NDLI: Poisson Dependency Networks: Gradient Boosted Models for Multivariate Count Data

Content Provider	Springer Nature Link
Author	Hadiji, Fabian Molina, Alejandro Natarajan, Sriraam Kersting, Kristian
Copyright Year	2015
Abstract	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.
Starting Page	477
Ending Page	507
Page Count	31
File Format	PDF
ISSN	08856125
Journal	Machine Learning
Volume Number	100
Issue Number	2-3
e-ISSN	15730565
Language	English
Publisher	Springer US
Publisher Date	2015-07-11
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Graphical models Dependency networks Poisson distribution Learning MAP inference Artificial Intelligence (incl. Robotics) Control, Robotics, Mechatronics Computing Methodologies Simulation and Modeling Language Translation and Linguistics
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Software

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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