Pairwise comparison

About: Pairwise comparison is a research topic. Over the lifetime, 6804 publications have been published within this topic receiving 174081 citations.

Tractable learning for structured probability spaces: a case study in learning preference distributions

Abstract: Probabilistic sentential decision diagrams (PSDDs) are a tractable representation of structured probability spaces, which are characterized by complex logical constraints on what constitutes a possible world. We develop general-purpose techniques for probabilistic reasoning and learning with PSDDs, allowing one to compute the probabilities of arbitrary logical formulas and to learn PSDDs from incomplete data. We illustrate the effectiveness of these techniques in the context of learning preference distributions, to which considerable work has been devoted in the past. We show, analytically and empirically, that our proposed framework is general enough to support diverse and complex data and query types. In particular, we show that it can learn maximum-likelihood models from partial rankings, pairwise preferences, and arbitrary preference constraints. Moreover, we show that it can efficiently answer many queries exactly, from expected and most likely rankings, to the probability of pairwise preferences, and diversified recommendations. This case study illustrates the effectiveness and flexibility of the developed PSDD framework as a domain-independent tool for learning and reasoning with structured probability spaces.

Pairwise parameter estimation in Rasch models

Abstract: Rasch model item parameters can be estimated consistently with a pseudo-likelihood method based on comparing responses to pairs of items irrespective of other items. The pseudo-likelihood method is comparable to Fischer's (1974) Minchi method. A simulation study found that the pseudo-likelihood estimates and their (estimated) standard errors were comparable to conditional and marginal maximum likelihood estimates. The method is extended to estimate parameters of the linear logistic test model allowing the design matrix to vary between persons.

Efficient Out-of-Sample Extension of Dominant-Set Clusters

Abstract: Dominant sets are a new graph-theoretic concept that has proven to be relevant in pairwise data clustering problems, such as image segmentation. They generalize the notion of a maximal clique to edge-weighted graphs and have intriguing, non-trivial connections to continuous quadratic optimization and spectral-based grouping. We address the problem of grouping out-of-sample examples after the clustering process has taken place. This may serve either to drastically reduce the computational burden associated to the processing of very large data sets, or to efficiently deal with dynamic situations whereby data sets need to be updated continually. We show that the very notion of a dominant set offers a simple and efficient way of doing this. Numerical experiments on various grouping problems show the effectiveness of the approach.