State Space Gaussian Processes with Non-Gaussian Likelihood
By Hannes Nickisch, Arno Solin, Alexander Grigorevskiy. 2018
35 citations recorded by the source corpus.
We provide a comprehensive overview and tooling for GP modeling with non-Gaussian likelihoods using state space methods. The state space formulation allows for solving one-dimensional GP models in $\mathcal{O}(n)$ time and memory complexity. While existing literature has focused on the connection between GP regression and state space methods, the computational primitives allowing for inference using general likelihoods in combination with the Laplace approximation (LA), variational Bayes (VB), and assumed density filtering (ADF, a.k.a. single-sweep expectation propagation, EP) schemes has been largely overlooked. We present means of combining the efficient $\mathcal{O}(n)$ state space methodology with existing inference methods. We extend existing methods, and provide unifying code implementing all approaches.
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Citations in the corpus
- Recurrent Neural Filters: Learning Independent Bayesian Filtering Steps for Time Series Prediction (2019, background): “Gaussian Process state space models (GP-SSMs) (Turner et al., 2010; Nickisch et al., 2018) and variational approximations (Doerr et al., 2018), provide an alternative non-parametric approach to forecasting non-linear state space models – modelling hidden states and observation dynamics using GPs.”