Qualitative and Quantitative Knowledge in Classical Mechanics

This thesis investigates what knowledge is necessary to solve mechanics problems. A program NEWTON is described which understands and solves problems in mechanics mini-world of objects moving on surfaces. Facts and equations such as those given in mechanics text need to be represented. However, this is far from sufficient to solve problems. Human problem solvers rely on "common sense" and "qualitative" knowledge which the physics text tacitly assumes to be present. A mechanics problem solver must embody such knowledge. Quantitative knowledge given by equations and more qualitative common sense knowledge are the major research points exposited in this thesis. The major issue in solving problems is planning. Planning involves tentatively outlining a possible path to the solution without actually solving the problem. Such a plan needs to be constructed and debugged in the process of solving the problem. Envisionment, or qualitative simulation of the event, plays a central role in this planning process.

Causal and Teleological Reasoning in Circuit Recognition

This thesis presents a theory of human-like reasoning in the general domain of designed physical systems, and in particular, electronic circuits. One aspect of the theory, causal analysis, describes how the behavior of individual components can be combined to explain the behavior of composite systems. Another aspect of the theory, teleological analysis, describes how the notion that the system has a purpose can be used to aid this causal analysis. The theory is implemented as a computer program, which, given a circuit topology, can construct by qualitative causal analysis a mechanism graph describing the functional topology of the system. This functional topology is then parsed by a grammar for common circuit functions. Ambiguities are introduced into the analysis by the approximate qualitative nature of the analysis. For example, there are often several possible mechanisms which might describe the circuit's function. These are disambiguated by teleological analysis. The requirement that each component be assigned an appropriate purpose in the functional topology imposes a severe constraint which eliminates all the ambiguities. Since both analyses are based on heuristics, the chosen mechanism is a rationalization of how the circuit functions, and does not guarantee that the circuit actually does function. This type of coarse understanding of circuits is useful for analysis, design and troubleshooting.

Learning-Based Approach to Real Time Tracking and Analysis of Faces

This paper describes a trainable system capable of tracking faces and facialsfeatures like eyes and nostrils and estimating basic mouth features such as sdegrees of openness and smile in real time. In developing this system, we have addressed the twin issues of image representation and algorithms for learning. We have used the invariance properties of image representations based on Haar wavelets to robustly capture various facial features. Similarly, unlike previous approaches this system is entirely trained using examples and does not rely on a priori (hand-crafted) models of facial features based on optical flow or facial musculature. The system works in several stages that begin with face detection, followed by localization of facial features and estimation of mouth parameters. Each of these stages is formulated as a problem in supervised learning from examples. We apply the new and robust technique of support vector machines (SVM) for classification in the stage of skin segmentation, face detection and eye detection. Estimation of mouth parameters is modeled as a regression from a sparse subset of coefficients (basis functions) of an overcomplete dictionary of Haar wavelets.

Statistical Models for Co-occurrence Data

Modeling and predicting co-occurrences of events is a fundamental problem of unsupervised learning. In this contribution we develop a statistical framework for analyzing co-occurrence data in a general setting where elementary observations are joint occurrences of pairs of abstract objects from two finite sets. The main challenge for statistical models in this context is to overcome the inherent data sparseness and to estimate the probabilities for pairs which were rarely observed or even unobserved in a given sample set. Moreover, it is often of considerable interest to extract grouping structure or to find a hierarchical data organization. A novel family of mixture models is proposed which explain the observed data by a finite number of shared aspects or clusters. This provides a common framework for statistical inference and structure discovery and also includes several recently proposed models as special cases. Adopting the maximum likelihood principle, EM algorithms are derived to fit the model parameters. We develop improved versions of EM which largely avoid overfitting problems and overcome the inherent locality of EM--based optimization. Among the broad variety of possible applications, e.g., in information retrieval, natural language processing, data mining, and computer vision, we have chosen document retrieval, the statistical analysis of noun/adjective co-occurrence and the unsupervised segmentation of textured images to test and evaluate the proposed algorithms.