# B'ezier Gaussian Processes for Tall and Wide Data

arXiv: https://arxiv.org/abs/2209.00343 · HTML: https://mlsanity.com/paper/2209.00343/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 1 Sep 2022.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [The Promises and Pitfalls of Deep Kernel Learning](https://mlsanity.com/paper/2102.12108/) (2021)
- [Convergence of Sparse Variational Inference in Gaussian Processes Regression](https://mlsanity.com/paper/2008.00323/) (2020)
- [Adversarial Examples, Uncertainty, and Transfer Testing Robustness in Gaussian Process Hybrid Deep Networks](https://mlsanity.com/paper/1707.02476/) (2017)
- [Product Kernel Interpolation for Scalable Gaussian Processes](https://mlsanity.com/paper/1802.08903/) (2018)
- [Sparse within Sparse Gaussian Processes using Neighbor Information](https://mlsanity.com/paper/2011.05041/) (2020)
- [SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processes](https://mlsanity.com/paper/2106.06695/) (2021)
- [Variational Nearest Neighbor Gaussian Process](https://mlsanity.com/paper/2202.01694/) (2022)
- [Hierarchical Inducing Point Gaussian Process for Inter-domain Observations](https://mlsanity.com/paper/2103.00393/) (2021)
- [B'ezier Curve Gaussian Processes](https://mlsanity.com/paper/2205.01754/) (2022)

## Built on by (most cited first, 2 of 2)

- [Integrated Variational Fourier Features for Fast Spatial Modelling with Gaussian Processes](https://mlsanity.com/paper/2308.14142/) (2023)
- [Domain Invariant Learning for Gaussian Processes and Bayesian Exploration](https://mlsanity.com/paper/2312.11318/) (2023)

## Abstract (arXiv)

Modern approximations to Gaussian processes are suitable for "tall data", with a cost that scales well in the number of observations, but under-performs on ``wide data'', scaling poorly in the number of input features. That is, as the number of input features grows, good predictive performance requires the number of summarising variables, and their associated cost, to grow rapidly. We introduce a kernel that allows the number of summarising variables to grow exponentially with the number of input features, but requires only linear cost in both number of observations and input features. This scaling is achieved through our introduction of the B'ezier buttress, which allows approximate inference without computing matrix inverses or determinants. We show that our kernel has close similarities to some of the most used kernels in Gaussian process regression, and empirically demonstrate the kernel's ability to scale to both tall and wide datasets.