Big Data Methods

The age of digitalization has lead to complex large-scale data that are too large or infeasible for traditional statistical methods, e.g., due to unstructured information such as videos. We develop algorithms and software that can address these challenges and that lead to fast and accurate estimation even for data with many observations or complex structures.

Bayesian Computational Methods

Bayesian computation is a powerful framework for tackling complex statistical problems. Our expertise lies in Markov Chain Monte Carlo (MCMC), Variational Inference, INLA and Approximate Bayesian Computation, which are used for estimating or approximating complex and high-dimensional posterior distributions with precision. By means of Bayesian principles, our methods excel in applications such as machine learning, data analysis, and decision-making under uncertainty. We specialize in modeling uncertainty and integrating prior knowledge seamlessly with data, providing a solid foundation for robust statistical analysis.

Bayesian Deep Learning

Bayesian Deep Learning is a state-of-the-art fusion of deep neural networks with Bayesian computational methods. There, we not only harness the power of neural networks for tasks like image recognition and natural language processing, but we also incorporate Bayesian principles. This means we can quantify uncertainty in predictions, improve model robustness, and enable reliable decision-making. Our research covers Bayesian neural networks, Bayesian optimization, and probabilistic programming to create models that not only make accurate predictions but also provide probabilistic measures of confidence in those predictions.

Copula Modelling and Regression Copulas

Copula modelling allows to characterize the joint distribution of multiple variables through a decomposition that separates modelling the marginal distributions and the dependence structure. This allows to study and model various forms of dependence, such as tail dependencies and non-linear relationships. Regression copulas further enhance this framework by incorporating regression structures through implicit copula processes, thereby enabling to model not only dependencies but also how they vary with covariates.

Distributional Regression

Distributional Regression is a cutting-edge statistical framework that goes beyond traditional mean regression models. We aim to model the entire distribution of the response variables, rather than just its mean. This enables us to capture richer and more nuanced information about the data, allowing for better insights and predictions. We leverage techniques such as quantile regression, conditional transformation models or regression copulas to accurately estimate the underlying conditional distributions as functions of structured but also unstructured input variables. Structured variables include classical tabular data, group-specific effects or spatial information and unstructured data can be images or text. Our research group specializes in developing and advancing Distributional Regression methods, exploring their applications in diverse fields, including economics, finance, and environmental science.

Network Analysis

Network analysis involves the study of complex systems involving connections between entities. When combined with probabilistic methods, it becomes a powerful tool for understanding uncertainty and relationships within real-world networks. We use techniques like Bayesian networks, Markov random fields, and probabilistic graphical models to capture dependencies, predict outcomes, and infer hidden information within networks to understand it better as a whole. By unveiling hidden patterns in these structures, ultimately decision-making in complex interconnected systems can be enhanced.

Smoothing, Regularization and Shrinkage

Smoothing plays a pivotal role in contemporary statistics and allows to avoid the common assumption that continuous covariates must have a linear effect on the response. Our preferred approach to smoothing entails the fusion of basis expansions with conditionally Gaussian regularization priors to prevent overfitting.
We offer theoretical guarantees, delve into the selection of appropriate hyperpriors and relax conventional assumptions to achieve adaptive or anisotropic smoothing.
Leveraging recent developments for Bayesian shrinkage priors allows us to perform effect selection in non-standard regression models, even when the response distribution diverges from the typical exponential family. Within this research area, we have the capability to estimate numerous smooth nonlinear effects and we apply these techniques across a wide range, including real estate economics, public health and climatology.

Spatial Statistics

Spatial statistics focuses on analysing and understanding geographic or spatial data. Such spatial models play a crucial role in various disciplines, such as urban planning, epidemiology, environmental science, and resource management. Our group develops state-of-the-art Bayesian spatial models with particular interest in nonparametric and distributional approaches, e.g. spatial implicit copulas. Such approaches allow us to incorporate prior knowledge and uncertainty into our spatial analyses, providing a more robust and flexible framework for capturing spatial dependencies and generating reliable predictions in the presence of limited data.

Sub-Project P5: Structured explainability for interactions in deep learning models applied to pathogen phenotype prediction
Explaining and understanding the underlying interactions of genomic regions are crucial for proper pathogen phenotype characterization such as predicting the virulence of an organism or the resistance to drugs. Existing methods for classifying the underlying large-scale data of genome sequences face challenges with regard to explainability due to the high dimensionality of data, making it difficult to visualize, access and justify classification decisions. This is particularly the case in the presence of interactions, such as of genomic regions. To address these challenges, we will develop methods for variable selection and structured explainability that capture the interactions of important input variables: More specifically, we address these challenges (i) within a deep mixed models framework for binary outcomes fusing generalized linear mixed models and a deep variant of structured predictors. We thereby combine statistical logistic regression models with deep learning for disentangling complex interactions in genomic data. We particularly enable estimation when no explicitly formulated inputs are available for the models, as for instance relevant with genomics data. Further, (ii), we will extend methods for explainability of classification decisions such as layerwise relevance propagation to explain these interactions. Investigating these two complementary approaches on both the model and explainability levels, it is our main objective to formulate and postulate structured explanations that not only give first-order, single variable explanations of classification decisions, but also regard their interactions. While our methods are motivated by our genomic data, they can be useful and extended to other application areas in which interactions are of interest.

Sub-Project P6: Probabilistic learning approaches for complex disease progression based on high-dimensional MRI data
This project proposes informed, data-driven methods to reveal pathological trajectories based on high-dimensional medical data obtained from magnetic resonance imaging (MRI), which are relevant as both inputs and outputs in regression equations to adequately perform early diagnosis and to model, understand, and predict actual and future disease progression. For this, we will fuse deep learning (DL) methods with Bayesian statistics to (1) accurately predict the complete outcome distributions of individual patients based on MRI data and further confounders and covariates (such as clinical or demographical variables) to adequately quantify uncertainty in predictions in contrast to point predictions not delivering any measures of confidence (2) model temporal dynamics in biomedical patient data. Regarding (1), we will develop deep distributional regression models for image inputs to accurately predict the entire distributions of the different disease scores (e.g. symptom severity), which can be multivariate and are typically highly non-normally distributed. Regarding (2), we will model the complex temporal evolution in neurological diseases by developing DL-based state-space models. Neither model is tailored to a specific disease, but both will be exemplary developed and tested for two neurological diseases, namely Alzheimer’s disease (AD) and multiple sclerosis (MS), chosen for their different disease progression profiles.

Weeds are one of the major contributors to crop yield loss. As a result, farmers deploy various approaches to manage and control weed growth in their agricultural fields, most common being chemical herbicides. However, the herbicides are often applied uniformly to the entire field, which has negative environmental and financial impacts. Site-specific weed management (SSWM) considers the variability in the field and localizes the treatment. Accurate localization of weeds is the first step for SSWM. Moreover, information on the prediction confidence is crucial to deploy methods in real-world applications. This project aims to develop methods for weed identification in croplands from low-altitude UAV remote sensing imagery and uncertainty quantification using Bayesian machine learning, in order to develop a holistic approach for SSWM.

The project is supported by Helmholtz Einstein International Berlin Research School in Data Science (HEIBRiDS) and co-supervised by Prof. Dr. Martin Herold from GFZ German Research Centre for Geosciences.

Despite significant overlap and synergy, machine learning and statistical science have developed largely in parallel. Deep Gaussian mixture models, a recently introduced model class in machine learning, are concerned with the unsupervised tasks of density estimation and high-dimensional clustering used for pattern recognition in many applied areas. In order to avoid over-parameterized solutions, dimension reduction by factor models can be applied at each layer of the architecture. However, the choice of architectures can be interpreted as a Bayesian model choice problem, meaning that every possible model satisfying the constraints is then fitted. The authors propose a much simpler approach: Only one large model needs to be trained and unnecessary components will empty out. The idea that parameters can be assigned prior distributions is highly unorthodox but extremely simple bringing together two sciences, namely machine learning and Bayesian statistics.

Traditional regression models often provide an overly simplistic view on complex associations and relationships to contemporary data problems in the area of biomedicine. In particular, capturing relevant associations between multiple clinical endpoints correctly is of high relevance to avoid model misspecifications, which can lead to biased results and even wrong or misleading conclusions and treatments. As such, methodological development of statistical methods tailored for such problems in biomedicine are of considerable interest. It is the aim of this project to develop novel conditional copula regression models for high-dimensional biomedical data structures by bringing together efficient statistical learning tools for high-dimensional data and established methods from economics for multivariate data structures that allow to capture complex dependence structuresbetween variables. These methods will allow us to model the entire joint distribution of multiple endpoints simultaneously and to automatically determine the relevant influential covariates and risk factors via algorithms originally proposed in the area of statistical and machine learning. The resulting models can then be used both for the interpretation and analysis of complex association-structures as well as for prediction inference (simultaneous prediction intervals for multiple endpoints). Additional implementation in open software and its application in various studies highlight the potentials of this project’s methodological developments in the area of digital medicine.

Recent progress in computer science has led to data structures of increasing size, detail and complexity in many scientific studies. In particular nowadays, where such big data applications do not only allow but also require more flexibility to overcome modelling restrictions that may result in model misspecification and biased inference, further insight in more accurate models and appropriate inferential methods is of enormous importance. This research group will therefore develop statistical tools for both univariate and multivariate regression models that are interpretable and that can be estimated extremely fast and accurate. Specifically, we aim to develop probabilistic approaches to recent innovations in machine learning in order to estimate models for huge data sets. To obtain more accurate regression models for the entire distribution we construct new distributional models that can be used for both univariate and multivariate responses. In all models we will address the issues of shrinkage and automatic variable selection to cope with a huge number of predictors, and the possibility to capture any type of covariate effect. This proposal also includes software development as well as applications in natural and social sciences (such as income distributions, marketing, weather forecasting, chronic diseases and others), highlighting its potential to successfully contribute to important facets in modern statistics and data science.