# Adaptive Basis Function Selection for Computationally Efficient Predictions

arXiv: https://arxiv.org/abs/2408.07480 · HTML: https://mlsanity.com/paper/2408.07480/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 12 of 12)

- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Scalable Gaussian Processes with Billions of Inducing Inputs via Tensor Train Decomposition](https://mlsanity.com/paper/1710.07324/) (2017)
- [Computationally Efficient Bayesian Learning of Gaussian Process State Space Models](https://mlsanity.com/paper/1506.02267/) (2015)
- [Scalable Magnetic Field SLAM in 3D Using Gaussian Process Maps](https://mlsanity.com/paper/1804.01926/) (2018)
- [Online Joint State Inference and Learning of Partially Unknown State-Space Models](https://mlsanity.com/paper/2102.07418/) (2021)
- [Spatially scalable recursive estimation of Gaussian process terrain maps using local basis functions](https://mlsanity.com/paper/2210.09168/) (2022)
- [Distributed multi-agent magnetic field norm SLAM with Gaussian processes](https://mlsanity.com/paper/2310.19400/) (2023)
- [Long-Term Autonomous Ocean Monitoring with Streaming Samples](https://mlsanity.com/paper/2306.06578/) (2023)

## Abstract (arXiv)

Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and straightforward model to use, they suffer from quadratic computational complexity in the number of BFs if the predictive variance is to be computed. We develop a method to automatically select the most important BFs for prediction in a sub-domain of the model domain. This significantly reduces the computational complexity of computing predictions while maintaining predictive accuracy. The proposed method is demonstrated using two numerical examples, where reductions up to 50-75% are possible without significantly reducing the predictive accuracy.