caa a22 4500 60547835X CHVBK 20210128100405.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10994-015-5506-z doi (NATIONALLICENCE)springer-10.1007/s10994-015-5506-z Poisson Dependency Networks: Gradient Boosted Models for Multivariate Count Data [Elektronische Daten] [Fabian Hadiji, Alejandro Molina, Sriraam Natarajan, Kristian Kersting] Although count data are increasingly ubiquitous, surprisingly little work has employed probabilistic graphical models for modeling count data. Indeed the univariate case has been well studied, however, in many situations counts influence each other and should not be considered independently. Standard graphical models such as multinomial or Gaussian ones are also often ill-suited, too, since they disregard either the infinite range over the natural numbers or the potentially asymmetric shape of the distribution of count variables. Existing classes of Poisson graphical models can only model negative conditional dependencies or neglect the prediction of counts or do not scale well. To ease the modeling of multivariate count data, we therefore introduce a novel family of Poisson graphical models, called Poisson Dependency Networks (PDNs). A PDN consists of a set of local conditional Poisson distributions, each representing the probability of a single count variable given the others, that naturally facilitates a simple Gibbs sampling inference. In contrast to existing Poisson graphical models, PDNs are non-parametric and trained using functional gradient ascent, i.e., boosting. The particularly simple form of the Poisson distribution allows us to develop the first multiplicative boosting approach: starting from an initial constant value, alternatively a log-linear Poisson model, or a Poisson regression tree, a PDN is represented as products of regression models grown in a stage-wise optimization. We demonstrate on several real world datasets that PDNs can model positive and negative dependencies and scale well while often outperforming state-of-the-art, in particular when using multiplicative updates. The Author(s), 2015 Graphical models nationallicence Dependency networks nationallicence Poisson distribution nationallicence Learning nationallicence MAP inference nationallicence Hadiji Fabian LS VIII, TU Dortmund University, Dortmund, Germany aut Molina Alejandro LS VIII, TU Dortmund University, Dortmund, Germany aut Natarajan Sriraam School of Informatics and Computing, Indiana University, Bloomington, IN, USA aut Kersting Kristian LS VIII, TU Dortmund University, Dortmund, Germany aut Machine Learning Springer US; http://www.springer-ny.com 100/2-3(2015-09-01), 477-507 0885-6125 100:2-3<477 2015 100 10994 https://doi.org/10.1007/s10994-015-5506-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10994-015-5506-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hadiji Fabian LS VIII, TU Dortmund University, Dortmund, Germany aut NATIONALLICENCE 700 1- Molina Alejandro LS VIII, TU Dortmund University, Dortmund, Germany aut NATIONALLICENCE 700 1- Natarajan Sriraam School of Informatics and Computing, Indiana University, Bloomington, IN, USA aut NATIONALLICENCE 700 1- Kersting Kristian LS VIII, TU Dortmund University, Dortmund, Germany aut NATIONALLICENCE 773 0- Machine Learning Springer US; http://www.springer-ny.com 100/2-3(2015-09-01), 477-507 0885-6125 100:2-3<477 2015 100 10994