# Non-Gaussian Bayesian functional regression

October 10, 2019 — May 25, 2023

Regression using non-Gaussian random fields. Generalised Gaussian process regression.

Is there ever an actual need for this? Or can we just use mostly-Gaussian process with some non-Gaussian distribution marginal and pretend, via GP quantile regression, or some variational GP approximation or non-Gaussian likelihood over Gaussian latents. Presumably if we suspect higher moments than the second are important, or that there is some actual stochastic process that we *know* matches our phenomenon, we might bother with this, but oh my it can get complicated.

TO: example, maybe using sparse stochastic process priors, Neural process regression; is that distinct Singh et al. (2019)?

## 1 References

Bostan, Kamilov, Nilchian, et al. 2013. “Sparse Stochastic Processes and Discretization of Linear Inverse Problems.”

*IEEE Transactions on Image Processing*.
Louizos, Shi, Schutte, et al. 2019. “The Functional Neural Process.” In

*Advances in Neural Information Processing Systems*.
Singh, Yoon, Son, et al. 2019. “Sequential Neural Processes.”

*arXiv:1906.10264 [Cs, Stat]*.
Unser, M. 2015. “Sampling and (Sparse) Stochastic Processes: A Tale of Splines and Innovation.” In

*2015 International Conference on Sampling Theory and Applications (SampTA)*.
Unser, Michael A., and Tafti. 2014.

*An Introduction to Sparse Stochastic Processes*.
Unser, M., Tafti, Amini, et al. 2014. “A Unified Formulation of Gaussian Vs Sparse Stochastic Processes - Part II: Discrete-Domain Theory.”

*IEEE Transactions on Information Theory*.
Unser, M., Tafti, and Sun. 2014. “A Unified Formulation of Gaussian Vs Sparse Stochastic Processes—Part I: Continuous-Domain Theory.”

*IEEE Transactions on Information Theory*.