Optimization methods based on ideas from statistical physics have been developed to tackle a diverse set of hard problems including image segmentation, data clustering, and graph partitioning. These problems involve the assignment of elements viewed as ``data'' to one of a set of classes, so as to minimize the resulting cost. This project develops a novel extension of physics-based approaches to tackle the important, challenging sub-class of structurally-constrained data association problems, wherein assignments are constrained to agree with a parameterized classification rule such as that of a neural network or decision tree model. Central to the project is supervised learning, including statistical classification and regression/function approximation. Physics-based learning approaches have the potential to address fundamental learning problems such as convergence to non-global optima, parsimonious modelling, and generalization. Preliminary classification work already suggests that there is great promise for these new methods in outperforming existing learning algorithms. The specific project objectives are of both practical and theoretical significance, as they include development of learning algorithms for widely used classifier structures, investigating parsimonious modelling in part via phase transition analysis, tackling application areas such as speech recognition and condition-based maintenance, and extending the methods to address regression/function approximation and missing data problems.
