# nuGPR: GPU-Accelerated Gaussian Process Regression with Iterative Algorithms and Low-Rank Approximations

arXiv: https://arxiv.org/abs/2510.12128 · HTML: https://mlsanity.com/paper/2510.12128/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 55 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Constant-Time Predictive Distributions for Gaussian Processes](https://mlsanity.com/paper/1803.06058/) (2018)
- [Scalable Log Determinants for Gaussian Process Kernel Learning](https://mlsanity.com/paper/1711.03481/) (2017)
- [Preconditioning Kernel Matrices](https://mlsanity.com/paper/1602.06693/) (2016)
- [Product Kernel Interpolation for Scalable Gaussian Processes](https://mlsanity.com/paper/1802.08903/) (2018)

## Built on by (most cited first, 1 of 1)

- [Amortized Acquisition Optimization for Bayesian Optimization with Variational Mutual Information](https://mlsanity.com/paper/2601.08172/) (2026)

## Abstract (arXiv)

Gaussian Process Regression (GPR) is an important type of supervised machine learning model with inherent uncertainty measure in its predictions. We propose a new framework, nuGPR, to address the well-known challenge of high computation cost associated with GPR training. Our framework includes several ideas from numerical linear algebra to reduce the amount of computation in key steps of GPR, and we combine them to establish an end-to-end training algorithm. Specifically, we leverage the preconditioned conjugate gradient method to accelerate the convergence of the linear solves required in GPR. We exploit clustering in the input data to identify block-diagonal structure of the covariance matrix and subsequently construct low-rank approximations of the off-diagonal blocks. These enhancements significantly reduce the time and space complexity of our computations. In addition, unlike other frameworks that rely on exact differentiation, we employ numerical gradients to optimize the hyperparameters of our GPR model, further reducing the training cost by eliminating the need for backpropagation. Lastly, we leverage the CUDA Toolkit to efficiently parallelize the training procedure on NVIDIA GPUs. As a result, nuGPR reduces total training time by up to 2x and peak memory consumption by up to 12x on various synthetic and real-world datasets when compared to the best existing GPU-based GPR implementation.