Can Uncertainty Quantification Benefit From Label Embeddings? A Case Study on Local Climate Zone Classification

Abstract

Modern deep learning models have achieved superior performance in almost all fields of remote sensing. An often neglected aspect of these models is the quantification and evaluation of predictive uncertainties. Regarding a classification task, this means that the focus of the analysis solely lies on performance metrics such as accuracy or the loss. On the other hand, a notion of uncertainty indicates the model’s indecisiveness among the given classes and is essential to understand where the model struggles to classify the data samples. In this work, three levels of uncertainty are distinguished, starting with the typical softmax pseudo-probabilities as level-1 uncertainty. As a next level, the more flexible Dirichlet framework is utilized as model output space, and hereby also, a Bayesian setting with an uninformative prior is considered. For the level-3 uncertainty, an empirical Bayes setting is incorporated where a latent embedding of the label space is iteratively estimated by the marginal likelihood of the fully parameterized label space. The estimated embeddings are then learned by the network in three different settings: Two regression losses use the embeddings directly, while the closed-form solution of the Kullback-Leibler (KL) divergence uses the embedding parameterized as a Dirichlet distribution. To assess the different levels of uncertainty, the label evaluation subset of the So2Sat LCZ42 dataset, which contains label votes from multiple remote sensing experts, is investigated. The predictive uncertainties are evaluated by means of out-of-distribution (OoD) detection and calibration performance. Overall, the embedding-based approaches show strong performance for calibration, while, for the OoD experiments, the Bayesian Dirichlet setting with an uninformative prior achieves the best performance. In conclusion, embedded labels offer a flexible framework for incorporating uncertain or ambiguous labels into a supervised training setup. They could be highly beneficial for applications in fields such as urban planning or disaster response.