# Variational Orthogonal Features

arXiv: https://arxiv.org/abs/2006.13170 · HTML: https://mlsanity.com/paper/2006.13170/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2020.

## Built on by (most cited first, 9 of 9)

- [Deep Neural Networks as Point Estimates for Deep Gaussian Processes](https://mlsanity.com/paper/2105.04504/) (2021)
- [SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data](https://mlsanity.com/paper/2105.04211/) (2021)
- [Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition](https://mlsanity.com/paper/2106.05992/) (2021)
- [Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processes](https://mlsanity.com/paper/2106.10210/) (2021)
- [Free-Form Variational Inference for Gaussian Process State-Space Models](https://mlsanity.com/paper/2302.09921/) (2023)
- [Integrated Variational Fourier Features for Fast Spatial Modelling with Gaussian Processes](https://mlsanity.com/paper/2308.14142/) (2023)
- [Spherical Inducing Features for Orthogonally-Decoupled Gaussian Processes](https://mlsanity.com/paper/2304.14034/) (2023)
- [Spectrum Gaussian Processes Based On Tunable Basis Functions](https://mlsanity.com/paper/2107.06473/) (2021)
- [Kernel Multigrid: Accelerate Back-fitting via Sparse Gaussian Process Regression](https://mlsanity.com/paper/2403.13300/) (2024)

## Abstract (arXiv)

Sparse stochastic variational inference allows Gaussian process models to be applied to large datasets. The per iteration computational cost of inference with this method is O(tildeNM2+M3), where tildeN is the number of points in a minibatch and M is the number of `inducing features', which determine the expressiveness of the variational family. Several recent works have shown that for certain priors, features can be defined that remove the O(M3) cost of computing a minibatch estimate of an evidence lower bound (ELBO). This represents a significant computational savings when Mgg tildeN. We present a construction of features for any stationary prior kernel that allow for computation of an unbiased estimator to the ELBO using T Monte Carlo samples in O(tildeNT+M2T) and in O(tildeNT+MT) with an additional approximation. We analyze the impact of this additional approximation on inference quality.