Area of Applicability for Deep Learning: Exploring Latent Space Geometry of Earth Observation Models

Machine learning methods are used ubiquitously within the Earth Sciences to model spatio-temporal phenomena. These methods scale very well to big data sets and are used to model complex non-linear relationships between the predictor and outcome variables. Yet, most methods might silently fail when used in extrapolation scenarios, e.g. when combinations of predictor variables are encountered that have not been seen during training. This might be the case when the model is applied to new geographic areas that differ from the areas the model was trained on. For traditional machine learning models, estimating the area of applicability based on distances in the predictor space has been proposed. New inputs with distances above a certain threshold are rejected from prediction since our confidence in the model's output is low and we do not expect the estimated performance to hold.

Inspired by the success of deep architectures in the field of computer vision, the use of deep neural networks has been steadily increasing, especially in Earth Observation. Translating the concept of the area of applicability to deep architectures, however, remains a open research challenge. For the safe deployment of such models in the real world it is required to flag inputs for which we expect the model to extrapolate and is thus operating outside the estimated performance measure.

In this work, we are extending the concept of the area of applicability to deep neural network architectures. As an application rooted in current practices for Earth Observation, we use networks trained end-to-end for scene classification. We use these models as feature extractors to obtain representations of input samples in embedding space. We derive the area of applicability of the model within this space based on distances between training and calibration samples. For this purpose, we test different distance measures (euclidean, mahalanobis), leveraging the concept of KNN-distances, which also takes local point densities into account and test whether principal components of the embeddings improve the delineation of the area of applicability.

Our results highlight practical relevant trade-offs between different distance metrics operating in high-dimensional embedding spaces to derive the area of applicability for deep neural networks. The methodology presented can serve as a baseline to ensure the reliability of deployed models in safety critical applications.