A multi-objective programming perspective to statistical learning problems
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It has been increasingly recognized that realistic problems often involve a tradeoff among many conflicting objectives. Traditional methods aim at satisfying multiple objectives by combining them into a global cost function, which in most cases overlooks the underlying tradeoffs between the conflicting objectives. This raises the issue about how different objectives should be combined to yield a final solution. Moreover, such approaches promise that the chosen overall objective function is optimized over the training samples. However, there is no guarantee on the performance in terms of the individual objectives since they are not considered on an individual basis. Motivated by these shortcomings of traditional methods, the objective in this dissertation is to investigate theory, algorithms, and applications for problems with competing objectives and to understand the behavior of the proposed algorithms in light of some applications. We develop a multi-objective programming (MOP) framework for finding compromise solutions that are satisfactory for each of multiple competing performance criteria. The fundamental idea for our formulation, which we refer to as iterative constrained optimization (ICO), evolves around improving one objective while allowing the rest to degrade. This is achieved by the optimization of individual objectives with proper constraints on the remaining competing objectives. The constraint bounds are adjusted based on the objective functions obtained in the most recent iteration. An aggregated utility function is used to evaluate the acceptability of local changes in competing criteria, i.e., changes from one iteration to the next. Conflicting objectives arise in different contexts in many problems of speech and language technologies. In this dissertation, we consider two applications. The first application is language model (LM) adaptation, where a general LM is adapted to a specific application domain so that the adapted LM is as close as possible to both the general model and the application domain data. Language modeling and adaptation is used in many speech and language processing applications such as speech recognition, machine translation, part-of-speech tagging, parsing, and information retrieval. The second application is automatic language identification (LID), where the standard detection performance evaluation measures false-rejection (or miss) and false-acceptance (or false alarm) rates for a number of languages are to be simultaneously minimized. LID systems might be used as a pre-processing stage for understanding systems and for human listeners, and find applications in, for example, a hotel lobby or an international airport where one might speak to a multi-lingual voice-controlled travel information retrieval system. This dissertation is expected to provide new insights and techniques for accomplishing significant performance improvement over existing approaches in terms of the individual competing objectives. Meantime, the designer has a better control over what is achieved in terms of the individual objectives. Although many MOP approaches developed so far are formal and extensible to large number of competing objectives, their capabilities are examined only with two or three objectives. This is mainly because practical problems become significantly harder to manage when the number of objectives gets larger. We, however, illustrate the proposed framework with a larger number of objectives.