Subgroup discovery for structured target concepts

The main object of study in this thesis is subgroup discovery, a theoretical framework for finding subgroups in data—i.e., named sub-populations— whose behaviour with respect to a specified target concept is exceptional when compared to the rest of the dataset. This is a powerful tool that conveys crucial information to a human audience, but despite past advances has been limited to simple target concepts. In this work we propose algorithms that bring this framework to novel application domains. We introduce the concept of representative subgroups, which we use not only to ensure the fairness of a sub-population with regard to a sensitive trait, such as race or gender, but also to go beyond known trends in the data. For entities with additional relational information that can be encoded as a graph, we introduce a novel measure of robust connectedness which improves on established alternative measures of density; we then provide a method that uses this measure to discover which named sub-populations are more well-connected. Our contributions within subgroup discovery crescent with the introduction of kernelised subgroup discovery: a novel framework that enables the discovery of subgroups on i.i.d. target concepts with virtually any kind of structure. Importantly, our framework additionally provides a concrete and efficient tool that works out-of-the-box without any modification, apart from specifying the Gramian of a positive definite kernel. To use within kernelised subgroup discovery, but also on any other kind of kernel method, we additionally introduce a novel random walk graph kernel. Our kernel allows the fine tuning of the alignment between the vertices of the two compared graphs, during the count of the random walks, while we also propose meaningful structure-aware vertex labels to utilise this new capability. With these contributions we thoroughly extend the applicability of subgroup discovery and ultimately re-define it as a kernel method.Der Hauptgegenstand dieser Arbeit ist die Subgruppenentdeckung (Subgroup Discovery), ein theoretischer Rahmen für das Auffinden von Subgruppen in Daten—d. h. benannte Teilpopulationen—deren Verhalten in Bezug auf ein bestimmtes Targetkonzept im Vergleich zum Rest des Datensatzes außergewöhnlich ist. Es handelt sich hierbei um ein leistungsfähiges Instrument, das einem menschlichen Publikum wichtige Informationen vermittelt. Allerdings ist es trotz bisherigen Fortschritte auf einfache Targetkonzepte beschränkt. In dieser Arbeit schlagen wir Algorithmen vor, die diesen Rahmen auf neuartige Anwendungsbereiche übertragen. Wir führen das Konzept der repräsentativen Untergruppen ein, mit dem wir nicht nur die Fairness einer Teilpopulation in Bezug auf ein sensibles Merkmal wie Rasse oder Geschlecht sicherstellen, sondern auch über bekannte Trends in den Daten hinausgehen können. Für Entitäten mit zusätzlicher relationalen Information, die als Graph kodiert werden kann, führen wir ein neuartiges Maß für robuste Verbundenheit ein, das die etablierten alternativen Dichtemaße verbessert; anschließend stellen wir eine Methode bereit, die dieses Maß verwendet, um herauszufinden, welche benannte Teilpopulationen besser verbunden sind. Unsere Beiträge in diesem Rahmen gipfeln in der Einführung der kernelisierten Subgruppenentdeckung: ein neuartiger Rahmen, der die Entdeckung von Subgruppen für u.i.v. Targetkonzepten mit praktisch jeder Art von Struktur ermöglicht. Wichtigerweise, unser Rahmen bereitstellt zusätzlich ein konkretes und effizientes Werkzeug, das ohne jegliche Modifikation funktioniert, abgesehen von der Angabe des Gramian eines positiv definitiven Kernels. Für den Einsatz innerhalb der kernelisierten Subgruppentdeckung, aber auch für jede andere Art von Kernel-Methode, führen wir zusätzlich einen neuartigen Random-Walk-Graph-Kernel ein. Unser Kernel ermöglicht die Feinabstimmung der Ausrichtung zwischen den Eckpunkten der beiden unter-Vergleich-gestelltenen Graphen während der Zählung der Random Walks, während wir auch sinnvolle strukturbewusste Vertex-Labels vorschlagen, um diese neue Fähigkeit zu nutzen. Mit diesen Beiträgen erweitern wir die Anwendbarkeit der Subgruppentdeckung gründlich und definieren wir sie im Endeffekt als Kernel-Methode neu

COMPUTATIONAL TOOLS FOR THE DYNAMIC CATEGORIZATION AND AUGMENTED UTILIZATION OF THE GENE ONTOLOGY

Ontologies provide an organization of language, in the form of a network or graph, which is amenable to computational analysis while remaining human-readable. Although they are used in a variety of disciplines, ontologies in the biomedical field, such as Gene Ontology, are of interest for their role in organizing terminology used to describe—among other concepts—the functions, locations, and processes of genes and gene-products. Due to the consistency and level of automation that ontologies provide for such annotations, methods for finding enriched biological terminology from a set of differentially identified genes in a tissue or cell sample have been developed to aid in the elucidation of disease pathology and unknown biochemical pathways. However, despite their immense utility, biomedical ontologies have significant limitations and caveats. One major issue is that gene annotation enrichment analyses often result in many redundant, individually enriched ontological terms that are highly specific and weakly justified by statistical significance. These large sets of weakly enriched terms are difficult to interpret without manually sorting into appropriate functional or descriptive categories. Also, relationships that organize the terminology within these ontologies do not contain descriptions of semantic scoping or scaling among terms. Therefore, there exists some ambiguity, which complicates the automation of categorizing terms to improve interpretability. We emphasize that existing methods enable the danger of producing incorrect mappings to categories as a result of these ambiguities, unless simplified and incomplete versions of these ontologies are used which omit problematic relations. Such ambiguities could have a significant impact on term categorization, as we have calculated upper boundary estimates of potential false categorizations as high as 121,579 for the misinterpretation of a single scoping relation, has_part, which accounts for approximately 18% of the total possible mappings between terms in the Gene Ontology. However, the omission of problematic relationships results in a significant loss of retrievable information. In the Gene Ontology, this accounts for a 6% reduction for the omission of a single relation. However, this percentage should increase drastically when considering all relations in an ontology. To address these issues, we have developed methods which categorize individual ontology terms into broad, biologically-related concepts to improve the interpretability and statistical significance of gene-annotation enrichment studies, meanwhile addressing the lack of semantic scoping and scaling descriptions among ontological relationships so that annotation enrichment analyses can be performed across a more complete representation of the ontological graph. We show that, when compared to similar term categorization methods, our method produces categorizations that match hand-curated ones with similar or better accuracy, while not requiring the user to compile lists of individual ontology term IDs. Furthermore, our handling of problematic relations produces a more complete representation of ontological information from a scoping perspective, and we demonstrate instances where medically-relevant terms--and by extension putative gene targets--are identified in our annotation enrichment results that would be otherwise missed when using traditional methods. Additionally, we observed a marginal, yet consistent improvement of statistical power in enrichment results when our methods were used, compared to traditional enrichment analyses that utilize ontological ancestors. Finally, using scalable and reproducible data workflow pipelines, we have applied our methods to several genomic, transcriptomic, and proteomic collaborative projects

Recurrences reveal shared causal drivers of complex time series

Many experimental time series measurements share unobserved causal drivers. Examples include genes targeted by transcription factors, ocean flows influenced by large-scale atmospheric currents, and motor circuits steered by descending neurons. Reliably inferring this unseen driving force is necessary to understand the intermittent nature of top-down control schemes in diverse biological and engineered systems. Here, we introduce a new unsupervised learning algorithm that uses recurrences in time series measurements to gradually reconstruct an unobserved driving signal. Drawing on the mathematical theory of skew-product dynamical systems, we identify recurrence events shared across response time series, which implicitly define a recurrence graph with glass-like structure. As the amount or quality of observed data improves, this recurrence graph undergoes a percolation transition manifesting as weak ergodicity breaking for random walks on the induced landscape -- revealing the shared driver's dynamics, even in the presence of strongly corrupted or noisy measurements. Across several thousand random dynamical systems, we empirically quantify the dependence of reconstruction accuracy on the rate of information transfer from a chaotic driver to the response systems, and we find that effective reconstruction proceeds through gradual approximation of the driver's dominant orbit topology. Through extensive benchmarks against classical and neural-network-based signal processing techniques, we demonstrate our method's strong ability to extract causal driving signals from diverse real-world datasets spanning ecology, genomics, fluid dynamics, and physiology.Comment: 8 pages, 5 figure

Determining Alpha-Helix Correspondence for Protein Structure Prediction from Cryo-EM Density Maps, Master\u27s Thesis, May 2007

Determining protein structure is an important problem for structural biologists, which has received a significant amount of attention in the recent years. In this thesis, we describe a novel, shape-modeling approach as an intermediate step towards recovering 3D protein structures from volumetric images. The input to our method is a sequence of alpha-helices that make up a protein, and a low-resolution volumetric image of the protein where possible locations of alpha-helices have been detected. Our task is to identify the correspondence between the two sets of helices, which will shed light on how the protein folds in space. The central theme of our approach is to cast the correspondence problem as that of shape matching between the 3D volume and the 1D sequence. We model both the shapes as attributed relational graphs, and formulate a constrained inexact graph matching problem. To compute the matching, we developed an optimal algorithm based on the A*-search with several choices of heuristic functions. As demonstrated in a suite of real protein data, the shape-modeling approach is capable of correctly identifying helix correspondences in noise-abundant volumes with minimal or no user intervention

Toward Efficient and Robust Large-Scale Structure-from-Motion Systems

The ever-increasing number of images that are uploaded and shared on the Internet has recently been leveraged by computer vision researchers to extract 3D information about the content seen in these images. One key mechanism to extract this information is structure-from-motion, which is the process of recovering the 3D geometry (structure) of a scene via a set of images from different viewpoints (camera motion). However, when dealing with crowdsourced datasets comprised of tens or hundreds of millions of images, the magnitude and diversity of the imagery poses challenges such as robustness, scalability, completeness, and correctness for existing structure-from-motion systems. This dissertation focuses on these challenges and demonstrates practical methods to address the problems of data association and verification within structure-from-motion systems. Data association within structure-from-motion systems consists of the discovery of pairwise image overlap within the input dataset. In order to perform this discovery, previous systems assumed that information about every image in the input dataset could be stored in memory, which is prohibitive for large-scale photo collections. To address this issue, we propose a novel streaming-based framework for the discovery of related sets of images, and demonstrate our approach on a crowdsourced dataset containing 100 million images from all around the world. Results illustrate that our streaming-based approach does not compromise model completeness, but achieves unprecedented levels of efficiency and scalability. The verification of individual data associations is difficult to perform during the process of structure-from-motion, as standard methods have limited scope when determining image overlap. Therefore, it is possible for erroneous associations to form, especially when there are symmetric, repetitive, or duplicate structures which can be incorrectly associated with each other. The consequences of these errors are incorrectly placed cameras and scene geometry within the 3D reconstruction. We present two methods that can detect these local inconsistencies and successfully resolve them into a globally consistent 3D model. In our evaluation, we show that our techniques are efficient, are robust to a variety of scenes, and outperform existing approaches.Doctor of Philosoph

Efficient Point-Cloud Processing with Primitive Shapes

This thesis presents methods for efficient processing of point-clouds based on primitive shapes. The set of considered simple parametric shapes consists of planes, spheres, cylinders, cones and tori. The algorithms developed in this work are targeted at scenarios in which the occurring surfaces can be well represented by this set of shape primitives which is the case in many man-made environments such as e.g. industrial compounds, cities or building interiors. A primitive subsumes a set of corresponding points in the point-cloud and serves as a proxy for them. Therefore primitives are well suited to directly address the unavoidable oversampling of large point-clouds and lay the foundation for efficient point-cloud processing algorithms. The first contribution of this thesis is a novel shape primitive detection method that is efficient even on very large and noisy point-clouds. Several applications for the detected primitives are subsequently explored, resulting in a set of novel algorithms for primitive-based point-cloud processing in the areas of compression, recognition and completion. Each of these application directly exploits and benefits from one or more of the detected primitives' properties such as approximation, abstraction, segmentation and continuability

Beyond Flatland : exploring graphs in many dimensions

Societies, technologies, economies, ecosystems, organisms, . . . Our world is composed of complex networks—systems with many elements that interact in nontrivial ways. Graphs are natural models of these systems, and scientists have made tremendous progress in developing tools for their analysis. However, research has long focused on relatively simple graph representations and problem specifications, often discarding valuable real-world information in the process. In recent years, the limitations of this approach have become increasingly apparent, but we are just starting to comprehend how more intricate data representations and problem formulations might benefit our understanding of relational phenomena. Against this background, our thesis sets out to explore graphs in five dimensions: descriptivity, multiplicity, complexity, expressivity, and responsibility. Leveraging tools from graph theory, information theory, probability theory, geometry, and topology, we develop methods to (1) descriptively compare individual graphs, (2) characterize similarities and differences between groups of multiple graphs, (3) critically assess the complexity of relational data representations and their associated scientific culture, (4) extract expressive features from and for hypergraphs, and (5) responsibly mitigate the risks induced by graph-structured content recommendations. Thus, our thesis is naturally situated at the intersection of graph mining, graph learning, and network analysis.Gesellschaften, Technologien, Volkswirtschaften, Ökosysteme, Organismen, . . . Unsere Welt besteht aus komplexen Netzwerken—Systemen mit vielen Elementen, die auf nichttriviale Weise interagieren. Graphen sind natürliche Modelle dieser Systeme, und die Wissenschaft hat bei der Entwicklung von Methoden zu ihrer Analyse große Fortschritte gemacht. Allerdings hat sich die Forschung lange auf relativ einfache Graphrepräsentationen und Problemspezifikationen beschränkt, oft unter Vernachlässigung wertvoller Informationen aus der realen Welt. In den vergangenen Jahren sind die Grenzen dieser Herangehensweise zunehmend deutlich geworden, aber wir beginnen gerade erst zu erfassen, wie unser Verständnis relationaler Phänomene von intrikateren Datenrepräsentationen und Problemstellungen profitieren kann. Vor diesem Hintergrund erkundet unsere Dissertation Graphen in fünf Dimensionen: Deskriptivität, Multiplizität, Komplexität, Expressivität, und Verantwortung. Mithilfe von Graphentheorie, Informationstheorie, Wahrscheinlichkeitstheorie, Geometrie und Topologie entwickeln wir Methoden, welche (1) einzelne Graphen deskriptiv vergleichen, (2) Gemeinsamkeiten und Unterschiede zwischen Gruppen multipler Graphen charakterisieren, (3) die Komplexität relationaler Datenrepräsentationen und der mit ihnen verbundenen Wissenschaftskultur kritisch beleuchten, (4) expressive Merkmale von und für Hypergraphen extrahieren, und (5) verantwortungsvoll den Risiken begegnen, welche die Graphstruktur von Inhaltsempfehlungen mit sich bringt. Damit liegt unsere Dissertation naturgemäß an der Schnittstelle zwischen Graph Mining, Graph Learning und Netzwerkanalyse

Latent Representation and Sampling in Network: Application in Text Mining and Biology.

In classical machine learning, hand-designed features are used for learning a mapping from raw data. However, human involvement in feature design makes the process expensive. Representation learning aims to learn abstract features directly from data without direct human involvement. Raw data can be of various forms. Network is one form of data that encodes relational structure in many real-world domains. Therefore, learning abstract features for network units is an important task. In this dissertation, we propose models for incorporating temporal information given as a collection of networks from subsequent time-stamps. The primary objective of our models is to learn a better abstract feature representation of nodes and edges in an evolving network. We show that the temporal information in the abstract feature improves the performance of link prediction task substantially. Besides applying to the network data, we also employ our models to incorporate extra-sentential information in the text domain for learning better representation of sentences. We build a context network of sentences to capture extra-sentential information. This information in abstract feature representation of sentences improves various text-mining tasks substantially over a set of baseline methods. A problem with the abstract features that we learn is that they lack interpretability. In real-life applications on network data, for some tasks, it is crucial to learn interpretable features in the form of graphical structures. For this we need to mine important graphical structures along with their frequency statistics from the input dataset. However, exact algorithms for these tasks are computationally expensive, so scalable algorithms are of urgent need. To overcome this challenge, we provide efficient sampling algorithms for mining higher-order structures from network(s). We show that our sampling-based algorithms are scalable. They are also superior to a set of baseline algorithms in terms of retrieving important graphical sub-structures, and collecting their frequency statistics. Finally, we show that we can use these frequent subgraph statistics and structures as features in various real-life applications. We show one application in biology and another in security. In both cases, we show that the structures and their statistics significantly improve the performance of knowledge discovery tasks in these domains