Nadja Klein

Clara Hoffmann, Nadja Klein

Predicting whether an individual with Alzheimer's disease will experience mild or severe disease progression is essential for personalized treatment. Typically, practitioners seek to predict the distribution of a discrete disease score, conditional on an individual's current MRI volume and their historical disease trajectory. Classical statistical regression models and single-task neural networks are not well-suited for this purpose because fitting separate models is infeasible (since each individual typically has few observations), while ignoring individual-level correlation leads to poor generalization. Meta-learning, in contrast, provides a natural avenue to dynamically predict distributions without retraining and model nonlinear relationships between the outcome and covariates. Motivated by this, we propose a Bayesian meta-learner that is trained on multiple individuals but tailors the predictive disease score distribution to each individual's historical data. Our model predicts on unseen individuals without retraining, scales linearly with the number of historical observations, and is guaranteed to be less overconfident when predicting long-term disease scores compared to its deterministic counterpart. On real-world data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, our model achieves performance competitive with both single-task models and deterministic meta-learners, while substantially improving performance when predicting long-term disease progression.

Tobias Fuchs, Florian Kalinke, Nadja Klein

Learning generative models in settings where the source and target distributions are only specified through unpaired samples is gaining in importance. Here, one frequently-used model are Schrödinger bridges (SB), which represent the most likely evolution between both endpoint distributions. To accelerate training, simulation-free SBs avoid the path simulation of the original SB models. However, learning simulation-free SBs requires paired data; a coupling of the source and target samples is obtained as the solution of the entropic optimal transport (OT) problem. As obtaining the optimal global coupling is infeasible in many practical cases, the entropic OT problem is iteratively solved on minibatches instead. Still, the repeated cost remains substantial and the locality can distort the global transport geometry. We propose quantized diffusion Schrödinger bridges (QDSB), which compute the endpoint coupling on anchor-quantized endpoint distributions and lift the resulting plan back to original data points through cell-wise sampling. We show that the regularized optimal coupling is stable w.r.t. anchor quantization, with an error controlled by the quality of the anchor approximation. In real-world experiments, QDSB matches the sample quality of existing baselines, requiring substantially less time. Code and data are available at github.com/mathefuchs/qdsb.

Moussa Kassem Sbeyti, Joshua Holstein, Philipp Spitzer et al.

High-quality labeled data is essential for training robust machine learning models, yet obtaining annotations at scale remains expensive. AI-assisted annotation has therefore become standard in large-scale labeling workflows. However, in tasks where model predictions carry two independent components, a class label and spatial boundaries, a model may classify an object with high confidence while mislocalizing it. Existing AI-assisted workflows offer annotators no signal about where spatial errors are most likely. Without such guidance, humans may systematically underinspect subtly misplaced boxes. We address this by studying the effect of visualizing spatial uncertainty via a purpose-built interface. In a controlled study with 120 participants, those receiving uncertainty cues achieve higher label quality while being faster overall. A box-level analysis confirms that the cues redirect annotator effort toward high-uncertainty predictions and away from well-localized boxes. These findings establish localization uncertainty as a lever to improve human-in-the-loop annotation. Code is available at https://mos-ks.github.io/MUHA/.

Benedikt Lütke Schwienhorst, Nadja Klein, Johannes Lederer

Score matching is an alternative to maximum likelihood estimation when the normalizing constant is unknown or too costly to evaluate. However, vanilla score matching has shown to be inefficient relative to maximum likelihood estimation for multimodal distributions with well-separated modes, which are commonly encountered in practical applications. We compare a novel diffusion-based denoising score matching estimator (DDSME) to the vanilla score matching estimator (SME) in this scenario. In particular, we prove statistical guarantees for both estimators, showing that the error bound for the vanilla SME worsens when the separation between the modes increases, which can be avoided in case of the DDSME with suitable hyperparameter tuning. This provides a novel theoretical explanation for the superior behavior of diffusion-based score matching over the vanilla version.

Philipp Dahlinger, Balázs Gyenes, Niklas Freymuth et al.

Graph Network Simulators (GNSs) have emerged as powerful surrogates for complex physics-based simulation, offering inherent differentiability and orders-of-magnitude speedups over traditional solvers. However, GNSs typically assume access to the underlying material parameters, such as stiffness or viscosity, severely limiting their utility in realistic experimental settings. While recent meta-learning approaches address the parameter dependency by inferring properties from mesh trajectories, reconstructing a mesh from an observed scene is challenging. In this work, we introduce Point Cloud Encoding for Accurate Context Handling (PEACH), a novel framework that applies in-context learning on point clouds to adapt a learned simulator to unseen physical properties during inference. Our approach relies on a novel spatio-temporal point cloud sequence encoder, as well as two forms of auxiliary supervision to help improve simulation fidelity. We demonstrate that PEACH is capable of accurate zero-shot sim-to-real transfer on a challenging, dynamic scene. Experiments on simulation scenes show that PEACH even outperforms mesh-based baselines on prediction accuracy, while being much more practical for real-world deployment.

Moussa Kassem Sbeyti, Nadja Klein

Detecting small and distant objects remains challenging for object detectors due to scale variation, low resolution, and background clutter. Safety-critical applications require reliable detection of these objects for safe planning. Depth information can improve detection, but existing approaches require complex, model-specific architectural modifications. We provide a theoretical analysis followed by an empirical investigation of the depth-detection relationship. Together, they explain how depth causes systematic performance degradation and why depth-informed supervision mitigates it. We introduce DepthPrior, a framework that uses depth as prior knowledge rather than as a fused feature, providing comparable benefits without modifying detector architectures. DepthPrior consists of Depth-Based Loss Weighting (DLW) and Depth-Based Loss Stratification (DLS) during training, and Depth-Aware Confidence Thresholding (DCT) during inference. The only overhead is the initial cost of depth estimation. Experiments across four benchmarks (KITTI, MS COCO, VisDrone, SUN RGB-D) and two detectors (YOLOv11, EfficientDet) demonstrate the effectiveness of DepthPrior, achieving up to +9% mAP$_S$ and +7% mAR$_S$ for small objects, with inference recovery rates as high as 95:1 (true vs. false detections). DepthPrior offers these benefits without additional sensors, architectural changes, or performance costs. Code is available at https://github.com/mos-ks/DepthPrior.

Zeyu Ding, Katja Ickstadt, Nadja Klein et al.

Efficient and scalable non-parametric or semi-parametric regression analysis and density estimation are of crucial importance to the fields of statistics and machine learning. However, available methods are limited in their ability to handle large-scale data. We address this issue by developing a novel coreset construction for multivariate conditional transformation models (MCTMs) to enhance their scalability and training efficiency. To the best of our knowledge, these are the first coresets for semi-parametric distributional models. Our approach yields substantial data reduction via importance sampling. It ensures with high probability that the log-likelihood remains within multiplicative error bounds of $(1\pm\varepsilon)$ and thereby maintains statistical model accuracy. Compared to conventional full-parametric models, where coresets have been incorporated before, our semi-parametric approach exhibits enhanced adaptability, particularly in scenarios where complex distributions and non-linear relationships are present, but not fully understood. To address numerical problems associated with normalizing logarithmic terms, we follow a geometric approximation based on the convex hull of input data. This ensures feasible, stable, and accurate inference in scenarios involving large amounts of data. Numerical experiments demonstrate substantially improved computational efficiency when handling large and complex datasets, thus laying the foundation for a broad range of applications within the statistics and machine learning communities.

Ekin Celikkan, Timo Kunzmann, Yertay Yeskaliyev et al.

Weeds are one of the major reasons for crop yield loss but current weeding practices fail to manage weeds in an efficient and targeted manner. Effective weed management is especially important for crops with high worldwide production such as maize, to maximize crop yield for meeting increasing global demands. Advances in near-sensing and computer vision enable the development of new tools for weed management. Specifically, state-of-the-art segmentation models, coupled with novel sensing technologies, can facilitate timely and accurate weeding and monitoring systems. However, learning-based approaches require annotated data and show a lack of generalization to aerial imaging for different crops. We present a novel dataset for semantic and instance segmentation of crops and weeds in agricultural maize fields. The multispectral UAV-based dataset contains images with RGB, red-edge, and near-infrared bands, a large number of plant instances, dense annotations for maize and four weed classes, and is multitemporal. We provide extensive baseline results for both tasks, including probabilistic methods to quantify prediction uncertainty, improve model calibration, and demonstrate the approach's applicability to out-of-distribution data. The results show the effectiveness of the two additional bands compared to RGB only, and better performance in our target domain than models trained on existing datasets. We hope our dataset advances research on methods and operational systems for fine-grained weed identification, enhancing the robustness and applicability of UAV-based weed management. The dataset and code are available at https://github.com/GFZ/weedsgalore

Moussa Kassem Sbeyti, Michelle Karg, Christian Wirth et al.

Object detectors in real-world applications often fail to detect objects due to varying factors such as weather conditions and noisy input. Therefore, a process that mitigates false detections is crucial for both safety and accuracy. While uncertainty-based thresholding shows promise, previous works demonstrate an imperfect correlation between uncertainty and detection errors. This hinders ideal thresholding, prompting us to further investigate the correlation and associated cost with different types of uncertainty. We therefore propose a cost-sensitive framework for object detection tailored to user-defined budgets on the two types of errors, missing and false detections. We derive minimum thresholding requirements to prevent performance degradation and define metrics to assess the applicability of uncertainty for failure recognition. Furthermore, we automate and optimize the thresholding process to maximize the failure recognition rate w.r.t. the specified budget. Evaluation on three autonomous driving datasets demonstrates that our approach significantly enhances safety, particularly in challenging scenarios. Leveraging localization aleatoric uncertainty and softmax-based entropy only, our method boosts the failure recognition rate by 36-60\% compared to conventional approaches. Code is available at https://mos-ks.github.io/publications.

Moussa Kassem Sbeyti, Nadja Klein, Michelle Karg et al.

Active learning (AL) for real-world object detection faces computational and reliability challenges that limit practical deployment. Developing new AL methods requires training multiple detectors across iterations to compare against existing approaches. This creates high costs for autonomous driving datasets where the training of one detector requires up to 282 GPU hours. Additionally, AL method rankings vary substantially across validation sets, compromising reliability in safety-critical transportation systems. We introduce object-based set similarity ($\mathrm{OSS}$), a metric that addresses these challenges. $\mathrm{OSS}$ (1) quantifies AL method effectiveness without requiring detector training by measuring similarity between training sets and target domains using object-level features. This enables the elimination of ineffective AL methods before training. Furthermore, $\mathrm{OSS}$ (2) enables the selection of representative validation sets for robust evaluation. We validate our similarity-based approach on three autonomous driving datasets (KITTI, BDD100K, CODA) using uncertainty-based AL methods as a case study with two detector architectures (EfficientDet, YOLOv3). This work is the first to unify AL training and evaluation strategies in object detection based on object similarity. $\mathrm{OSS}$ is detector-agnostic, requires only labeled object crops, and integrates with existing AL pipelines. This provides a practical framework for deploying AL in real-world applications where computational efficiency and evaluation reliability are critical. Code is available at https://mos-ks.github.io/publications/.

Mohamed-Khalil Bouzidi, Christian Schlauch, Nicole Scheuerer et al.

Fueled by motion prediction competitions and benchmarks, recent years have seen the emergence of increasingly large learning based prediction models, many with millions of parameters, focused on improving open-loop prediction accuracy by mere centimeters. However, these benchmarks fail to assess whether such improvements translate to better performance when integrated into an autonomous driving stack. In this work, we systematically evaluate the interplay between state-of-the-art motion predictors and motion planners. Our results show that higher open-loop accuracy does not always correlate with better closed-loop driving behavior and that other factors, such as temporal consistency of predictions and planner compatibility, also play a critical role. Furthermore, we investigate downsized variants of these models, and, surprisingly, find that in some cases models with up to 86% fewer parameters yield comparable or even superior closed-loop driving performance. Our code is available at https://github.com/continental/pred2plan.

Moussa Kassem Sbeyti, Nadja Klein, Azarm Nowzad et al.

Semi-supervised object detection (SSOD) based on pseudo-labeling significantly reduces dependence on large labeled datasets by effectively leveraging both labeled and unlabeled data. However, real-world applications of SSOD often face critical challenges, including class imbalance, label noise, and labeling errors. We present an in-depth analysis of SSOD under real-world conditions, uncovering causes of suboptimal pseudo-labeling and key trade-offs between label quality and quantity. Based on our findings, we propose four building blocks that can be seamlessly integrated into an SSOD framework. Rare Class Collage (RCC): a data augmentation method that enhances the representation of rare classes by creating collages of rare objects. Rare Class Focus (RCF): a stratified batch sampling strategy that ensures a more balanced representation of all classes during training. Ground Truth Label Correction (GLC): a label refinement method that identifies and corrects false, missing, and noisy ground truth labels by leveraging the consistency of teacher model predictions. Pseudo-Label Selection (PLS): a selection method for removing low-quality pseudo-labeled images, guided by a novel metric estimating the missing detection rate while accounting for class rarity. We validate our methods through comprehensive experiments on autonomous driving datasets, resulting in up to 6% increase in SSOD performance. Overall, our investigation and novel, data-centric, and broadly applicable building blocks enable robust and effective SSOD in complex, real-world scenarios. Code is available at https://mos-ks.github.io/publications.

Christopher Ries, Moussa Kassem Sbeyti, Nicolas Bianco et al.

Conformal Prediction (CP) is a distribution-free method for constructing prediction sets with marginal finite-sample coverage guarantees, making it a suitable framework for reliable uncertainty quantification in safety-critical object detection. However, object detection introduces structured multi-output predictions, complicating the application of classical CP theory developed for single outputs. In addition, standard, unscaled CP produces fixed-width prediction intervals across inputs, leading to unnecessary width for low-uncertainty predictions. While scaled CP addresses this by adapting the interval width to an input-dependent uncertainty estimate, prior work has neither systematically compared unscaled and scaled CP for multi-class object detection, nor integrated CP with a complementary uncertainty quantification method in this setting. We fill this gap by: (i) applying CP coordinate-wise to bounding box corners with a Bonferroni correction for box-level guarantees; (ii) scaling the resulting intervals using per-prediction aleatoric uncertainty estimates derived from a probabilistic object detector trained with loss attenuation, evaluated in uncalibrated and two calibrated variants; (iii) extending to a two-step pipeline that constructs prediction sets for the class using RAPS and conditions the conformalized bounding boxes on the predicted class set. Across three autonomous driving datasets (KITTI, BDD, CODA), including a cross-domain setting under distribution shift, scaled CP consistently improves interval sharpness over unscaled CP, achieving up to 19% higher IoU and 39% lower interval scores, without sacrificing coverage. Class-wise calibration further improves coverage for both variants with a negligible effect on sharpness. Together, these improvements yield more actionable uncertainty estimates for real-time, real-world object detection.

Victor Medina-Olivares, Wangzhen Xia, Stefan Lessmann et al.

We propose a semi-structured discrete-time multi-state model to analyse mortgage delinquency transitions. This model combines an easy-to-understand structured additive predictor, which includes linear effects and smooth functions of time and covariates, with a flexible neural network component that captures complex nonlinearities and higher-order interactions. To ensure identifiability when covariates are present in both components, we orthogonalise the unstructured part relative to the structured design. For discrete-time competing transitions, we derive exact transformations that map binary logistic models to valid competing transition probabilities, avoiding the need for continuous-time approximations. In simulations, our framework effectively recovers structured baseline and covariate effects while using the neural component to detect interaction patterns. We demonstrate the method using the Freddie Mac Single-Family Loan-Level Dataset, employing an out-of-time test design. Compared with a structured generalised additive benchmark, the semi-structured model provides modest but consistent gains in discrimination across the earliest prediction spans, while maintaining similar Brier scores. Adding macroeconomic indicators provides limited incremental benefit in this out-of-time evaluation and does not materially change the estimated borrower-, loan-, or duration-driven effects. Overall, semi-structured multi-state modelling offers a practical compromise between transparent effect estimates and flexible pattern learning, with potential applications beyond credit-transition forecasting.

Christian Schlauch, Nadja Klein, Christian Wirth

Informed machine learning methods allow the integration of prior knowledge into learning systems. This can increase accuracy and robustness or reduce data needs. However, existing methods often assume hard constraining knowledge, that does not require to trade-off prior knowledge with observations, but can be used to directly reduce the problem space. Other approaches use specific, architectural changes as representation of prior knowledge, limiting applicability. We propose an informed machine learning method, based on continual learning. This allows the integration of arbitrary, prior knowledge, potentially from multiple sources, and does not require specific architectures. Furthermore, our approach enables probabilistic and multi-modal predictions, that can improve predictive accuracy and robustness. We exemplify our approach by applying it to a state-of-the-art trajectory predictor for autonomous driving. This domain is especially dependent on informed learning approaches, as it is subject to an overwhelming large variety of possible environments and very rare events, while requiring robust and accurate predictions. We evaluate our model on a commonly used benchmark dataset, only using data already available in a conventional setup. We show that our method outperforms both non-informed and informed learning methods, that are often used in the literature. Furthermore, we are able to compete with a conventional baseline, even using half as many observation examples.

Kumar Manas, Christian Schlauch, Adrian Paschke et al.

Deep learning-based trajectory prediction models have demonstrated promising capabilities in capturing complex interactions. However, their out-of-distribution generalization remains a significant challenge, particularly due to unbalanced data and a lack of enough data and diversity to ensure robustness and calibration. To address this, we propose SHIFT (Spectral Heteroscedastic Informed Forecasting for Trajectories), a novel framework that uniquely combines well-calibrated uncertainty modeling with informative priors derived through automated rule extraction. SHIFT reformulates trajectory prediction as a classification task and employs heteroscedastic spectral-normalized Gaussian processes to effectively disentangle epistemic and aleatoric uncertainties. We learn informative priors from training labels, which are automatically generated from natural language driving rules, such as stop rules and drivability constraints, using a retrieval-augmented generation framework powered by a large language model. Extensive evaluations over the nuScenes dataset, including challenging low-data and cross-location scenarios, demonstrate that SHIFT outperforms state-of-the-art methods, achieving substantial gains in uncertainty calibration and displacement metrics. In particular, our model excels in complex scenarios, such as intersections, where uncertainty is inherently higher. Project page: https://kumarmanas.github.io/SHIFT/.

Katharina Winter, Abhishek Vivekanandan, Rupert Polley et al.

Generative AI (GenAI) is rapidly advancing the field of Autonomous Driving (AD), extending beyond traditional applications in text, image, and video generation. We explore how generative models can enhance automotive tasks, such as static map creation, dynamic scenario generation, trajectory forecasting, and vehicle motion planning. By examining multiple generative approaches ranging from Variational Autoencoder (VAEs) over Generative Adversarial Networks (GANs) and Invertible Neural Networks (INNs) to Generative Transformers (GTs) and Diffusion Models (DMs), we highlight and compare their capabilities and limitations for AD-specific applications. Additionally, we discuss hybrid methods integrating conventional techniques with generative approaches, and emphasize their improved adaptability and robustness. We also identify relevant datasets and outline open research questions to guide future developments in GenAI. Finally, we discuss three core challenges: safety, interpretability, and realtime capabilities, and present recommendations for image generation, dynamic scenario generation, and planning.

Christian Schlauch, Christian Wirth, Nadja Klein

Prior parameter distributions provide an elegant way to represent prior expert and world knowledge for informed learning. Previous work has shown that using such informative priors to regularize probabilistic deep learning (DL) models increases their performance and data-efficiency. However, commonly used sampling-based approximations for probabilistic DL models can be computationally expensive, requiring multiple inference passes and longer training times. Promising alternatives are compute-efficient last layer kernel approximations like spectral normalized Gaussian processes (SNGPs). We propose a novel regularization-based continual learning method for SNGPs, which enables the use of informative priors that represent prior knowledge learned from previous tasks. Our proposal builds upon well-established methods and requires no rehearsal memory or parameter expansion. We apply our informed SNGP model to the trajectory prediction problem in autonomous driving by integrating prior drivability knowledge. On two public datasets, we investigate its performance under diminishing training data and across locations, and thereby demonstrate an increase in data-efficiency and robustness to location-transfers over non-informed and informed baselines.

David Martens, Galit Shmueli, Theodoros Evgeniou et al.

Understanding the decisions made and actions taken by increasingly complex AI system remains a key challenge. This has led to an expanding field of research in explainable artificial intelligence (XAI), highlighting the potential of explanations to enhance trust, support adoption, and meet regulatory standards. However, the question of what constitutes a "good" explanation is dependent on the goals, stakeholders, and context. At a high level, psychological insights such as the concept of mental model alignment can offer guidance, but success in practice is challenging due to social and technical factors. As a result of this ill-defined nature of the problem, explanations can be of poor quality (e.g. unfaithful, irrelevant, or incoherent), potentially leading to substantial risks. Instead of fostering trust and safety, poorly designed explanations can actually cause harm, including wrong decisions, privacy violations, manipulation, and even reduced AI adoption. Therefore, we caution stakeholders to beware of explanations of AI: while they can be vital, they are not automatically a remedy for transparency or responsible AI adoption, and their misuse or limitations can exacerbate harm. Attention to these caveats can help guide future research to improve the quality and impact of AI explanations.

Tobias Fuchs, Nadja Klein

Real-world data is frequently noisy and ambiguous. In crowdsourcing, for example, human annotators may assign conflicting class labels to the same instances. Partial-label learning (PLL) addresses this challenge by training classifiers when each instance is associated with a set of candidate labels, only one of which is correct. While early PLL methods approximate the true label posterior, they are often computationally intensive. Recent deep learning approaches improve scalability but rely on surrogate losses and heuristic label refinement. We introduce a novel probabilistic framework that directly approximates the posterior distribution over true labels using amortized variational inference. Our method employs neural networks to predict variational parameters from input data, enabling efficient inference. This approach combines the expressiveness of deep learning with the rigor of probabilistic modeling, while remaining architecture-agnostic. Theoretical analysis and extensive experiments on synthetic and real-world datasets demonstrate that our method achieves state-of-the-art performance in both accuracy and efficiency.

Paulo Yanez Sarmiento, Simon Witzke, Nadja Klein et al.

Explainability is a key component in many applications involving deep neural networks (DNNs). However, current explanation methods for DNNs commonly leave it to the human observer to distinguish relevant explanations from spurious noise. This is not feasible anymore when going from easily human-accessible data such as images to more complex data such as genome sequences. To facilitate the accessibility of DNN outputs from such complex data and to increase explainability, we present a modification of the widely used explanation method layer-wise relevance propagation. Our approach enforces sparsity directly by pruning the relevance propagation for the different layers. Thereby, we achieve sparser relevance attributions for the input features as well as for the intermediate layers. As the relevance propagation is input-specific, we aim to prune the relevance propagation rather than the underlying model architecture. This allows to prune different neurons for different inputs and hence, might be more appropriate to the local nature of explanation methods. To demonstrate the efficacy of our method, we evaluate it on two types of data: images and genome sequences. We show that our modification indeed leads to noise reduction and concentrates relevance on the most important features compared to the baseline.

Maximilian Kertel, Nadja Klein

We present a boosting-based method to learn additive Structural Equation Models (SEMs) from observational data, with a focus on the theoretical aspects of determining the causal order among variables. We introduce a family of score functions based on arbitrary regression techniques, for which we establish necessary conditions to consistently favor the true causal ordering. Our analysis reveals that boosting with early stopping meets these criteria and thus offers a consistent score function for causal orderings. To address the challenges posed by high-dimensional data sets, we adapt our approach through a component-wise gradient descent in the space of additive SEMs. Our simulation study underlines our theoretical results for lower dimensions and demonstrates that our high-dimensional adaptation is competitive with state-of-the-art methods. In addition, it exhibits robustness with respect to the choice of the hyperparameters making the procedure easy to tune.

Victor Medina-Olivares, Stefan Lessmann, Nadja Klein

We propose a novel method for predicting time-to-event in the presence of cure fractions based on flexible survivals models integrated into a deep neural network framework. Our approach allows for non-linear relationships and high-dimensional interactions between covariates and survival and is suitable for large-scale applications. Furthermore, we allow the method to incorporate an identified predictor formed of an additive decomposition of interpretable linear and non-linear effects and add an orthogonalization layer to capture potential higher dimensional interactions. We demonstrate the usefulness and computational efficiency of our method via simulations and apply it to a large portfolio of US mortgage loans. Here, we find not only a better predictive performance of our framework but also a more realistic picture of covariate effects.

Benedikt Lütke Schwienhorst, Lucas Kock, Nadja Klein et al.

Even though dropout is a popular regularization technique, its theoretical properties are not fully understood. In this paper we study dropout regularization in extended generalized linear models based on double exponential families, for which the dispersion parameter can vary with the features. A theoretical analysis shows that dropout regularization prefers rare but important features in both the mean and dispersion, generalizing an earlier result for conventional generalized linear models. To illustrate, we apply dropout to adaptive smoothing with B-splines, where both the mean and dispersion parameters are modeled flexibly. The important B-spline basis functions can be thought of as rare features, and we confirm in experiments that dropout is an effective form of regularization for mean and dispersion parameters that improves on a penalized maximum likelihood approach with an explicit smoothness penalty. An application to traffic detection data from Berlin further illustrates the benefits of our method.

Clara Hoffmann, Nadja Klein

End-to-end learners for autonomous driving are deep neural networks that predict the instantaneous steering angle directly from images of the ahead-lying street. These learners must provide reliable uncertainty estimates for their predictions in order to meet safety requirements and initiate a switch to manual control in areas of high uncertainty. Yet end-to-end learners typically only deliver point predictions, since distributional predictions are associated with large increases in training time or additional computational resources during prediction. To address this shortcoming we investigate efficient and scalable approximate inference for the implicit copula neural linear model of Klein, Nott and Smith (2021) in order to quantify uncertainty for the predictions of end-to-end learners. The result are densities for the steering angle that are marginally calibrated, i.e.~the average of the estimated densities equals the empirical distribution of steering angles. To ensure the scalability to large $n$ regimes, we develop efficient estimation based on variational inference as a fast alternative to computationally intensive, exact inference via Hamiltonian Monte Carlo. We demonstrate the accuracy and speed of the variational approach in comparison to Hamiltonian Monte Carlo on two end-to-end learners trained for highway driving using the comma2k19 data set. The implicit copula neural linear model delivers accurate calibration, high-quality prediction intervals and allows to identify overconfident learners. Our approach also contributes to the explainability of black-box end-to-end learners, since predictive densities can be used to understand which steering actions the end-to-end learner sees as valid.

David Rügamer, Chris Kolb, Cornelius Fritz et al.

In this paper we describe the implementation of semi-structured deep distributional regression, a flexible framework to learn conditional distributions based on the combination of additive regression models and deep networks. Our implementation encompasses (1) a modular neural network building system based on the deep learning library \pkg{TensorFlow} for the fusion of various statistical and deep learning approaches, (2) an orthogonalization cell to allow for an interpretable combination of different subnetworks, as well as (3) pre-processing steps necessary to set up such models. The software package allows to define models in a user-friendly manner via a formula interface that is inspired by classical statistical model frameworks such as \pkg{mgcv}. The packages' modular design and functionality provides a unique resource for both scalable estimation of complex statistical models and the combination of approaches from deep learning and statistics. This allows for state-of-the-art predictive performance while simultaneously retaining the indispensable interpretability of classical statistical models.

Nadja Klein, Michael Stanley Smith, David J. Nott

Recurrent neural networks (RNNs) with rich feature vectors of past values can provide accurate point forecasts for series that exhibit complex serial dependence. We propose two approaches to constructing deep time series probabilistic models based on a variant of RNN called an echo state network (ESN). The first is where the output layer of the ESN has stochastic disturbances and a shrinkage prior for additional regularization. The second approach employs the implicit copula of an ESN with Gaussian disturbances, which is a deep copula process on the feature space. Combining this copula with a non-parametrically estimated marginal distribution produces a deep distributional time series model. The resulting probabilistic forecasts are deep functions of the feature vector and also marginally calibrated. In both approaches, Bayesian Markov chain Monte Carlo methods are used to estimate the models and compute forecasts. The proposed models are suitable for the complex task of forecasting intraday electricity prices. Using data from the Australian National Electricity Market, we show that our deep time series models provide accurate short term probabilistic price forecasts, with the copula model dominating. Moreover, the models provide a flexible framework for incorporating probabilistic forecasts of electricity demand as additional features, which increases upper tail forecast accuracy from the copula model significantly.

David Rügamer, Chris Kolb, Nadja Klein

Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the two modeling approaches are, however, limited to very specific combinations and, more importantly, involve an identifiability issue. As a consequence, interpretability and stable estimation are typically lost. We propose a general framework to combine structured regression models and deep neural networks into a unifying network architecture. To overcome the inherent identifiability issues between different model parts, we construct an orthogonalization cell that projects the deep neural network into the orthogonal complement of the statistical model predictor. This enables proper estimation of structured model parts and thereby interpretability. We demonstrate the framework's efficacy in numerical experiments and illustrate its special merits in benchmarks and real-world applications.

Nikolaus Umlauf, Nadja Klein, Thorsten Simon et al.

Over the last decades, the challenges in applied regression and in predictive modeling have been changing considerably: (1) More flexible model specifications are needed as big(ger) data become available, facilitated by more powerful computing infrastructure. (2) Full probabilistic modeling rather than predicting just means or expectations is crucial in many applications. (3) Interest in Bayesian inference has been increasing both as an appealing framework for regularizing or penalizing model estimation as well as a natural alternative to classical frequentist inference. However, while there has been a lot of research in all three areas, also leading to associated software packages, a modular software implementation that allows to easily combine all three aspects has not yet been available. For filling this gap, the R package bamlss is introduced for Bayesian additive models for location, scale, and shape (and beyond). At the core of the package are algorithms for highly-efficient Bayesian estimation and inference that can be applied to generalized additive models (GAMs) or generalized additive models for location, scale, and shape (GAMLSS), also known as distributional regression. However, its building blocks are designed as "Lego bricks" encompassing various distributions (exponential family, Cox, joint models, ...), regression terms (linear, splines, random effects, tensor products, spatial fields, ...), and estimators (MCMC, backfitting, gradient boosting, lasso, ...). It is demonstrated how these can be easily recombined to make classical models more flexible or create new custom models for specific modeling challenges.

Nadja Klein, David J. Nott, Michael Stanley Smith

Deep neural network (DNN) regression models are widely used in applications requiring state-of-the-art predictive accuracy. However, until recently there has been little work on accurate uncertainty quantification for predictions from such models. We add to this literature by outlining an approach to constructing predictive distributions that are `marginally calibrated'. This is where the long run average of the predictive distributions of the response variable matches the observed empirical margin. Our approach considers a DNN regression with a conditionally Gaussian prior for the final layer weights, from which an implicit copula process on the feature space is extracted. This copula process is combined with a non-parametrically estimated marginal distribution for the response. The end result is a scalable distributional DNN regression method with marginally calibrated predictions, and our work complements existing methods for probability calibration. The approach is first illustrated using two applications of dense layer feed-forward neural networks. However, our main motivating applications are in likelihood-free inference, where distributional deep regression is used to estimate marginal posterior distributions. In two complex ecological time series examples we employ the implicit copulas of convolutional networks, and show that marginal calibration results in improved uncertainty quantification. Our approach also avoids the need for manual specification of summary statistics, a requirement that is burdensome for users and typical of competing likelihood-free inference methods.

Elisabeth Waldmann, David Taylor-Robinson, Nadja Klein et al.

Joint Models for longitudinal and time-to-event data have gained a lot of attention in the last few years as they are a helpful technique to approach common a data structure in clinical studies where longitudinal outcomes are recorded alongside event times. Those two processes are often linked and the two outcomes should thus be modeled jointly in order to prevent the potential bias introduced by independent modelling. Commonly, joint models are estimated in likelihood based expectation maximization or Bayesian approaches using frameworks where variable selection is problematic and which do not immediately work for high-dimensional data. In this paper, we propose a boosting algorithm tackling these challenges by being able to simultaneously estimate predictors for joint models and automatically select the most influential variables even in high-dimensional data situations. We analyse the performance of the new algorithm in a simulation study and apply it to the Danish cystic fibrosis registry which collects longitudinal lung function data on patients with cystic fibrosis together with data regarding the onset of pulmonary infections. This is the first approach to combine state-of-the art algorithms from the field of machine-learning with the model class of joint models, providing a fully data-driven mechanism to select variables and predictor effects in a unified framework of boosting joint models.