267,586 research outputs found
Inducing Gaussian Process Networks
Gaussian processes (GPs) are powerful but computationally expensive machine
learning models, requiring an estimate of the kernel covariance matrix for
every prediction. In large and complex domains, such as graphs, sets, or
images, the choice of suitable kernel can also be non-trivial to determine,
providing an additional obstacle to the learning task. Over the last decade,
these challenges have resulted in significant advances being made in terms of
scalability and expressivity, exemplified by, e.g., the use of inducing points
and neural network kernel approximations. In this paper, we propose inducing
Gaussian process networks (IGN), a simple framework for simultaneously learning
the feature space as well as the inducing points. The inducing points, in
particular, are learned directly in the feature space, enabling a seamless
representation of complex structured domains while also facilitating scalable
gradient-based learning methods. We consider both regression and (binary)
classification tasks and report on experimental results for real-world data
sets showing that IGNs provide significant advances over state-of-the-art
methods. We also demonstrate how IGNs can be used to effectively model complex
domains using neural network architectures
Propagation on networks: an exact alternative perspective
By generating the specifics of a network structure only when needed
(on-the-fly), we derive a simple stochastic process that exactly models the
time evolution of susceptible-infectious dynamics on finite-size networks. The
small number of dynamical variables of this birth-death Markov process greatly
simplifies analytical calculations. We show how a dual analytical description,
treating large scale epidemics with a Gaussian approximations and small
outbreaks with a branching process, provides an accurate approximation of the
distribution even for rather small networks. The approach also offers important
computational advantages and generalizes to a vast class of systems.Comment: 8 pages, 4 figure
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