Disease surveillance, traffic management, and weather forecasting are some of the key applications that could benefit from block maxima forecasting of a time series as the extreme block maxima values often signify events of critical importance such as disease outbreaks, traffic gridlock, and severe weather conditions. As the use of deep neural network models for block maxima forecasting increases, so does the need for explainable AI methods that could unravel the inner workings of such black box models. To fill this need, this paper presents a novel counterfactual explanation framework for block maxima forecasting models. Unlike existing methods, our proposed framework, DiffusionCF, combines deep anomaly detection with a conditional diffusion model to identify unusual patterns in the time series that could help explain the forecasted extreme block maxima. Experimental results on several real-world datasets demonstrate the superiority of DiffusionCF over other baseline methods when evaluated according to various metrics, particularly their informativeness and closeness. Our data and codes are available at https://github.com/yue2023cs/DiffusionCF.

Time series generation is a crucial aspect of data analysis, playing a pivotal role in learning the temporal patterns and their underlying dynamics across diverse fields. Conventional time series generation methods often struggle to capture extreme values adequately, diminishing their value in critical applications such as scenario planning and management for healthcare, finance, climate change adaptation, and beyond. In this paper, we introduce a conditional diffusion model called FIDE to address the challenge of preserving the distribution of extreme values in generative modeling for time series. FIDE employs a novel high-frequency inflation strategy in the frequency domain, preventing premature fade-out of the extreme value. It also extends traditional diffusion-based model, enabling the generation of samples conditioned on the block maxima, thereby enhancing the model's capacity to capture extreme events. Additionally, the FIDE framework incorporates the Generalized Extreme Value (GEV) distribution within its generative modeling framework, ensuring fidelity to both block maxima and overall data distribution. Experimental results on real-world and synthetic data showcase the efficacy of FIDE over baseline methods, highlighting its potential in advancing Generative AI for time series analysis, specifically in accurately modeling extreme events.

Forecasting extreme values in time series is an important but challenging problem as the extreme values are rarely observed even when a large amount of historical data is available. The modeling of extreme values requires a specific focus on estimating the tail distribution of the time series, whose statistical properties may differ from the distribution of its non-extreme values. To overcome this challenge, we present a novel self-supervised learning framework, SimEXT, to learn a robust representation of the time series that preserves the fidelity of its tail distribution. The framework employs a combination of contrastive learning and a reconstruction-based autoencoder architecture to facilitate robust representation learning of the temporal patterns associated with the extreme events. SimEXT also incorporates a wavelet-based data augmentation technique with a distribution-based loss function to prioritize the learning of extreme value distribution. We provide probabilistic guarantees on the wavelet-based augmentation that enables the wavelet coefficients to be perturbed during data augmentation without significantly altering the extreme values of the time series. Experimental results on real-world datasets show that SimEXT can effectively learn a robust representation of the time series to boost the performance of downstream tasks for forecasting block maxima values.

Forecasting the block maxima of a future time window is a challenging task due to the difficulty in inferring the tail distribution of a target variable. As the historical observations alone may not be sufficient to train robust models to predict the block maxima, domain-driven process models are often available in many scientific domains to supplement the observation data and improve the forecast accuracy. Unfortunately, coupling the historical observations with process model outputs is a challenge due to their disparate temporal coverage. This paper presents Self-Recover, a deep learning framework to predict the block maxima of a time window by employing self-supervised learning to address the varying temporal data coverage problem. Specifically Self-Recover uses a combination of contrastive and generative self-supervised learning schemes along with a denoising autoencoder to impute the missing values. The framework also combines representations of the historical observations with process model outputs via a residual learning approach and learns the generalized extreme value (GEV) distribution characterizing the block maxima values. This enables the framework to reliably estimate the block maxima of each time window along with its confidence interval. Extensive experiments on real-world datasets demonstrate the superiority of Self-Recover compared to other state-of-the-art forecasting methods.

Accurate forecasting of extreme values in time series is critical due to the significant impact of extreme events on human and natural systems. This paper presents DeepExtrema, a novel framework that combines a deep neural network (DNN) with generalized extreme value (GEV) distribution to forecast the block maximum value of a time series. Implementing such a network is a challenge as the framework must preserve the inter-dependent constraints among the GEV model parameters even when the DNN is initialized. We describe our approach to address this challenge and present an architecture that enables both conditional mean and quantile prediction of the block maxima. The extensive experiments performed on both real-world and synthetic data demonstrated the superiority of DeepExtrema compared to other baseline methods.

Zero-inflated, heavy-tailed spatiotemporal data is common across science and engineering, from climate science to meteorology and seismology. A central modeling objective in such settings is to forecast the intensity, frequency, and timing of extreme and non-extreme events; yet in the context of deep learning, this objective presents several key challenges. First, a deep learning framework applied to such data must unify a mixture of distributions characterizing the zero events, moderate events, and extreme events. Second, the framework must be capable of enforcing parameter constraints across each component of the mixture distribution. Finally, the framework must be flexible enough to accommodate for any changes in the threshold used to define an extreme event after training. To address these challenges, we propose Deep Extreme Mixture Model (DEMM), fusing a deep learning-based hurdle model with extreme value theory to enable point and distribution prediction of zero-inflated, heavy-tailed spatiotemporal variables. The framework enables users to dynamically set a threshold for defining extreme events at inference-time without the need for retraining. We present an extensive experimental analysis applying DEMM to precipitation forecasting, and observe significant improvements in point and distribution prediction. All code is available at https://github.com/andrewmcdonald27/DeepExtremeMixtureModel.