Degree-Driven Design of Geometric Algorithms for Point Location, Proximity, and Volume Calculation

Correct implementation of published geometric algorithms is surprisingly difficult. Geometric algorithms are often designed for Real-RAM, a computational model that provides arbitrary precision arithmetic operations at unit cost. Actual commodity hardware provides only finite precision and may result in arithmetic errors. While the errors may seem small, if ignored, they may cause incorrect branching, which may cause an implementation to reach an undefined state, produce erroneous output, or crash. In 1999 Liotta, Preparata and Tamassia proposed that in addition to considering the resources of time and space, an algorithm designer should also consider the arithmetic precision necessary to guarantee a correct implementation. They called this design technique degree-driven algorithm design. Designers who consider the time, space, and precision for a problem up-front arrive at new solutions, gain further insight, and find simpler representations. In this thesis, I show that degree-driven design supports the development of new and robust geometric algorithms. I demonstrate this claim via several new algorithms. For n point sites on a UxU grid I consider three problems. First, I show how to compute the nearest neighbor transform in O(U^2) expected time, O(U^2) space, and double precision. Second, I show how to create a data structure in O(n log Un) expected time, O(n) expected space, and triple precision that supports O(log n) time and double precision post-office queries. Third, I show how to compute the Gabriel graph in O(n^2) time, O(n^2) space and double precision. For computing volumes of CSG models, I describe a framework that uses a minimal set of predicates that use at most five-fold precision. The framework is over 500x faster and two orders of magnitude more accurate than a Monte Carlo volume calculation algorithm.Doctor of Philosoph

Oracle-Guided Design and Analysis of Learning-Based Cyber-Physical Systems

We are in world where autonomous systems, such as self-driving cars, surgical robots, robotic manipulators are becoming a reality. Such systems are considered \textit{safety-critical} since they interact with humans on a regular basis. Hence, before such systems can be integrated into our day to day life, we need to guarantee their safety. Recent success in machine learning (ML) and artificial intelligence (AI) has led to an increase in their use in real world robotic systems. For example, complex perception modules in self-driving cars and deep reinforcement learning controllers in robotic manipulators. Although powerful, they introduce an additional level of complexity when it comes to the formal analysis of autonomous systems. In this thesis, such systems are designated as Learning-Based Cyber-Physical Systems~(LB-CPS). In this thesis, we take inspiration from the Oracle-Guided Inductive Synthesis~(OGIS) paradigm to develop frameworks which can aid in achieving formal guarantees in different stages of an autonomous system design and analysis pipeline. Furthermore, we show that to guarantee the safety of LB-CPS, the design (synthesis) and analysis (verification) must consider feedback from the other. We consider five important parts of the design and analysis process and show a strong coupling among them, namely (i) Robust Control Synthesis from High Level Safety Specifications; (ii) Diagnosis and Repair of Safety Requirements for Control Synthesis; (iii) Counter-example Guided Data Augmentation for training high-accuracy ML models; (iv) Simulation-Guided Falsification and Verification against Adversarial Environments; and (v) Bridging Model and Real-World Gap. Finally, we introduce a software toolkit \verifai{} for the design and analysis of AI based systems, which was developed to provide a common formal platform to implement design and analysis frameworks for LB-CPS

A domain independent adaptive imaging system for visual inspection

Computer vision is a rapidly growing area. The range of applications is increasing very quickly, robotics, inspection, medicine, physics and document processing are all computer vision applications still in their infancy. All these applications are written with a specific task in mind and do not perform well unless there under a controlled environment. They do not deploy any knowledge to produce a meaningful description of the scene, or indeed aid in the analysis of the image. The construction of a symbolic description of a scene from a digitised image is a difficult problem. A symbolic interpretation of an image can be viewed as a mapping from the image pixels to an identification of the semantically relevant objects. Before symbolic reasoning can take place image processing and segmentation routines must produce the relevant information. This part of the imaging system inherently introduces many errors. The aim of this project is to reduce the error rate produced by such algorithms and make them adaptable to change in the manufacturing process. Thus a prior knowledge is needed about the image and the objects they contain as well as knowledge about how the image was acquired from the scene (image geometry, quality, object decomposition, lighting conditions etc,). Knowledge on algorithms must also be acquired. Such knowledge is collected by studying the algorithms and deciding in which areas of image analysis they work well in. In most existing image analysis systems, knowledge of this kind is implicitly embedded into the algorithms employed in the system. Such an approach assumes that all these parameters are invariant. However, in complex applications this may not be the case, so that adjustment must be made from time to time to ensure a satisfactory performance of the system. A system that allows for such adjustments to be made, must comprise the explicit representation of the knowledge utilised in the image analysis procedure. In addition to the use of a priori knowledge, rules are employed to improve the performance of the image processing and segmentation algorithms. These rules considerably enhance the correctness of the segmentation process. The most frequently given goal, if not the only one in industrial image analysis is to detect and locate objects of a given type in the image. That is, an image may contain objects of different types, and the goal is to identify parts of the image. The system developed here is driven by these goals, and thus by teaching the system a new object or fault in an object the system may adapt the algorithms to detect these new objects as well compromise for changes in the environment such as a change in lighting conditions. We have called this system the Visual Planner, this is due to the fact that we use techniques based on planning to achieve a given goal. As the Visual Planner learns the specific domain it is working in, appropriate algorithms are selected to segment the object. This makes the system domain independent, because different algorithms may be selected for different applications and objects under different environmental condition

Maximum Entropy Models For Natural Language Ambiguity Resolution

This thesis demonstrates that several important kinds of natural language ambiguities can be resolved to state-of-the-art accuracies using a single statistical modeling technique based on the principle of maximum entropy. We discuss the problems of sentence boundary detection, part-of-speech tagging, prepositional phrase attachment, natural language parsing, and text categorization under the maximum entropy framework. In practice, we have found that maximum entropy models offer the following advantages: State-of-the-art Accuracy: The probability models for all of the tasks discussed perform at or near state-of-the-art accuracies, or outperform competing learning algorithms when trained and tested under similar conditions. Methods which outperform those presented here require much more supervision in the form of additional human involvement or additional supporting resources. Knowledge-Poor Features: The facts used to model the data, or features, are linguistically very simple, or knowledge-poor but yet succeed in approximating complex linguistic relationships. Reusable Software Technology: The mathematics of the maximum entropy framework are essentially independent of any particular task, and a single software implementation can be used for all of the probability models in this thesis. The experiments in this thesis suggest that experimenters can obtain state-of-the-art accuracies on a wide range of natural language tasks, with little task-specific effort, by using maximum entropy probability models

Proceedings of the Workshop on Change of Representation and Problem Reformulation

The proceedings of the third Workshop on Change of representation and Problem Reformulation is presented. In contrast to the first two workshops, this workshop was focused on analytic or knowledge-based approaches, as opposed to statistical or empirical approaches called 'constructive induction'. The organizing committee believes that there is a potential for combining analytic and inductive approaches at a future date. However, it became apparent at the previous two workshops that the communities pursuing these different approaches are currently interested in largely non-overlapping issues. The constructive induction community has been holding its own workshops, principally in conjunction with the machine learning conference. While this workshop is more focused on analytic approaches, the organizing committee has made an effort to include more application domains. We have greatly expanded from the origins in the machine learning community. Participants in this workshop come from the full spectrum of AI application domains including planning, qualitative physics, software engineering, knowledge representation, and machine learning