There is great interest in supporting imprecise queries over databases today. To support such queries, the system is typically required to disambiguate parts of the user-specified query against the database, using whatever resources are intrinsically available to it (the database schema, value distributions, natural language models etc). Often, systems will also have a user-interaction log available, which can supplement their model based on their own intrinsic resources. This leads to a problem of how best to combine the system's prior ranking with insight derived from the user-interaction log. Statistical inference techniques such as maximum likelihood or Bayesian updates from a subjective prior turn out not to apply in a straightforward way due to possible noise from user search behavior and to encoding biases endemic to the system's models. In this paper, we address such learning problems in interactive data retrieval, with specific focus on type classification for user-specified query terms. We develop a novel Bayesian smoothing algorithm, Bsmooth, which is simple, fast, flexible and accurate. We analytically establish some desirable properties and show, through experiments against an independent benchmark, that the addition of such a learning layer performs much better than standard methods.
The Dempster-Shafer (DS) theory of evidence @cite_5 has been applied in related work to combine two DB-intrinsic scorings @cite_6 . It does not seem to be fit to the interaction log scenario. The inferential scheme (Dempster's rule of combination) derives shared belief from multiple sources and ignores all the conflicting (non-shared) belief by a normalization factor. Zadeh gives an example of how counter-intuitive this is when beliefs should be rather integrated cumulatively @cite_26 . Let doctors @math have beliefs for diagnosis on conditions ( @math ) meningitis, ( @math ) brain tumor, ( @math ) concussion, viz., @math and @math . Then @math is inferred @cite_26 . The doctors agree only that brain tumor is very unlikely, but such a weak consensus is pushed through anyway. Now if we think of @math as movies @math plan to see together then the inference finds the movie shared by their belief constraints. This shows that the matching between abstract framework and applied use case is really important.
@cite_5 @cite_26 @cite_6
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Abstract We present a measure of performance (MOP) for identification algorithms based on the evidential theory of Dempster–Shafer. As an MOP, we introduce a principled distance between two basic probability assignments (BPAs) (or two bodies of evidence) based on a quantification of the similarity between sets. We give a geometrical interpretation of BPA and show that the proposed distance satisfies all the requirements for a metric. We also show the link with the quantification of Dempster's weight of conflict proposed by George and Pal. We compare this MOP to that described by Fixsen and Mahler and illustrate the behaviors of the two MOPs with numerical examples. Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem. This paper proposes a multimodal biometric system through Gaussian Mixture Model (GMM) for face and ear biometrics with belief fusion of the estimated scores characterized by Gabor responses and the proposed fusion is accomplished by Dempster-Shafer (DS) decision theory. Face and ear images are convolved with Gabor wavelet filters to extracts spatially enhanced Gabor facial features and Gabor ear features. Further, GMM is applied to the high-dimensional Gabor face and Gabor ear responses separately for quantitive measurements. Expectation Maximization (EM) algorithm is used to estimate density parameters in GMM. This produces two sets of feature vectors which are then fused using Dempster-Shafer theory. Experiments are conducted on two multimodal databases, namely, IIT Kanpur database and virtual database. Former contains face and ear images of 400 individuals while later consist of both images of 17 subjects taken from BANCA face database and TUM ear database. It is found that use of Gabor wavelet filters along with GMM and DS theory can provide robust and efficient multimodal fusion strategy. 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.