Continuous Time Bayesian Networks
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Continuous Time Bayesian Networks |
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Thore Graepel and Ralf Herbrich
Modelling structured multivariate point process data has wide ranging
applications like understanding neural activity, developing faster file access
systems and learning dependencies
among servers in large networks. In this project, we develop the Poisson network
model for representing multivariate structured Poisson processes. In our model
each node of the network represents a Poisson process. The novelty of our work
is that waiting times of a process are modelled by an exponential distribution
with a piecewise constant rate function that depends on the event counts of its
parents in the network in a generalised linear way. Our choice of model allows
to perform exact sampling from arbitrary structures. We adopt a Bayesian
approach for learning the network structure. We also develop fixed point and
sampling based approximations for performing inference of rate functions in
Poisson networks.
We investigate the problem of learning the dependencies among
servers in large networks based on failure patterns in their up-time behaviour.
We model up-times in terms of exponential distributions whose inverse lifetime
parameters may vary with the state of other servers. Based on a conjugate Gamma
prior over inverse lifetimes we
identify the most likely network configuration given that any node has at most
one parent. The method can be viewed as a special case of learning a continuous
time Bayesian network. Our approach enables us to easily incorporate existing
expert prior knowledge. Furthermore our method enjoys advantages over a
state-of-the-art rule-based approach. We validate the approach on synthetic data
and apply it to five year
data for a set of over 500 servers at a server farm of a major Microsoft web
site.
Machine Learning and Perception—Machine Learning—Continuous Time Bayesian Networks