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1. Evidential Deep Learning: Enhancing Predictive Uncertainty Estimation for Earth System Science Applications

   https://doi.org/10.1175/AIES-D-23-0093.1  

   Schreck, John S; Gagne, David John; Becker, Charlie; Chapman, William E; Elmore, Kim; Fan, Da; Gantos, Gabrielle; Kim, Eliot; Kimpara, Dhamma; Martin, Thomas; et al (October 2024, Artificial Intelligence for the Earth Systems)

   Abstract Robust quantification of predictive uncertainty is a critical addition needed for machine learning applied to weather and climate problems to improve the understanding of what is driving prediction sensitivity. Ensembles of machine learning models provide predictive uncertainty estimates in a conceptually simple way but require multiple models for training and prediction, increasing computational cost and latency. Parametric deep learning can estimate uncertainty with one model by predicting the parameters of a probability distribution but does not account for epistemic uncertainty. Evidential deep learning, a technique that extends parametric deep learning to higher-order distributions, can account for both aleatoric and epistemic uncertainties with one model. This study compares the uncertainty derived from evidential neural networks to that obtained from ensembles. Through applications of the classification of winter precipitation type and regression of surface-layer fluxes, we show evidential deep learning models attaining predictive accuracy rivaling standard methods while robustly quantifying both sources of uncertainty. We evaluate the uncertainty in terms of how well the predictions are calibrated and how well the uncertainty correlates with prediction error. Analyses of uncertainty in the context of the inputs reveal sensitivities to underlying meteorological processes, facilitating interpretation of the models. The conceptual simplicity, interpretability, and computational efficiency of evidential neural networks make them highly extensible, offering a promising approach for reliable and practical uncertainty quantification in Earth system science modeling. To encourage broader adoption of evidential deep learning, we have developed a new Python package, Machine Integration and Learning for Earth Systems (MILES) group Generalized Uncertainty for Earth System Science (GUESS) (MILES-GUESS) (https://github.com/ai2es/miles-guess), that enables users to train and evaluate both evidential and ensemble deep learning. Significance StatementThis study demonstrates a new technique, evidential deep learning, for robust and computationally efficient uncertainty quantification in modeling the Earth system. The method integrates probabilistic principles into deep neural networks, enabling the estimation of both aleatoric uncertainty from noisy data and epistemic uncertainty from model limitations using a single model. Our analyses reveal how decomposing these uncertainties provides valuable insights into reliability, accuracy, and model shortcomings. We show that the approach can rival standard methods in classification and regression tasks within atmospheric science while offering practical advantages such as computational efficiency. With further advances, evidential networks have the potential to enhance risk assessment and decision-making across meteorology by improving uncertainty quantification, a longstanding challenge. This work establishes a strong foundation and motivation for the broader adoption of evidential learning, where properly quantifying uncertainties is critical yet lacking. 

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2. Function-Space Regularization in Neural Networks

   Rudner, T; Kapoor, S; Qiu, S; Wilson, AG (July 2023, International Conference on Machine Learning)

   Parameter-space regularization in neural network optimization is a fundamental tool for improving generalization. However, standard parameter-space regularization methods make it challenging to encode explicit preferences about desired predictive functions into neural network training. In this work, we approach regularization in neural networks from a probabilistic perspective and show that by viewing parameter-space regularization as specifying an empirical prior distribution over the model parameters, we can derive a probabilistically well-motivated regularization technique that allows explicitly encoding information about desired predictive functions into neural network training. This method—which we refer to as function-space empirical Bayes (FS-EB)—includes both parameter- and function-space regularization, is mathematically simple, easy to implement, and incurs only minimal computational overhead compared to standard regularization techniques. We evaluate the utility of this regularization technique empirically and demonstrate that the proposed method leads to near-perfect semantic shift detection, highly-calibrated predictive uncertainty estimates, successful task adaption from pre-trained models, and improved generalization under covariate shift. 

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3. Prune and Tune Ensembles: Low-Cost Ensemble Learning with Sparse Independent Subnetworks

   Whitaker, T.; Whitley, D. (January 2022, Proceedings of the AAAI Conference on Artificial Intelligence)

   na (Ed.)

   Ensemble Learning is an effective method for improving gen- eralization in machine learning. However, as state-of-the-art neural networks grow larger, the computational cost associ- ated with training several independent networks becomes ex- pensive. We introduce a fast, low-cost method for creating di- verse ensembles of neural networks without needing to train multiple models from scratch. We do this by first training a single parent network. We then create child networks by cloning the parent and dramatically pruning the parameters of each child to create an ensemble of members with unique and diverse topologies. We then briefly train each child net- work for a small number of epochs, which now converge significantly faster when compared to training from scratch. We explore various ways to maximize diversity in the child networks, including the use of anti-random pruning and one- cycle tuning. This diversity enables “Prune and Tune” ensem- bles to achieve results that are competitive with traditional ensembles at a fraction of the training cost. We benchmark our approach against state of the art low-cost ensemble meth- ods and display marked improvement in both accuracy and uncertainty estimation on CIFAR-10 and CIFAR-100. 

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4. Prune and Tune Ensembles: Low Cost Ensemble Learning with Sparse Independent Subnetworks

   Whitaker, T.; Whitley, D. (January 2022, Proceedings of the AAAI Conference on Artificial Intelligence)

   NA (Ed.)

   Ensemble Learning is an effective method for improving gen- eralization in machine learning. However, as state-of-the-art neural networks grow larger, the computational cost associ- ated with training several independent networks becomes ex- pensive. We introduce a fast, low-cost method for creating di- verse ensembles of neural networks without needing to train multiple models from scratch. We do this by first training a single parent network. We then create child networks by cloning the parent and dramatically pruning the parameters of each child to create an ensemble of members with unique and diverse topologies. We then briefly train each child net- work for a small number of epochs, which now converge significantly faster when compared to training from scratch. We explore various ways to maximize diversity in the child networks, including the use of anti-random pruning and one- cycle tuning. This diversity enables “Prune and Tune” ensem- bles to achieve results that are competitive with traditional ensembles at a fraction of the training cost. We benchmark our approach against state of the art low-cost ensemble meth- ods and display marked improvement in both accuracy and uncertainty estimation on CIFAR-10 and CIFAR-100. 

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5. Neural Bootstrapper

   Shin, M.; Cho, H.; Min, H-S.; Lim, S. (January 2021, Advances in neural information processing systems)

   Ranzato, M.; Beygelzimer, A.; Dauphin, Y.; Liang, P. S.; Wortman Vaughan, J. (Ed.)

   Bootstrapping has been a primary tool for ensemble and uncertainty quantification in machine learning and statistics. However, due to its nature of multiple training and resampling, bootstrapping deep neural networks is computationally burdensome; hence it has difficulties in practical application to the uncertainty estimation and related tasks. To overcome this computational bottleneck, we propose a novel approach called Neural Bootstrapper (NeuBoots), which learns to generate bootstrapped neural networks through single model training. NeuBoots injects the bootstrap weights into the high-level feature layers of the backbone network and outputs the bootstrapped predictions of the target, without additional parameters and the repetitive computations from scratch. We apply NeuBoots to various machine learning tasks related to uncertainty quantification, including prediction calibrations in image classification and semantic segmentation, active learning, and detection of out-of-distribution samples. Our empirical results show that NeuBoots outperforms other bagging based methods under a much lower computational cost without losing the validity of bootstrapping. 

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