Semiparametric learning in signal processing, communication systems and pattern recognition

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Learning is the process of moving from concrete examples (training data) to models that can explain and predict the underlying process. Formally learning is the problem of recovering (from the training data) a mapping from input signals to output ones. The accuracy of the mapping to be learned from the data depends on the a priori knowledge of the process. Fully nonparametric learning methods do not need any a priori information and therefore are robust and do not suffer from risk of misspecification. On the other hand they exhibit slow learning rate, which deteriorates considerably with the dimensionality of the underlying objects, e.g., images. In contrast, classical parametric learning algorithms carries a great risk of misspecification, but if they are correctly specified they will enjoy fast learning rates with no deterioration caused by multivariate data. These two basic learning schemes have found numerous applications in such diverse areas as: medical diagnostics, data mining, qualitative economics, communication engineering, speech and pattern recognition. In practice, the dimensionality and sparseness of data force us to accept an intermediate model (semiparametric model) which lies between parametric and fully nonparametric cases. The parametric part of the model defines parameters of finite-dimensional projections of multivariate nonlinearities, whereas nonlinear characteristics run through a nonparametric class of univariate functions. This semiparametric model allows one to design practical learning algorithms which share the efficiency of parametric modeling while preserving the high flexibility of the nonparametric case, i.e., we wish to take the best of both worlds. In fact, in semiparametric models the curse of dimensionality can be entirely eliminated. The purpose of this research is twofold. First we propose to examine theoretical advancements, numerical implementations, and testing the accuracy of specific learning schemes within the aforementioned semiparametric framework. Second, we intend to apply this methodology to concrete cases beyond the traditional AI field such as: signal processing, communication systems, pattern recognition , and image analysis.