# Upgrading from Gaussian Processes to Student's-T Processes

arXiv: https://arxiv.org/abs/1801.06147 · HTML: https://mlsanity.com/paper/1801.06147/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2018.

## Built on by (most cited first, 5 of 5)

- [Student-t processes as infinite-width limits of posterior Bayesian neural networks](https://mlsanity.com/paper/2502.04247/) (2025)
- [Empirical analysis of representation learning and exploration in neural kernel bandits](https://mlsanity.com/paper/2111.03543/) (2021)
- [Epistemic Modeling Uncertainty of Rapid Neural Network Ensembles for Adaptive Learning](https://mlsanity.com/paper/2309.06628/) (2023)
- [One-parameter family of acquisition functions for efficient global optimization](https://mlsanity.com/paper/2104.12363/) (2021)
- [From Target Tracking to Targeting Track -- Part III: Stochastic Process Modeling and Online Learning](https://mlsanity.com/paper/2503.05799/) (2025)

## Abstract (arXiv)

Gaussian process priors are commonly used in aerospace design for performing Bayesian optimization. Nonetheless, Gaussian processes suffer two significant drawbacks: outliers are a priori assumed unlikely, and the posterior variance conditioned on observed data depends only on the locations of those data, not the associated sample values. Student's-T processes are a generalization of Gaussian processes, founded on the Student's-T distribution instead of the Gaussian distribution. Student's-T processes maintain the primary advantages of Gaussian processes (kernel function, analytic update rule) with additional benefits beyond Gaussian processes. The Student's-T distribution has higher Kurtosis than a Gaussian distribution and so outliers are much more likely, and the posterior variance increases or decreases depending on the variance of observed data sample values. Here, we describe Student's-T processes, and discuss their advantages in the context of aerospace optimization. We show how to construct a Student's-T process using a kernel function and how to update the process given new samples. We provide a clear derivation of optimization-relevant quantities such as expected improvement, and contrast with the related computations for Gaussian processes. Finally, we compare the performance of Student's-T processes against Gaussian process on canonical test problems in Bayesian optimization, and apply the Student's-T process to the optimization of an aerostructural design problem.