Efficient Algorithms for Moral Lineage Tracing

Lineage tracing, the joint segmentation and tracking of living cells as they move and divide in a sequence of light microscopy images, is a challenging task. Jug et al. have proposed a mathematical abstraction of this task, the moral lineage tracing problem (MLTP), whose feasible solutions define both a segmentation of every image and a lineage forest of cells. Their branch-and-cut algorithm, however, is prone to many cuts and slow convergence for large instances. To address this problem, we make three contributions: (i) we devise the first efficient primal feasible local search algorithms for the MLTP, (ii) we improve the branch-and-cut algorithm by separating tighter cutting planes and by incorporating our primal algorithms, (iii) we show in experiments that our algorithms find accurate solutions on the problem instances of Jug et al. and scale to larger instances, leveraging moral lineage tracing to practical significance.Comment: Accepted at ICCV 201

Computational inference beyond Kingman's coalescent

Full likelihood inference under Kingman's coalescent is a computationally challenging problem to which importance sampling (IS) and the product of approximate conditionals (PAC) method have been applied successfully. Both methods can be expressed in terms of families of intractable conditional sampling distributions (CSDs), and rely on principled approximations for accurate inference. Recently, more general Λ- and Ξ- coalescents have been observed to provide better modelling ts to some genetic data sets. We derive families of approximate CSDs for nite sites Λ- and Ξ-coalescents, and use them to obtain "approximately optimal" IS and PAC algorithms for Λ coalescents, yielding substantial gains in efficiency over existing methods

Generalizations of the Multicut Problem for Computer Vision

Graph decomposition has always been a very important concept in machine learning and computer vision. Many tasks like image and mesh segmentation, community detection in social networks, as well as object tracking and human pose estimation can be formulated as a graph decomposition problem. The multicut problem in particular is a popular model to optimize for a decomposition of a given graph. Its main advantage is that no prior knowledge about the number of components or their sizes is required. However, it has several limitations, which we address in this thesis: Firstly, the multicut problem allows to specify only cost or reward for putting two direct neighbours into distinct components. This limits the expressibility of the cost function. We introduce special edges into the graph that allow to define cost or reward for putting any two vertices into distinct components, while preserving the original set of feasible solutions. We show that this considerably improves the quality of image and mesh segmentations. Second, multicut is notorious to be NP-hard for general graphs, that limits its applications to small super-pixel graphs. We define and implement two primal feasible heuristics to solve the problem. They do not provide any guarantees on the runtime or quality of solutions, but in practice show good convergence behaviour. We perform an extensive comparison on multiple graphs of different sizes and properties. Third, we extend the multicut framework by introducing node labels, so that we can jointly optimize for graph decomposition and nodes classification by means of exactly the same optimization algorithm, thus eliminating the need to hand-tune optimizers for a particular task. To prove its universality we applied it to diverse computer vision tasks, including human pose estimation, multiple object tracking, and instance-aware semantic segmentation. We show that we can improve the results over the prior art using exactly the same data as in the original works. Finally, we use employ multicuts in two applications: 1) a client-server tool for interactive video segmentation: After the pre-processing of the video a user draws strokes on several frames and a time-coherent segmentation of the entire video is performed on-the-fly. 2) we formulate a method for simultaneous segmentation and tracking of living cells in microscopy data. This task is challenging as cells split and our algorithm accounts for this, creating parental hierarchies. We also present results on multiple model fitting. We find models in data heavily corrupted by noise by finding components defining these models using higher order multicuts. We introduce an interesting extension that allows our optimization to pick better hyperparameters for each discovered model. In summary, this thesis extends the multicut problem in different directions, proposes algorithms for optimization, and applies it to novel data and settings.Die Zerlegung von Graphen ist ein sehr wichtiges Konzept im maschinellen Lernen und maschinellen Sehen. Viele Aufgaben wie Bild- und Gittersegmentierung, Kommunitätserkennung in sozialen Netzwerken, sowie Objektverfolgung und Schätzung von menschlichen Posen können als Graphzerlegungsproblem formuliert werden. Der Mehrfachschnitt-Ansatz ist ein populäres Mittel um über die Zerlegungen eines gegebenen Graphen zu optimieren. Sein größter Vorteil ist, dass kein Vorwissen über die Anzahl an Komponenten und deren Größen benötigt wird. Dennoch hat er mehrere ernsthafte Limitierungen, welche wir in dieser Arbeit behandeln: Erstens erlaubt der klassische Mehrfachschnitt nur die Spezifikation von Kosten oder Belohnungen für die Trennung von zwei Nachbarn in verschiedene Komponenten. Dies schränkt die Ausdrucksfähigkeit der Kostenfunktion ein und führt zu suboptimalen Ergebnissen. Wir fügen dem Graphen spezielle Kanten hinzu, welche es erlauben, Kosten oder Belohnungen für die Trennung von beliebigen Paaren von Knoten in verschiedene Komponenten zu definieren, ohne die Menge an zulässigen Lösungen zu verändern. Wir zeigen, dass dies die Qualität von Bild- und Gittersegmentierungen deutlich verbessert. Zweitens ist das Mehrfachschnittproblem berüchtigt dafür NP-schwer für allgemeine Graphen zu sein, was die Anwendungen auf kleine superpixel-basierte Graphen einschränkt. Wir definieren und implementieren zwei primal-zulässige Heuristiken um das Problem zu lösen. Diese geben keine Garantien bezüglich der Laufzeit oder der Qualität der Lösungen, zeigen in der Praxis jedoch gutes Konvergenzverhalten. Wir führen einen ausführlichen Vergleich auf vielen Graphen verschiedener Größen und Eigenschaften durch. Drittens erweitern wir den Mehrfachschnitt-Ansatz um Knoten-Kennzeichnungen, sodass wir gemeinsam über Zerlegungen und Knoten-Klassifikationen mit dem gleichen Optimierungs-Algorithmus optimieren können. Dadurch wird der Bedarf der Feinabstimmung einzelner aufgabenspezifischer Löser aus dem Weg geräumt. Um die Allgemeingültigkeit dieses Ansatzes zu überprüfen, haben wir ihn auf verschiedenen Aufgaben des maschinellen Sehens, einschließlich menschliche Posenschätzung, Mehrobjektverfolgung und instanz-bewusste semantische Segmentierung, angewandt. Wir zeigen, dass wir Resultate von vorherigen Arbeiten mit exakt den gleichen Daten verbessern können. Abschließend benutzen wir Mehrfachschnitte in zwei Anwendungen: 1) Ein Nutzer-Server-Werkzeug für interaktive Video Segmentierung: Nach der Vorbearbeitung eines Videos zeichnet der Nutzer Striche auf mehrere Einzelbilder und eine zeit-kohärente Segmentierung des gesamten Videos wird in Echtzeit berechnet. 2) Wir formulieren eine Methode für simultane Segmentierung und Verfolgung von lebenden Zellen in Mikroskopie-Aufnahmen. Diese Aufgabe ist anspruchsvoll, da Zellen sich aufteilen und unser Algorithmus dies in der Erstellung von Eltern-Hierarchien mitberücksichtigen muss. Wir präsentieren außerdem Resultate zur Mehrmodellanpassung. Wir berechnen Modelle in stark verrauschten Daten indem wir mithilfe von Mehrfachschnitten höherer Ordnung Komponenten finden, die diesen Modellen entsprechen. Wir führen eine interessante Erweiterung ein, die es unserer Optimierung erlaubt, bessere Hyperparameter für jedes entdeckte Modell auszuwählen. Zusammenfassend erweitert diese Arbeit den Mehrfachschnitt-Ansatz in unterschiedlichen Richtungen, schlägt Algorithmen zur Inferenz in den resultierenden Modellen vor und wendet ihn auf neuartigen Daten und Umgebungen an

A benchmark for epithelial cell tracking

Segmentation and tracking of epithelial cells in light microscopy (LM) movies of developing tissue is an abundant task in cell- and developmental biology. Epithelial cells are densely packed cells that form a honeycomb-like grid. This dense packing distinguishes membrane-stained epithelial cells from the types of objects recent cell tracking benchmarks have focused on, like cell nuclei and freely moving individual cells. While semi-automated tools for segmentation and tracking of epithelial cells are available to biologists, common tools rely on classical watershed based segmentation and engineered tracking heuristics, and entail a tedious phase of manual curation. However, a different kind of densely packed cell imagery has become a focus of recent computer vision research, namely electron microscopy (EM) images of neurons. In this work we explore the benefits of two recent neuron EM segmentation methods for epithelial cell tracking in light microscopy. In particular we adapt two different deep learning approaches for neuron segmentation, namely Flood Filling Networks and MALA, to epithelial cell tracking. We benchmark these on a dataset of eight movies with up to 200 frames. We compare to Moral Lineage Tracing, a combinatorial optimization approach that recently claimed state of the art results for epithelial cell tracking. Furthermore, we compare to Tissue Analyzer, an off-the-shelf tool used by Biologists that serves as our baseline

Toxicity in Evolving Twitter Topics - Employing a novel Dynamic Topic volution Model (DyTEM) onTwitter data

Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced Analytics, specialization in Data ScienceThis thesis presents an extensive investigation into the evolution of topics and their association with speech toxicity on Twitter, based on a large corpus of tweets, providing crucial insights for monitoring online discourse and potentially informing interventions to combat toxic behavior in digital communities. A Dynamic Topic Evolution Model (DyTEM) is introduced, constructed by combining static Topic Modelling techniques and sentence embeddings through the state-of-the-art sentence transformer, sBERT. The DyTEM, tested and validated on a substantial sample of tweets, is represented as a directed graph, encapsulating the inherent dynamism of Twitter discussions. For validating the consistency of DyTEM and providing guidance for hyperparameter selection, a novel, hashtag-based validation method is proposed. The analysis identifies and scrutinizes five distinct Topic Transition Types: Topic Stagnation, Topic Merge, Topic Split, Topic Disappearance, and Topic Emergence. A speech toxicity classification model is employed to delve into the toxicity dynamics within topic evolution. A standout finding of this study is the positive correlation between topic popularity and its toxicity, implying that trending or viral topics tend to contain more inflammatory speech. This insight, along with the methodologies introduced in this study, contributes significantly to the broader understanding of digital discourse dynamics and could guide future strategies aimed at fostering healthier and more constructive online spaces

Methods and practice of detecting selection in human cancers

Cancer development and progression is an evolutionary process, understanding these evolutionary dynamics is important for treatment and diagnosis as how a cancer evolves determines its future prognosis. This thesis focuses on elucidating selective evolutionary pressures in cancers and somatic tissues using population genetics models and cancer genomics data. First a model for the expected diversity in the absence of selection was developed. This neutral model of evolution predicts that under neutrality the frequency of subclonal mutations is expected to follow a power law distribution. Surprisingly more than 30% of cancer across multiple cohorts fitted this model. The next part of the thesis develops models to explore the effects of selection given these should be observable as deviations from the neutral prediction. For this I developed two approaches. The first approach investigated selection at the level of individual samples and showed that a characteristic pattern of clusters of mutations is observed in deep sequencing experiments. Using a mathematical model, information encoded within these clusters can be used to measure the relative fitness of subclones and the time they emerge during tumour evolution. With this I observed strikingly high fitness advantages for subclones of above 20%. The second approach enables measuring recurrent patterns of selection in cohorts of sequenced cancers using dN/dS, the ratio of non-synonymous to synonymous mutations, a method originally developed for molecular species evolution. This approach demonstrates how selection coefficients can be extracted by combining measurements of dN/dS with the size of mutational lineages. With this approach selection coefficients were again observed to be strikingly high. Finally I looked at population dynamics in normal colonic tissue given that many mutations accumulate in physiologically normal tissue. I found that the current view of stem cell dynamics was unable to explain sequencing data from individual colonic crypts. Some new models were proposed that introduce a longer time scale evolution that suppresses the accumulation of mutations which appear consistent with the data