# Deep Gaussian Processes for Biogeophysical Parameter Retrieval and Model Inversion

arXiv: https://arxiv.org/abs/2104.10638 · HTML: https://mlsanity.com/paper/2104.10638/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 62 references that are in the map.
- First posted on arXiv 16 Apr 2021.

## Builds on (most cited first, 15 of 15)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Physics-Aware Gaussian Processes in Remote Sensing](https://mlsanity.com/paper/2012.07986/) (2020)
- [Scalable Training of Inference Networks for Gaussian-Process Models](https://mlsanity.com/paper/1905.10969/) (2019)
- [A Perspective on Gaussian Processes for Earth Observation](https://mlsanity.com/paper/2007.01238/) (2020)
- [Remote Sensing Image Classification with Large Scale Gaussian Processes](https://mlsanity.com/paper/1710.00575/) (2017)
- [Dimensionality Reduction via Regression in Hyperspectral Imagery](https://mlsanity.com/paper/1602.00214/) (2016)
- [Accounting for Input Noise in Gaussian Process Parameter Retrieval](https://mlsanity.com/paper/2005.09907/) (2020)
- [Spectral band selection for vegetation properties retrieval using Gaussian processes regression](https://mlsanity.com/paper/2012.08640/) (2020)
- [Semi-described and semi-supervised learning with Gaussian processes](https://mlsanity.com/paper/1509.01168/) (2015)
- [Retrieval of Case 2 Water Quality Parameters with Machine Learning](https://mlsanity.com/paper/2012.04495/) (2020)
- [Spatial noise-aware temperature retrieval from infrared sounder data](https://mlsanity.com/paper/2012.05839/) (2020)
- [Deep Gaussian Processes for geophysical parameter retrieval](https://mlsanity.com/paper/2012.12099/) (2020)

## Built on by (most cited first, 4 of 4)

- [Probabilistic Attention based on Gaussian Processes for Deep Multiple Instance Learning](https://mlsanity.com/paper/2302.04061/) (2023)
- [Probabilistic Machine Learning for Noisy Labels in Earth Observation](https://mlsanity.com/paper/2504.03478/) (2025)
- [On the Generalization of Representation Uncertainty in Earth Observation](https://mlsanity.com/paper/2503.07082/) (2025)
- [GeoDose-CP: Graph-Local Conformal Inference for Continuous-Treatment Earth Observation](https://mlsanity.com/paper/2609.28895/) (2026)

## Abstract (arXiv)

Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with in situ data that often results in problems with extrapolation outside the study area; and the most widely adopted hybrid modeling by which statistical models, mostly nonlinear and non-parametric machine learning algorithms, are applied to invert RTM simulations. We will focus on the latter. Among the different existing algorithms, in the last decade kernel based methods, and Gaussian Processes (GPs) in particular, have provided useful and informative solutions to such RTM inversion problems. This is in large part due to the confidence intervals they provide, and their predictive accuracy. However, RTMs are very complex, highly nonlinear, and typically hierarchical models, so that often a shallow GP model cannot capture complex feature relations for inversion. This motivates the use of deeper hierarchical architectures, while still preserving the desirable properties of GPs. This paper introduces the use of deep Gaussian Processes (DGPs) for bio-geo-physical model inversion. Unlike shallow GP models, DGPs account for complicated (modular, hierarchical) processes, provide an efficient solution that scales well to big datasets, and improve prediction accuracy over their single layer counterpart. In the experimental section, we provide empirical evidence of performance for the estimation of surface temperature and dew point temperature from infrared sounding data, as well as for the prediction of chlorophyll content, inorganic suspended matter, and coloured dissolved matter from multispectral data acquired by the Sentinel-3 OLCI sensor. The presented methodology allows for more expressive forms of GPs in remote sensing model inversion problems.