ABSTRACT In many domains of information retrieval, system estimates of document relevance are based on multidimensional quality criteria that have to be accommodated in a unidimensional result ranking. Current solutions to this challenge are often inconsistent with the formal probabilistic framework in which constituent scores were estimated, or use sophisticated learning methods that make it difficult for humans to understand the origin of the final ranking. To address these issues, we introduce the use of copulas, a powerful statistical framework for modeling complex multi-dimensional dependencies, to information retrieval tasks. We provide a formal background to copulas and demonstrate their effectiveness on standard IR tasks such as combining multidimensional relevance estimates and fusion of results from multiple search engines. We introduce copula-based versions of standard relevance estimators and fusion methods and show that these lead to significant performance improvements on several tasks, as evaluated on large-scale standard corpora, compared to their non-copula counterparts. We also investigate criteria for understanding the likely effect of using copula models in a given retrieval scenario.

Statistical models of neural activity are integral to modern neuro-science. Recently interest has grown in modeling the spiking activity of populations of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing. However, any statistical model must be validated by an appropriate goodness-of-fit test. Kolmogorov-Smirnov tests based on the time-rescaling theorem have proven to be useful for evaluating point-process-based statistical models of single-neuron spike trains. Here we discuss the extension of the time-rescaling theorem to the multivariate (neural population) case. We show that even in the presence of strong correlations between spike trains,models that neglect couplings between neurons can be erroneously passed by the univariate time-rescaling test. We present the multivariate version of the time-rescaling theorem and provide a practical step-by-step procedure for applying it to testing the sufficiency of neural population models. Using several simple analytically tractable models and more complex simulated and real data sets, we demonstrate that important features of the population activity can be detected only using the multivariate extension of the test.

Near–optimal decoding of transient stimuli from coupled neuronal subpopulations

Probabilistic modeling of temporal phenomena is of central importance in a variety of fields ranging from neuroscience to economics to speech recognition. While the task has received extensive attention in recent decades, learning temporal models for multivariate real-valued data that is non-Gaussian is still a formidable challenge. Recently, the power of copulas, a framework for representing complex multi-modal and heavy-tailed distributions, was fused with the formalism of Bayesian networks to allow for flexible modeling of high-dimensional distributions. In this work we introduce Dynamic Copula Bayesian Networks, a generalization aimed at capturing the distribution of rich temporal sequences. We apply our model to three markedly different real-life domains and demonstrate substantial quantitative and qualitative advantage. 1