Large-Scale Cox Process Inference using Variational Fourier Features
Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few thousand data points. Here we introduce Cox process inference based on Fourier features. This sparse representation induces global rather than local constraints on the function space and is computationally efficient. This allows us to formulate a grid-free approximation that scales well with the number of data points and the size of the domain. We demonstrate that this allows MCMC approximations to the non-Gaussian posterior. We also find that, in practice, Fourier features have more consistent optimization behavior than previous approaches. Our approximate Bayesian method can fit over 100,000 events with complex spatiotemporal patterns in three dimensions on a single GPU.
Code (0)
등록된 구현이 없습니다.
Tasks
GPUSmall Data Image ClassificationSimilar Papers 제목 키워드 기반
Integrated Variational Fourier Features for Fast Spatial Modelling with Gaussian Processes
Sparse variational approximations are popular methods for scaling up inference and learning in Gaussian processes to larger datasets. For $N$ training points, exact inference has $O(N^3)$ cost; with $M \ll N$ features, s…
Gaussian ProcessesHarmonizable mixture kernels with variational Fourier features
The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels deriv…
Gaussian ProcessesSparse Gaussian Processes with Spherical Harmonic Features
We introduce a new class of inter-domain variational Gaussian processes (GP) where data is mapped onto the unit hypersphere in order to use spherical harmonic representations. Our inference scheme is comparable to variat…
Gaussian ProcessesAdaptive RKHS Fourier Features for Compositional Gaussian Process Models
Deep Gaussian Processes (DGPs) leverage a compositional structure to model non-stationary processes. DGPs typically rely on local inducing point approximations across intermediate GP layers. Recent advances in DGP infere…
Gaussian ProcessesVariational InferenceImproving Variational Autoencoder using Random Fourier Transformation: An Aviation Safety Anomaly Detection Case-Study
In this study, we focus on the training process and inference improvements of deep neural networks (DNNs), specifically Autoencoders (AEs) and Variational Autoencoders (VAEs), using Random Fourier Transformation (RFT). W…
Anomaly Detection