Advances in Graph-Cut Optimization: Multi-Surface Models, Label Costs, and Hierarchical Costs

Computer vision is full of problems that are elegantly expressed in terms of mathematical optimization, or energy minimization. This is particularly true of low-level inference problems such as cleaning up noisy signals, clustering and classifying data, or estimating 3D points from images. Energies let us state each problem as a clear, precise objective function. Minimizing the correct energy would, hypothetically, yield a good solution to the corresponding problem. Unfortunately, even for low-level problems we are confronted by energies that are computationally hard—often NP-hard—to minimize. As a consequence, a rather large portion of computer vision research is dedicated to proposing better energies and better algorithms for energies. This dissertation presents work along the same line, specifically new energies and algorithms based on graph cuts. We present three distinct contributions. First we consider biomedical segmentation where the object of interest comprises multiple distinct regions of uncertain shape (e.g. blood vessels, airways, bone tissue). We show that this common yet difficult scenario can be modeled as an energy over multiple interacting surfaces, and can be globally optimized by a single graph cut. Second, we introduce multi-label energies with label costs and provide algorithms to minimize them. We show how label costs are useful for clustering and robust estimation problems in vision. Third, we characterize a class of energies with hierarchical costs and propose a novel hierarchical fusion algorithm with improved approximation guarantees. Hierarchical costs are natural for modeling an array of difficult problems, e.g. segmentation with hierarchical context, simultaneous estimation of motions and homographies, or detecting hierarchies of patterns

Big Data Analytics and Information Science for Business and Biomedical Applications

The analysis of Big Data in biomedical as well as business and financial research has drawn much attention from researchers worldwide. This book provides a platform for the deep discussion of state-of-the-art statistical methods developed for the analysis of Big Data in these areas. Both applied and theoretical contributions are showcased

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science

Factor analysis of dynamic PET images

Thanks to its ability to evaluate metabolic functions in tissues from the temporal evolution of a previously injected radiotracer, dynamic positron emission tomography (PET) has become an ubiquitous analysis tool to quantify biological processes. Several quantification techniques from the PET imaging literature require a previous estimation of global time-activity curves (TACs) (herein called \textit{factors}) representing the concentration of tracer in a reference tissue or blood over time. To this end, factor analysis has often appeared as an unsupervised learning solution for the extraction of factors and their respective fractions in each voxel. Inspired by the hyperspectral unmixing literature, this manuscript addresses two main drawbacks of general factor analysis techniques applied to dynamic PET. The first one is the assumption that the elementary response of each tissue to tracer distribution is spatially homogeneous. Even though this homogeneity assumption has proven its effectiveness in several factor analysis studies, it may not always provide a sufficient description of the underlying data, in particular when abnormalities are present. To tackle this limitation, the models herein proposed introduce an additional degree of freedom to the factors related to specific binding. To this end, a spatially-variant perturbation affects a nominal and common TAC representative of the high-uptake tissue. This variation is spatially indexed and constrained with a dictionary that is either previously learned or explicitly modelled with convolutional nonlinearities affecting non-specific binding tissues. The second drawback is related to the noise distribution in PET images. Even though the positron decay process can be described by a Poisson distribution, the actual noise in reconstructed PET images is not expected to be simply described by Poisson or Gaussian distributions. Therefore, we propose to consider a popular and quite general loss function, called the $\beta$-divergence, that is able to generalize conventional loss functions such as the least-square distance, Kullback-Leibler and Itakura-Saito divergences, respectively corresponding to Gaussian, Poisson and Gamma distributions. This loss function is applied to three factor analysis models in order to evaluate its impact on dynamic PET images with different reconstruction characteristics

Towards Reliable Machine Learning in Evolving Data Streams

Data streams are ubiquitous in many areas of modern life. For example, applications in healthcare, education, finance, or advertising often deal with large-scale and evolving data streams. Compared to stationary applications, data streams pose considerable additional challenges for automated decision making and machine learning. Indeed, online machine learning methods must cope with limited memory capacities, real-time requirements, and drifts in the data generating process. At the same time, online learning methods should provide a high predictive quality, stability in the presence of input noise, and good interpretability in order to be reliably used in practice. In this thesis, we address some of the most important aspects of machine learning in evolving data streams. Specifically, we identify four open issues related to online feature selection, concept drift detection, online classification, local explainability, and the evaluation of online learning methods. In these contexts, we present new theoretical and empirical findings as well as novel frameworks and implementations. In particular, we propose new approaches for online feature selection and concept drift detection that can account for model uncertainties and thus achieve more stable results. Moreover, we introduce a new incremental decision tree that retains valuable interpretability properties and a new change detection framework that allows for more efficient explanations based on local feature attributions. In fact, this is one of the first works to address intrinsic model interpretability and local explainability in the presence of incremental updates and concept drift. Along with this thesis, we provide extensive open resources related to online machine learning. Notably, we introduce a new Python framework that enables simplified and standardized evaluations and can thus serve as a basis for more comparable online learning experiments in the future. In total, this thesis is based on six publications, five of which were peer-reviewed at the time of publication of this thesis. Our work touches all major areas of predictive modeling in data streams and proposes novel solutions for efficient, stable, interpretable and thus reliable online machine learning.Datenströme sind in vielen Bereichen des modernen Lebens allgegenwärtig. Beispielsweise haben Anwendungen im Gesundheitswesen, im Bildungswesen, im Finanzwesen oder in der Werbung häufig mit großen und sich verändernden Datenströmen zu tun. Im Vergleich zu stationären Anwendungen stellen Datenströme eine erhebliche zusätzliche Herausforderung für die automatisierte Entscheidungsfindung und das maschinelle Lernen dar. So müssen Online Machine Learning-Verfahren mit begrenzten Speicherkapazitäten, Echtzeitanforderungen und Veränderungen des Daten-generierenden Prozesses zurechtkommen. Gleichzeitig sollten Online Learning-Verfahren eine hohe Vorhersagequalität, Stabilität bei Eingangsrauschen und eine gute Interpretierbarkeit aufweisen, um in der Praxis zuverlässig eingesetzt werden zu können. In dieser Arbeit befassen wir uns mit einigen der wichtigsten Aspekte des maschinellen Lernens in sich entwickelnden Datenströmen. Insbesondere identifizieren wir vier offene Fragen im Zusammenhang mit Online Feature Selection, Concept Drift Detection, Online-Klassifikation, lokaler Erklärbarkeit und der Bewertung von Online Learning-Methoden. In diesem Kontext präsentieren wir neue theoretische und empirische Erkenntnisse sowie neue Frameworks und Implementierungen. Insbesondere schlagen wir neue Ansätze für Online Feature Selection und Concept Drift Detection vor, die Unsicherheiten im Modell berücksichtigen und dadurch stabilere Ergebnisse erzielen können. Darüber hinaus stellen wir einen neuen inkrementellen Entscheidungsbaum vor, der wertvolle Eigenschaften hinsichtlich der Interpretierbarkeit einhält, sowie ein neues Framework zur Erkennung von Veränderungen, das effizientere Erklärungen auf der Grundlage lokaler Feature Attributions ermöglicht. Tatsächlich ist dies eine der ersten Arbeiten, die sich mit intrinsischer Interpretierbarkeit von Modellen und lokaler Erklärbarkeit bei inkrementellen Aktualisierungen und Concept Drift befasst. Gemeinsam mit dieser Arbeit stellen wir umfangreiche Ressourcen für Online Machine Learning zur Verfügung. Insbesondere stellen wir ein neues Python-Framework vor, das vereinfachte und standardisierte Auswertungen ermöglicht und künftig somit als Grundlage für vergleichbare Online Learning-Experimente dienen kann. Insgesamt stützt sich diese Arbeit auf sechs Publikationen, von denen fünf zum Zeitpunkt der Veröffentlichung der Dissertation bereits im Peer-Review Format begutachtet wurden. Unsere Arbeit berührt alle wichtigen Bereiche der prädiktiven Modellierung in Datenströmen und schlägt neuartige Lösungen für effizientes, stabiles, interpretierbares und damit zuverlässiges Online Machine Learning vor