# Online Student-t Processes with an Overall-local Scale Structure for Modelling Non-stationary Data

arXiv: https://arxiv.org/abs/2311.00564 · HTML: https://mlsanity.com/paper/2311.00564/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 1 Nov 2023.

## Builds on (most cited first, 10 of 10)

- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [Streaming Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1705.07131/) (2017)
- [Kernel Interpolation for Scalable Online Gaussian Processes](https://mlsanity.com/paper/2103.01454/) (2021)
- [Marginalizing Gaussian Process Hyperparameters using Sequential Monte Carlo](https://mlsanity.com/paper/1502.01908/) (2015)
- [Embarrassingly Parallel Inference for Gaussian Processes](https://mlsanity.com/paper/1702.08420/) (2017)
- [Mixtures of Gaussian Process Experts with SMC2](https://mlsanity.com/paper/2208.12830/) (2022)
- [Sequential Gaussian Processes for Online Learning of Nonstationary Functions](https://mlsanity.com/paper/1905.10003/) (2019)

## Abstract (arXiv)

Time-dependent data often exhibit characteristics, such as non-stationarity and heavy-tailed errors, that would be inappropriate to model with the typical assumptions used in popular models. Thus, more flexible approaches are required to be able to accommodate such issues. To this end, we propose a Bayesian mixture of student-t processes with an overall-local scale structure for the covariance. Moreover, we use a sequential Monte Carlo (SMC) sampler in order to perform online inference as data arrive in real-time. We demonstrate the superiority of our proposed approach compared to typical Gaussian process-based models on real-world data sets in order to prove the necessity of using mixtures of student-t processes.