Sebastian Engelke

Nicola Gnecco, Jonas Peters, Sebastian Engelke et al.

Modern machine learning methods and the availability of large-scale data have significantly advanced our ability to predict target quantities from large sets of covariates. However, these methods often struggle under distributional shifts, particularly in the presence of hidden confounding. While the impact of hidden confounding is well-studied in causal effect estimation, e.g., instrumental variables, its implications for prediction tasks under shifting distributions remain underexplored. This work addresses this gap by introducing a strong notion of invariance that, unlike existing weaker notions, allows for distribution generalization even in the presence of nonlinear, non-identifiable structural functions. Central to this framework is the Boosted Control Function (BCF), a novel, identifiable target of inference that satisfies the proposed strong invariance notion and is provably worst-case optimal under distributional shifts. The theoretical foundation of our work lies in Simultaneous Equation Models for Distribution Generalization (SIMDGs), which bridge machine learning with econometrics by describing data-generating processes under distributional shifts. To put these insights into practice, we propose the ControlTwicing algorithm to estimate the BCF using nonparametric machine-learning techniques and study its generalization performance on synthetic and real-world datasets compared to robust and empirical risk minimization approaches.

Sebastian Engelke, Nicola Gnecco, Anne Sabourin

Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from these advances, including regression and classification beyond the training data, extreme quantile regression, supervised and unsupervised dimension reduction, generative artificial intelligence and anomaly detection. This review synthesizes recent developments in these fields at the intersection of statistical learning and extreme value theory, with a focus on principled methods based on asymptotically motivated representations of the tail of univariate and multivariate distributions. We consider different theoretical frameworks for both asymptotically dependent and independent data and discuss how they translate into efficient statistical methods for extrapolation to extreme regions. By addressing both theoretical and practical aspects, we offer a comprehensive overview of the state-of-the-art in this quickly evolving field, and identify promising directions for future research.

Olivier C. Pasche, Jonathan Wider, Zhongwei Zhang et al.

The forecast accuracy of machine learning (ML) weather prediction models is improving rapidly, leading many to speak of a "second revolution in weather forecasting". With numerous methods being developed and limited physical guarantees offered by ML models, there is a critical need for a comprehensive evaluation of these emerging techniques. While this need has been partly fulfilled by benchmark datasets, they provide little information on rare and impactful extreme events or on compound impact metrics, for which model accuracy might degrade due to misrepresented dependencies between variables. To address these issues, we compare ML weather prediction models (GraphCast, PanguWeather, and FourCastNet) and ECMWF's high-resolution forecast system (HRES) in three case studies: the 2021 Pacific Northwest heatwave, the 2023 South Asian humid heatwave, and the North American winter storm in 2021. We find that ML weather prediction models locally achieve similar accuracy to HRES on the record-shattering Pacific Northwest heatwave but underperform when aggregated over space and time. However, they forecast the compound winter storm substantially better. We also highlight structural differences in how the errors of HRES and the ML models build up to that event. The ML forecasts lack important variables for a detailed assessment of the health risks of the 2023 humid heatwave. Using a possible substitute variable, prediction errors show spatial patterns with the highest danger levels over Bangladesh being underestimated by the ML models. Generally, case-study-driven, impact-centric evaluation can complement existing research, increase public trust, and aid in developing reliable ML weather prediction models.

Zhongwei Zhang, Erich Fischer, Jakob Zscheischler et al.

Artificial intelligence (AI)-based models are revolutionizing weather forecasting and have surpassed leading numerical weather prediction systems on various benchmark tasks. However, their ability to extrapolate and reliably forecast unprecedented extreme events remains unclear. Here, we show that for record-breaking weather extremes, the numerical model High RESolution forecast (HRES) from the European Centre for Medium-Range Weather Forecasts still consistently outperforms state-of-the-art AI models GraphCast, GraphCast operational, Pangu-Weather, Pangu-Weather operational, and Fuxi. We demonstrate that forecast errors in AI models are consistently larger for record-breaking heat, cold, and wind than in HRES across nearly all lead times. We further find that the examined AI models tend to underestimate both the frequency and intensity of record-breaking events, and they underpredict hot records and overestimate cold records with growing errors for larger record exceedance. Our findings underscore the current limitations of AI weather models in extrapolating beyond their training domain and in forecasting the potentially most impactful record-breaking weather events that are particularly frequent in a rapidly warming climate. Further rigorous verification and model development is needed before these models can be solely relied upon for high-stakes applications such as early warning systems and disaster management.

Almut Rödder, Manuel Hentschel, Sebastian Engelke

Neural estimators are simulation-based estimators for the parameters of a family of statistical models, which build a direct mapping from the sample to the parameter vector. They benefit from the versatility of available network architectures and efficient training methods developed in the field of deep learning. Neural estimators are amortized in the sense that, once trained, they can be applied to any new data set with almost no computational cost. While many papers have shown very good performance of these methods in simulation studies and real-world applications, so far no statistical guarantees are available to support these observations theoretically. In this work, we study the risk of neural estimators by decomposing it into several terms that can be analyzed separately. We formulate easy-to-check assumptions ensuring that each term converges to zero, and we verify them for popular applications of neural estimators. Our results provide a general recipe to derive theoretical guarantees also for broader classes of architectures and estimation problems.

Younes Boulaguiem, Jakob Zscheischler, Edoardo Vignotto et al.

Modelling dependencies between climate extremes is important for climate risk assessment, for instance when allocating emergency management funds. In statistics, multivariate extreme value theory is often used to model spatial extremes. However, most commonly used approaches require strong assumptions and are either too simplistic or over-parameterized. From a machine learning perspective, Generative Adversarial Networks (GANs) are a powerful tool to model dependencies in high-dimensional spaces. Yet in the standard setting, GANs do not well represent dependencies in the extremes. Here we combine GANs with extreme value theory (evtGAN) to model spatial dependencies in summer maxima of temperature and winter maxima in precipitation over a large part of western Europe. We use data from a stationary 2000-year climate model simulation to validate the approach and explore its sensitivity to small sample sizes. Our results show that evtGAN outperforms classical GANs and standard statistical approaches to model spatial extremes. Already with about 50 years of data, which corresponds to commonly available climate records, we obtain reasonably good performance. In general, dependencies between temperature extremes are better captured than dependencies between precipitation extremes due to the high spatial coherence in temperature fields. Our approach can be applied to other climate variables and can be used to emulate climate models when running very long simulations to determine dependencies in the extremes is deemed infeasible.

Talia B. Kimber, Sebastian Engelke, Igor V. Tetko et al.

In our study, we demonstrate the synergy effect between convolutional neural networks and the multiplicity of SMILES. The model we propose, the so-called Convolutional Neural Fingerprint (CNF) model, reaches the accuracy of traditional descriptors such as Dragon (Mauri et al. [22]), RDKit (Landrum [18]), CDK2 (Willighagen et al. [43]) and PyDescriptor (Masand and Rastija [20]). Moreover the CNF model generally performs better than highly fine-tuned traditional descriptors, especially on small data sets, which is of great interest for the chemical field where data sets are generally small due to experimental costs, the availability of molecules or accessibility to private databases. We evaluate the CNF model along with SMILES augmentation during both training and testing. To the best of our knowledge, this is the first time that such a methodology is presented. We show that using the multiplicity of SMILES during training acts as a regulariser and therefore avoids overfitting and can be seen as ensemble learning when considered for testing.

Edoardo Vignotto, Sebastian Engelke

Classification tasks usually assume that all possible classes are present during the training phase. This is restrictive if the algorithm is used over a long time and possibly encounters samples from unknown classes. The recently introduced extreme value machine, a classifier motivated by extreme value theory, addresses this problem and achieves competitive performance in specific cases. We show that this algorithm can fail when the geometries of known and unknown classes differ. To overcome this problem, we propose two new algorithms relying on approximations from extreme value theory. We show the effectiveness of our classifiers in simulations and on the LETTER and MNIST data sets.