PROBABILISTIC MODEL DISCOVERY RELATIONAL LEARNING AND SCALABLE INFERENCE

Department of Computer Science and EngineeringThis thesis studies interesting problems in compositionality for machine learning models under some settings including relational learning, scalability and deep models. Compositionality is the terminology describing the process of building small objects to complex ones. Bringing this concept into machine learning is important because it appears in many aspects from infinitesimal atomic to planetary structures. In this thesis, machine learning models center around Gaussian process of which covariance function is compositionally constructed. The proposed approach builds methods that can explore compositional model space automatically and efficiently as well as strives to address the interpretability for obtained models. The aforementioned problems are both important and challenging. Considering multivariate or relational learning is de facto in time series analysis for many domains. However, the existing methods of compositional learning are inapplicable to extend to such a setting since the explosion in model space makes it infeasible to use. Learning compositional structures is already a time-consuming task. Although there are existing approximation methods, they do not work well for compositional covariances. This makes it even harder to propose a scalable approach without sacrificing model performances. Finally, analyzing hierarchical deep Gaussian processes is notoriously difficult especially when incorporating different covariance functions. Previous work focuses on a single case of covariance function and is difficult to generalize for many other cases. The goal of this thesis is to propose solutions to the given problems. The first contribution of this thesis is a general framework for modeling multiple time series which provides descriptive relations between time series. Second, this thesis presents efficient probabilistic approaches to address the model search problem which previously is done by exhaustive enumerating evaluation. Furthermore, a scalable inference for Gaussian process is proposed, providing accurate approximation with guarantees of error bounds. Last but not least, to address the existing issues in deep Gaussian process, this thesis presents a unified theoretical framework to explain the pathology in deep Gasssian processes with better error bounds for various kernels compared to existing work and rates of convergence.ope

FALKON: An Optimal Large Scale Kernel Method

Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited applicability in large scale scenarios because of stringent computational requirements in terms of time and especially memory. In this paper, we take a substantial step in scaling up kernel methods, proposing FALKON, a novel algorithm that allows to efficiently process millions of points. FALKON is derived combining several algorithmic principles, namely stochastic subsampling, iterative solvers and preconditioning. Our theoretical analysis shows that optimal statistical accuracy is achieved requiring essentially $O(n)$ memory and $O(n\sqrt{n})$ time. An extensive experimental analysis on large scale datasets shows that, even with a single machine, FALKON outperforms previous state of the art solutions, which exploit parallel/distributed architectures.Comment: NIPS 201

Hierarchische Modelle für das visuelle Erkennen und Lernen von Objekten, Szenen und Aktivitäten

In many computer vision applications, objects have to be learned and recognized in images or image sequences. Most of these objects have a hierarchical structure.For example, 3d objects can be decomposed into object parts, and object parts, in turn, into geometric primitives. Furthermore, scenes are composed of objects. And also activities or behaviors can be divided hierarchically into actions, these into individual movements, etc. Hierarchical models are therefore ideally suited for the representation of a wide range of objects used in applications such as object recognition, human pose estimation, or activity recognition. In this work new probabilistic hierarchical models are presented that allow an efficient representation of multiple objects of different categories, scales, rotations, and views. The idea is to exploit similarities between objects, object parts or actions and movements in order to share calculations and avoid redundant information. We will introduce online and offline learning methods, which enable to create efficient hierarchies based on small or large training datasets, in which poses or articulated structures are given by instances. Furthermore, we present inference approaches for fast and robust detection. These new approaches combine the idea of compositional and similarity hierarchies and overcome limitations of previous methods. They will be used in an unified hierarchical framework spatially for object recognition as well as spatiotemporally for activity recognition. The unified generic hierarchical framework allows us to apply the proposed models in different projects. Besides classical object recognition it is used for detection of human poses in a project for gait analysis. The activity detection is used in a project for the design of environments for ageing, to identify activities and behavior patterns in smart homes. In a project for parking spot detection using an intelligent vehicle, the proposed approaches are used to hierarchically model the environment of the vehicle for an efficient and robust interpretation of the scene in real-time.In zahlreichen Computer Vision Anwendungen müssen Objekte in einzelnen Bildern oder Bildsequenzen erlernt und erkannt werden. Viele dieser Objekte sind hierarchisch aufgebaut.So lassen sich 3d Objekte in Objektteile zerlegen und Objektteile wiederum in geometrische Grundkörper. Und auch Aktivitäten oder Verhaltensmuster lassen sich hierarchisch in einzelne Aktionen aufteilen, diese wiederum in einzelne Bewegungen usw. Für die Repräsentation sind hierarchische Modelle dementsprechend gut geeignet. In dieser Arbeit werden neue probabilistische hierarchische Modelle vorgestellt, die es ermöglichen auch mehrere Objekte verschiedener Kategorien, Skalierungen, Rotationen und aus verschiedenen Blickrichtungen effizient zu repräsentieren. Eine Idee ist hierbei, Ähnlichkeiten unter Objekten, Objektteilen oder auch Aktionen und Bewegungen zu nutzen, um redundante Informationen und Mehrfachberechnungen zu vermeiden. In der Arbeit werden online und offline Lernverfahren vorgestellt, die es ermöglichen, effiziente Hierarchien auf Basis von kleinen oder großen Trainingsdatensätzen zu erstellen, in denen Posen und bewegliche Strukturen durch Beispiele gegeben sind. Des Weiteren werden Inferenzansätze zur schnellen und robusten Detektion vorgestellt. Diese werden innerhalb eines einheitlichen hierarchischen Frameworks sowohl räumlich zur Objekterkennung als auch raumzeitlich zur Aktivitätenerkennung verwendet. Das einheitliche Framework ermöglicht die Anwendung des vorgestellten Modells innerhalb verschiedener Projekte. Neben der klassischen Objekterkennung wird es zur Erkennung von menschlichen Posen in einem Projekt zur Ganganalyse verwendet. Die Aktivitätenerkennung wird in einem Projekt zur Gestaltung altersgerechter Lebenswelten genutzt, um in intelligenten Wohnräumen Aktivitäten und Verhaltensmuster von Bewohnern zu erkennen. Im Rahmen eines Projektes zur Parklückenvermessung mithilfe eines intelligenten Fahrzeuges werden die vorgestellten Ansätze verwendet, um das Umfeld des Fahrzeuges hierarchisch zu modellieren und dadurch das Szenenverstehen zu ermöglichen