# Gaussian orthogonal latent factor processes for large incomplete matrices of correlated data

arXiv: https://arxiv.org/abs/2011.10863 · HTML: https://mlsanity.com/paper/2011.10863/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2020.

## Built on by (most cited first, 6 of 6)

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- [Bayesian Complementary Kernelized Learning for Multidimensional Spatiotemporal Data](https://mlsanity.com/paper/2208.09978/) (2022)
- [Dynamic Bayesian Learning for Spatiotemporal Mechanistic Models](https://mlsanity.com/paper/2208.06528/) (2022)
- [Spatio-Temporal Gaussian Process for Building Terrain-Incorporating Wind Power Curves](https://mlsanity.com/paper/2607.00051/) (2026)
- [Unsupervised cell segmentation by fast Gaussian Processes](https://mlsanity.com/paper/2505.18902/) (2025)
- [Long-Term Probabilistic Forecast of Vegetation Conditions Using Climate Attributes in the Four Corners Region](https://mlsanity.com/paper/2601.16347/) (2026)

## Abstract (arXiv)

We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a multi-dimensional input domain into a product of densities at the orthogonal components with lower-dimensional inputs. The continuous-time Kalman filter is implemented to compute the likelihood function efficiently without making approximations. We also show that the posterior distribution of the factor processes is independent, as a consequence of prior independence of factor processes and orthogonal factor loading matrix. For studies with large sample sizes, we propose a flexible way to model the mean, and we derive the marginal posterior distribution to solve identifiability issues in sampling these parameters. Both simulated and real data applications confirm the outstanding performance of this method.