@MISC{Agwaral_geometricmethods, author = {Arvind Agwaral}, title = {Geometric Methods in Machine Learning}, year = {} }

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Abstract

The standard goal of machine learning to take a finite set of data and induce a model using that data that is able to generalize beyond that finite set. In particular, a learning problem finds an appropriate statistical model from a model space based on the training data from a data space. For many such problems, these spaces carry geometric structures that can be exploited using geometric methods, or the problems themselves can be formulated in a way that naturally appeals to geometry-based methods. In such cases, studying these geometric structures and then using appropriate geometry-driven methods not only gives insight into existing algorithms, but also helps build new and better algorithms. In my research, I apply geometric methods to a variety of learning problems, and provide strong theoretical and empirical evidence in favor of using them. The first part of my proposal is devoted to the study of the geometry of the space of probabilistic models associated with the statistical process that generated the data. This study – based on the theory well grounded in information geometry – allows me to reason about the appropriateness of conjugate priors from a geometric perspective, and hence gain insight into the large number of existing models that rely on these priors. Furthermore, I use this study to build a family of kernels called generative kernels that can be used as off-the-shelf tool in any kernel learning method such as support vector machines. Preliminary experiments of generative kernels based on simple statistical process show promising results, and in the future I propose to extend this work for more complex statistical