Variational Inference for Gaussian Process Modulated Poisson Processes

By Chris M. Lloyd, Tom Gunter, Michael A. Osborne, Stephen J. Roberts. 2014

127 citations recorded by the source corpus.

We present the first fully variational Bayesian inference scheme for continuous Gaussian-process-modulated Poisson processes. Such point processes are used in a variety of domains, including neuroscience, geo-statistics and astronomy, but their use is hindered by the computational cost of existing inference schemes. Our scheme: requires no discretisation of the domain; scales linearly in the number of observed events; and is many orders of magnitude faster than previous sampling based approaches. The resulting algorithm is shown to outperform standard methods on synthetic examples, coal mining disaster data and in the prediction of Malaria incidences in Kenya.

Subfields: Artificial Intelligence

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Citations in the corpus

Functional Regularisation for Continual Learning using Gaussian Processes (2019, background): “This ELBO is generally written in the form (Hensman et al., 2013; Lloyd et al., 2015; Dezfouli & Bonilla, 2015; Hensman et al., 2015; Sheth et al., 2015),”
A Multitask Point Process Predictive Model (2015, methodology): “We use a square transformation (γu(·) = {fu(·)}2) rather than the common γu(·) = exp{fu(·)}, because the uncertainty of fu(·) cannot be properly estimated in the latter construction, as discussed by Lloyd et al. (2014); this issue is addressed thoroughly in Section 5.”
MCMC for Variationally Sparse Gaussian Processes (2015, methodology): “Recent works [18, 19, 20] have proposed inducing point schemes which can reduce the”
Blitzkriging: Kronecker-structured Stochastic Gaussian Processes (2015, background): “…(where it is also known as kriging ) and classiﬁcation [1]; in non-linear dimensionality reduction as the Gaussian process latent variable model (GPLVM) [2]; as a prior over the rate function in Cox processes [3] and broadly within Probabilistic Numerics (see probabilistic-numerics.org ).”