thereby expanding the coverage beyond each subspace’s dimensionality. Experimental evaluation validates our solution’s effectiveness and advantages over previous solutions. We propose a new probabilistic approach to information retrieval based upon the ideas and methods of statistical machine translation. The central ingredient in this approach is a statistical model of how a user might distill or "translate" a given document into a query. To assess the relevance of a document to a user's query, we estimate the probability that the query would have been generated as a translation of the document, and factor in the user's general preferences in the form of a prior distribution over documents. We propose a simple, well motivated model of the document-to-query translation process, and describe an algorithm for learning the parameters of this model in an unsupervised manner from a collection of documents. As we show, one can view this approach as a generalization and justification of the "language modeling" strategy recently proposed by Ponte and Croft. In a series of experiments on TREC data, a simple translation-based retrieval system performs well in comparison to conventional retrieval techniques. This prototype system only begins to tap the full potential of translation-based retrieval. Motivated by online recommendation and advertising systems, we consider a causal model for stochastic contextual bandits with a latent low-dimensional confounder. In our model, there are @math observed contexts and @math arms of the bandit. The observed context influences the reward obtained through a latent confounder variable with cardinality @math ( @math ). The arm choice and the latent confounder causally determines the reward while the observed context is correlated with the confounder. Under this model, the @math mean reward matrix @math (for each context in @math and each arm in @math ) factorizes into non-negative factors @math ( @math ) and @math ( @math ). This insight enables us to propose an @math -greedy NMF-Bandit algorithm that designs a sequence of interventions (selecting specific arms), that achieves a balance between learning this low-dimensional structure and selecting the best arm to minimize regret. Our algorithm achieves a regret of @math at time @math , as compared to @math for conventional contextual bandits, assuming a constant gap between the best arm and the rest for each context. These guarantees are obtained under mild sufficiency conditions on the factors that are weaker versions of the well-known Statistical RIP condition. We further propose a class of generative models that satisfy our sufficient conditions, and derive a lower bound of @math . These are the first regret guarantees for online matrix completion with bandit feedback, when the rank is greater than one. We further compare the performance of our algorithm with the state of the art, on synthetic and real world data-sets. This paper is motivated by two applications, namely i) generalizations of cuckoo hashing, a computationally simple approach to assigning keys to objects, and ii) load balancing in content distribution networks, where one is interested in determining the impact of content replication on performance. These two problems admit a common abstraction: in both scenarios, performance is characterized by the maximum weight of a generalization of a matching in a bipartite graph, featuring node and edge capacities. Our main result is a law of large numbers characterizing the asymptotic maximum weight matching in the limit of large bipartite random graphs, when the graphs admit a local weak limit that is a tree. This result specializes to the two application scenarios, yielding new results in both contexts. In contrast with previous results, the key novelty is the ability to handle edge capacities with arbitrary integer values. An analysis of belief propagation algorithms (BP) with multivariate belief vectors underlies the proof. In particular, we show convergence of the corresponding BP by exploiting monotonicity of the belief vectors with respect to the so-called upshifted likelihood ratio stochastic order. This auxiliary result can be of independent interest, providing a new set of structural conditions which ensure convergence of BP. We study the problem of online subspace learning in the context of sequential observations involving structured perturbations. In online subspace learning, the observations are an unknown mixture of two components presented to the model sequentially - the main effect which pertains to the subspace and a residual error term. If no additional requirement is imposed on the residual, it often corresponds to noise terms in the signal which were unaccounted for by the main effect. To remedy this, one may impose "structural" contiguity, which has the intended effect of leveraging the secondary terms as a covariate that helps the estimation of the subspace itself, instead of merely serving as a noise residual. We show that the corresponding online estimation procedure can be written as an approximate optimization process on a Grassmannian. We propose an efficient numerical solution, GOSUS, Grassmannian Online Subspace Updates with Structured-sparsity, for this problem. GOSUS is expressive enough in modeling both homogeneous perturbations of the subspace and structural contiguities of outliers, and after certain manipulations, solvable via an alternating direction method of multipliers (ADMM). We evaluate the empirical performance of this algorithm on two problems of interest: online background subtraction and online multiple face tracking, and demonstrate that it achieves competitive performance with the state-of-the-art in near real time. Abstract One of the most important problems in information retrieval is determining the order of documents in the answer returned to the user. Many methods and algorithms for document ordering have been proposed. The method introduced in this paper differs from them especially in that it uses a probabilistic model of a document set. In this model documents are regarded as states of a Markov chain, where transition probabilities are directly proportional to similarities between documents. Steady-state probabilities reflect similarities of particular documents to the whole answer set. If documents are ordered according to these probabilities, at the top of a list there will be documents that are the best representatives of the set, and at the bottom those which are the worst representatives. The method was tested against databases INSPEC and Networked Computer Science Technical Reference Library (NCSTRL). Test results are positive. Values of the Kendall rank correlation coefficient indicate high similarity between rankings generated by the proposed method and rankings produced by experts. Results are comparable with rankings generated by the vector model using standard weighting schema tf·idf. A novel probabilistic retrieval model is presented. It forms a basis to interpret the TF-IDF term weights as making relevance decisions. It simulates the local relevance decision-making for every location of a document, and combines all of these “local” relevance decisions as the “document-wide” relevance decision for the document. The significance of interpreting TF-IDF in this way is the potential to: (1) establish a unifying perspective about information retrieval as relevance decision-making; and (2) develop advanced TF-IDF-related term weights for future elaborate retrieval models. Our novel retrieval model is simplified to a basic ranking formula that directly corresponds to the TF-IDF term weights. In general, we show that the term-frequency factor of the ranking formula can be rendered into different term-frequency factors of existing retrieval systems. In the basic ranking formula, the remaining quantity - log p(rvt ∈ d) is interpreted as the probability of randomly picking a nonrelevant usage (denoted by r) of term t. Mathematically, we show that this quantity can be approximated by the inverse document-frequency (IDF). Empirically, we show that this quantity is related to IDF, using four reference TREC ad hoc retrieval data collections. The probability that a user will click a search result depends both on its relevance and its position on the results page. The position based model explains this behavior by ascribing to every item an attraction probability, and to every position an examination probability. To be clicked, a result must be both attractive and examined. The probabilities of an item-position pair being clicked thus form the entries of a rank- @math matrix. We propose the learning problem of a Bernoulli rank- @math bandit where at each step, the learning agent chooses a pair of row and column arms, and receives the product of their Bernoulli-distributed values as a reward. This is a special case of the stochastic rank- @math bandit problem considered in recent work that proposed an elimination based algorithm Rank1Elim, and showed that Rank1Elim's regret scales linearly with the number of rows and columns on "benign" instances. These are the instances where the minimum of the average row and column rewards @math is bounded away from zero. The issue with Rank1Elim is that it fails to be competitive with straightforward bandit strategies as @math . In this paper we propose Rank1ElimKL which simply replaces the (crude) confidence intervals of Rank1Elim with confidence intervals based on Kullback-Leibler (KL) divergences, and with the help of a novel result concerning the scaling of KL divergences we prove that with this change, our algorithm will be competitive no matter the value of @math . Experiments with synthetic data confirm that on benign instances the performance of Rank1ElimKL is significantly better than that of even Rank1Elim, while experiments with models derived from real data confirm that the improvements are significant across the board, regardless of whether the data is benign or not. The fundamental problem of multiple secondary users contending for opportunistic spectrum access over multiple channels in cognitive radio networks has been formulated recently as a decentralized multi-armed bandit (D-MAB) problem. In a D-MAB problem there are @math users and @math arms (channels) that each offer i.i.d. stochastic rewards with unknown means so long as they are accessed without collision. The goal is to design a decentralized online learning policy that incurs minimal regret, defined as the difference between the total expected rewards accumulated by a model-aware genie, and that obtained by all users applying the policy. We make two contributions in this paper. First, we consider the setting where the users have a prioritized ranking, such that it is desired for the @math -th-ranked user to learn to access the arm offering the @math -th highest mean reward. For this problem, we present the first distributed policy that yields regret that is uniformly logarithmic over time without requiring any prior assumption about the mean rewards. Second, we consider the case when a fair access policy is required, i.e., it is desired for all users to experience the same mean reward. For this problem, we present a distributed policy that yields order-optimal regret scaling with respect to the number of users and arms, better than previously proposed policies in the literature. Both of our distributed policies make use of an innovative modification of the well known UCB1 policy for the classic multi-armed bandit problem that allows a single user to learn how to play the arm that yields the @math -th largest mean reward. Current document retrieval methods use a vector space similarity measure to give scores of relevance to documents when related to a specific query. The central problem with these methods is that they neglect any spatial information within the documents in question. We present a new method, called Fourier Domain Scoring (FDS), which takes advantage of this spatial information, via the Fourier transform, to give a more accurate ordering of relevance to a document set. We show that FDS gives an improvement in precision over the vector space similarity measures for the common case of Web like queries, and it gives similar results to the vector space measures for longer queries. Latent Dirichlet Allocation (LDA) mining thematic structure of documents plays an important role in nature language processing and machine learning areas. However, the probability distribution from LDA only describes the statistical relationship of occurrences in the corpus and usually in practice, probability is not the best choice for feature representations. Recently, embedding methods have been proposed to represent words and documents by learning essential concepts and representations, such as Word2Vec and Doc2Vec. The embedded representations have shown more effectiveness than LDA-style representations in many tasks. In this paper, we propose the Topic2Vec approach which can learn topic representations in the same semantic vector space with words, as an alternative to probability. The experimental results show that Topic2Vec achieves interesting and meaningful results. Many real world datasets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to estimate and track the low-dimensional structure with small storage requirements and computational complexity when the data dimension is high. Therefore we consider the problem of reconstructing a data stream from a small subset of its entries, where the data is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise. We further consider tracking the change of the underlying subspace, which can be applied to applications such as video denoising, network monitoring and anomaly detection. Our setting can be viewed as a sequential low-rank matrix completion problem in which the subspace is learned in an online fashion. The proposed algorithm, dubbed Parallel Estimation and Tracking by REcursive Least Squares (PETRELS), first identifies the underlying low-dimensional subspace, and then reconstructs the missing entries via least-squares estimation if required. Subspace identification is performed via a recursive procedure for each row of the subspace matrix in parallel with discounting for previous observations. Numerical examples are provided for direction-of-arrival estimation and matrix completion, comparing PETRELS with state of the art batch algorithms. Because of the world wide web, information retrieval systems are now used by millions of untrained users all over the world. The search engines that perform the information retrieval tasks, often retrieve thousands of potentially interesting documents to a query. The documents should be ranked in decreasing order of relevance in order to be useful to the user. This book describes a mathematical model of information retrieval based on the use of statistical language models. The approach uses simple document-based unigram models to compute for each document the probability that it generates the query. This probability is used to rank the documents. The study makes the following research contributions. * The development of a model that integrates term weighting, relevance feedback and structured queries. * The development of a model that supports multiple representations of a request or information need by integrating a statistical translation model. * The development of a model that supports multiple representations of a document, for instance by allowing proximity searches or searches for terms from a particular record field (e.g. a search for terms from the title). * A mathematical interpretation of stop word removal and stemming. * A mathematical interpretation of operators for mandatory terms, wildcards and synonyms. * A practical comparison of a language model-based retrieval system with similar systems that are based on well-established models and term weighting algorithms in a controlled experiment. * The application of the model to cross-language information retrieval and adaptive information filtering, and the evaluation of two prototype systems in a controlled experiment. Experimental results on three standard tasks show that the language model-based algorithms work as well as, or better than, today's top-performing retrieval algorithms. The standard tasks investigated are ad-hoc retrieval (when there are no previously retrieved documents to guide the search), retrospective relevance weighting (find the optimum model for a given set of relevant documents), and ad-hoc retrieval using manually formulated Boolean queries. The application to cross-language retrieval and adaptive filtering shows the practical use of respectively structured queries, and relevance feedback. We propose a framework for inferring the latent attitudes or preferences of users by performing probabilistic first-order logical reasoning over the social network graph. Our method answers questions about Twitter users like Does this user like sushi? or Is this user a New York Knicks fan? by building a probabilistic model that reasons over user attributes (the user's location or gender) and the social network (the user's friends and spouse), via inferences like homophily (I am more likely to like sushi if spouse or friends like sushi, I am more likely to like the Knicks if I live in New York). The algorithm uses distant supervision, semi-supervised data harvesting and vector space models to extract user attributes (e.g. spouse, education, location) and preferences (likes and dislikes) from text. The extracted propositions are then fed into a probabilistic reasoner (we investigate both Markov Logic and Probabilistic Soft Logic). Our experiments show that probabilistic logical reasoning significantly improves the performance on attribute and relation extraction, and also achieves an F-score of 0.791 at predicting a users likes or dislikes, significantly better than two strong baselines. In this article, we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular:---We show that, for any p ∈ (0, 2], one can maintain (using only O(log n e2) words of storage) a sketch C(q) of a point q ∈ lnp under dynamic updates of its coordinates. The sketch has the property that, given C(q) and C(s), one can estimate Vq − sVp up to a factor of (1 p e) with large probability. This solves the main open problem of [1999].---We show that the aforementioned sketching approach directly translates into an approximate algorithm that, for a fixed linear mapping A, and given x ∈ ℜn and y ∈ ℜm, estimates VAx − yVp in O(n p m) time, for any p ∈ (0, 2]. This generalizes an earlier algorithm of Wasserman and Blum [1997] which worked for the case p e 2.---We obtain another sketch function C′ which probabilistically embeds ln1 into a normed space lm1. The embedding guarantees that, if we set m e log(1 Δ)O(1 e), then for any pair of points q, s ∈ ln1, the distance between q and s does not increase by more than (1 p e) with constant probability, and it does not decrease by more than (1 − e) with probability 1 − Δ. This is the only known dimensionality reduction theorem for the l1 norm. In fact, stronger theorems of this type (i.e., that guarantee very low probability of expansion as well as of contraction) cannot exist [Brinkman and Charikar 2003].---We give an explicit embedding of ln2 into lnO(log n)1 with distortion (1 p 1 nΘ(1)).