Real-world learning tasks present a range of issues for learning systems. Learning tasks can be complex and the training data noisy. When operating as part of a larger system, there may be limitations on available memory and computational resources. Learners may also be required to provide results from a stream. This thesis investigates the problem of incremental, relational learning from imperfect data with constrained time and memory resources. The learning process involves incremental update of a theory when an example is presented that contradicts the theory. Contradictions occur if there is an incorrect theory or noisy data. The learner cannot discriminate between the two possibilities, so both are considered and the better possibility used. Additionally, all changes to the theory must have support from multiple examples. These two principles allow learning from imperfect data. The Minimum Description Length principle is used for selection between possible worlds and determining appropriate levels of additional justification. A new encoding scheme allows the use of MDL within the framework of Inductive Logic Programming. Examples must be stored to provide additional justification for revisions without violating resource requirements. A new algorithm determines when to discard examples, minimising total usage while ensuring sufficient storage for justifications. Searching for revisions is the most computationally expensive part of the process, yet not all searches are successful. Another new algorithm uses a notion of theory stability as a guide to occasionally disallow entire searches to reduce overall time. The approach has been implemented as a learner called NILE. Empirical tests include two challenging domains where this type of learner acts as one component of a larger task. The first of these involves recognition of behavior activation conditions in another agent as part of an opponent modeling task. The second, more challenging task is learning to identify objects in visual images by recognising relationships between image features. These experiments highlight NILE'S strengths and limitations as well as providing new n domains for future work in ILP.

Raman spectroscopy provides a powerful means of chemical identification in a variety of fields, partly because of its non-contact nature and the speed at which measurements can be taken. The development of powerful, inexpensive lasers and sensitive charge-coupled device (CCD) detectors has led to widespread use of commercial and scientific Raman systems. However, relatively little work has been done developing physics-based probabilistic models for Raman measurement systems and crafting inference algorithms within the framework of statistical estimation and detection theory. The objective of this thesis is to develop algorithms and performance bounds for the identification of chemicals from their Raman spectra. First, a Poisson measurement model based on the physics of a dispersive Raman device is presented. The problem is then expressed as one of deterministic parameter estimation, and several methods are analyzed for computing the maximum-likelihood (ML) estimates of the mixing coefficients under our data model. The performance of these algorithms is compared against the Cramer-Rao lower bound (CRLB). Next, the Raman detection problem is formulated as one of multiple hypothesis detection (MHD), and an approximation to the optimal decision rule is presented. The resulting approximations are related to the minimum description length (MDL) approach to inference. In our simulations, this method is seen to outperform two common general detection approaches, the spectral unmixing approach and the generalized likelihood ratio test (GLRT). The MHD framework is applied naturally to both the detection of individual target chemicals and to the detection of chemicals from a given class. The common, yet vexing, scenario is then considered in which chemicals are present that are not in the known reference library. A novel variation of nonnegative matrix factorization (NMF) is developed to address this problem. Our simulations indicate that this algorithm gives better estimation performance than the standard two-stage NMF approach and the fully supervised approach when there are chemicals present that are not in the library. Finally, estimation algorithms are developed that take into account errors that may be present in the reference library. In particular, an algorithm is presented for ML estimation under a Poisson errors-in-variables (EIV) model. It is shown that this same basic approach can also be applied to the nonnegative total least squares (NNTLS) problem. Most of the techniques developed in this thesis are applicable to other problems in which an object is to be identified by comparing some measurement of it to a library of known constituent signatures.