# State Space Gaussian Processes with Non-Gaussian Likelihood

arXiv: https://arxiv.org/abs/1802.04846 · HTML: https://mlsanity.com/paper/1802.04846/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2018.

## Built on by (most cited first, 12 of 12)

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- [Recurrent Neural Networks and Universal Approximation of Bayesian Filters](https://mlsanity.com/paper/2211.00335/) (2022)
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- [Gaussian Process Upper Confidence Bounds in Distributed Point Target Tracking over Wireless Sensor Networks](https://mlsanity.com/paper/2409.07652/) (2024)
- [Privacy-aware Gaussian Process Regression](https://mlsanity.com/paper/2305.16541/) (2023)
- [Gaussian Processes Sampling with Sparse Grids under Additive Schwarz Preconditioner](https://mlsanity.com/paper/2408.00206/) (2024)
- [Aggregation Models with Optimal Weights for Distributed Gaussian Processes](https://mlsanity.com/paper/2408.00955/) (2024)
- [GNet: A scalable and flexible Gaussian process network with nonparametric neurons](https://mlsanity.com/paper/2607.10735/) (2026)

## Abstract (arXiv)

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 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 O(n) state space methodology with existing inference methods. We extend existing methods, and provide unifying code implementing all approaches.