We propose a novel approach for learning causal response representations. Our method aims to extract directions in which a multidimensional outcome is most directly caused by a treatment variable. By bridging conditional independence testing with causal representation learning, we formulate an optimisation problem that maximises the evidence against conditional independence between the treatment and outcome, given a conditioning set. This formulation employs flexible regression models tailored to specific applications, creating a versatile framework. The problem is addressed through a generalised eigenvalue decomposition. We show that, under mild assumptions, the distribution of the largest eigenvalue can be bounded by a known $F$-distribution, enabling testable conditional independence. We also provide theoretical guarantees for the optimality of the learned representation in terms of signal-to-noise ratio and Fisher information maximisation. Finally, we demonstrate the empirical effectiveness of our approach in simulation and real-world experiments. Our results underscore the utility of this framework in uncovering direct causal effects within complex, multivariate settings.

Earth observation from satellite sensors offers the possibility to monitor natural ecosystems by deriving spatially explicit and temporally resolved biogeophysical parameters. Optical remote sensing, however, suffers from missing data mainly due to the presence of clouds, sensor malfunctioning, and atmospheric conditions. This study proposes a novel deep learning architecture to address gap filling of satellite reflectances, more precisely the visible and near-infrared bands, and illustrates its performance at high-resolution Sentinel-2 data. We introduce GANFilling, a generative adversarial network capable of sequence-to-sequence translation, which comprises convolutional long short-term memory layers to effectively exploit complete dependencies in space–time series data. We focus on Europe and evaluate the method’s performance quantitatively (through distortion and perceptual metrics) and qualitatively (via visual inspection and visual quality metrics). Quantitatively, our model offers the best trade-off between denoising corrupted data and preserving noise-free information, underscoring the importance of considering multiple metrics jointly when assessing gap filling tasks. Qualitatively, it successfully deals with various noise sources, such as clouds and missing data, constituting a robust solution to multiple scenarios and settings. We also illustrate and quantify the quality of the generated product in the relevant downstream application of vegetation greenness forecasting, where using GANFilling enhances forecasting in approximately 70% of the considered regions in Europe. This research contributes to underlining the utility of deep learning for Earth observation data, which allows for improved spatially and temporally resolved monitoring of the Earth surface.

Satellite remote sensing is the primary source of global aerosol observations, providing essential data for understanding aerosol-climate interactions and constraining global climate models. To solve the inverse problem at the heart of the retrieval process, traditional algorithms must make simplifications and often cannot quantify uncertainty. In this study, we explore the use of Invertible Neural Networks (INNs) for retrieving aerosol optical depth (AOD) from spectral top-ofatmosphere reflectance. INNs can handle the inherent uncertainty of underdetermined inverse problems. They model the forward and inverse processes simultaneously, while learning additional random latent variables used to recover full non-parametric posterior distributions for the inverse predictions. We develop location-specific INNs for MODIS sensor data, training on synthetic datasets generated by combining atmospheric reflectance from MODIS Dark Target (DT) look-up tables and surface reflectance from a MODIS bidirectional reflectance product. The INNs successfully emulate the forward problem, and achieve accurate AOD inversion results on synthetic test sets (RMSE ≈ 0.05). The posterior distributions obtained are reliable (mean absolute calibration error ≈ 2.5%), efficiently providing informative predictive uncertainty estimates. Additionally, the INNs’ invertible architecture is found to promote physically consistent predictions and uncertainties. To further validate them in a realworld context, the INNs are applied to MODIS L1B reflectance observations to produce full-resolution AOD estimates with pixellevel uncertainties. The retrievals are compared to collocated ground measurements from the Aeronet network. The INNs obtain good accuracy in all tested locations in line with the operational DT AOD product (RMSE ≈ 0.1, 74% within DT expected error bounds). The INNs are also able to retrieve AOD over bright surfaces where DT cannot be applied. Despite uncovered limitations out-of-distribution, the INNs show consistent skill in target domains across diverse land surfaces. The INNs’ unique modelling and uncertainty quantification features have the potential to enhance aerosol and climate studies in various real-world contexts.

Information theory is an outstanding framework for measuring uncertainty, dependence, and relevance in data and systems. It has several desirable properties for real-world applications: naturally deals with multivariate data, can handle heterogeneous data, and the measures can be interpreted. However, it has not been adopted by a wider audience because obtaining information from multidimensional data is a challenging problem due to the curse of dimensionality. We propose an indirect way of estimating information based on a multivariate iterative Gaussianization transform. The proposed method has a multivariate-to-univariate property: it reduces the challenging estimation of multivariate measures to a composition of marginal operations applied in each iteration of the Gaussianization. Therefore, the convergence of the resulting estimates depends on the convergence of well-understood univariate entropy estimates, and the global error linearly depends on the number of times the marginal estimator is invoked. We introduce Gaussianization-based estimates for Total Correlation, Entropy, Mutual Information, and Kullback-Leibler Divergence. Results on artificial data show that our approach is superior to previous estimators, particularly in high-dimensional scenarios. We also illustrate the method's performance in different fields to obtain interesting insights. We make the tools and datasets publicly available to provide a test bed for analyzing future methodologies.

With climate change-related extreme events on the rise, high dimensional Earth observation data presents a unique opportunity for forecasting and understanding impacts on ecosystems. This is, however, impeded by the complexity of processing, visualizing, modeling, and explaining this data. To showcase how this challenge can be met, here we train a convolutional long short-term memory-based architecture on the novel DeepExtremeCubes dataset. DeepExtremeCubes includes around 40,000 long-term Sentinel-2 minicubes (January 2016-October 2022) worldwide, along with labeled extreme events, meteorological data, vegetation land cover, and topography map, sampled from locations affected by extreme climate events and surrounding areas. When predicting future reflectances and vegetation impacts through kernel normalized difference vegetation index, the model achieved an R$^2$ score of 0.9055 in the test set. Explainable artificial intelligence was used to analyze the model's predictions during the October 2020 Central South America compound heatwave and drought event. We chose the same area exactly one year before the event as counterfactual, finding that the average temperature and surface pressure are generally the best predictors under normal conditions. In contrast, minimum anomalies of evaporation and surface latent heat flux take the lead during the event. A change of regime is also observed in the attributions before the event, which might help assess how long the event was brewing before happening. The code to replicate all experiments and figures in this paper is publicly available at https://github.com/DeepExtremes/txyXAI