Fast Gaussian process methods for point process intensity estimation

By John P. Cunningham, Krishna V. Shenoy, Maneesh Sahani. 2008

126 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Artificial Intelligence, Computational Theory and Mathematics

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Citations in the corpus

Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP) (2015, methodology): “Turner (2010) and Cunningham et al. (2008) contain examples of Toeplitz methods applied to GPs.”
Thoughts on Massively Scalable Gaussian Processes (2015, methodology): “Toeplitz structure has been exploited for GP inference (e.g., Zhang et al., 2005; Cunningham et al., 2008) in O ( n log n ) computations.”
Tractable nonparametric Bayesian inference in Poisson processes with Gaussian process intensities (2009, methodology): “There have been several methods proposed for approximation to this model, most notably the discretization method of Rathbun and Cressie (1994) and Møller et al. (1998), to which we have compared the SGCP. Cunningham et al. (2008a) also use a discretization-based approximation for the Cox process and”
A Scalable Hierarchical Gaussian Process Classifier (2019, methodology): “However, the limitation of KISS-GP is that to exploit Toeplitz or Kronecker structure, its inducing points must live in a low dimensional space (e.g.”
Variational Implicit Processes (2018, background): “Therefore , people often resort to complicated approximate methods [12, 13, 16, 35, 72, 77, 80, 84, 85, 88].”
Variational Inference for Gaussian Process Modulated Poisson Processes (2014, methodology): “This flexible approach has been adopted for applications in neuroscience (Cunningham et al., 2008b), finance (Basu & Dassios, 2002) and forestry (Heikkinen & Arjas, 1999). However, existing inference schemes for such models scale poorly with the number of data, preventing them from finding greater u”
Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversion (2018, background): “If one can also find Toeplitz structure in the spatiotemporal points, then this can be further prolonged [29, 30, 31], but no such structure will exist in general for the high-dimensional stochastic inputs in X.”
When Gaussian Process Meets Big Data: A Review of Scalable GPs (2018, methodology): “11 Another one is the Toeplitz methods [95]—complementary to the Kronecker methods— that exploit the kernel matrix built from regularly spaced 1-D points, resulting in the time complexity of O(dnd log n).”
Kalman filtering and smoothing solutions to temporal Gaussian process regression models (2010, methodology): “We show how the reformulation can be done for Matérn family of covariance functions analytically and for squared exponential covariance function by applying spectral Taylor series approximation.”