ITR: Representation Learning: Transformations and Kernels for Collections of Tuples

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Statistical machine learning tools permit scientists and engineers to automatically estimate computational models directly from real-world data for making predictions, classifications and inferences. However, before learning can take place, the practitioner needs to know how to properly represent data in a consistent, invariant and well-behavednumerical form for processing by the various techniques. This proposal reduces this burden and facilitates applications of machine learning via novel algorithms that not only model data but also automatically handle invariances and discover appropriaterepresentations of the data.This proposal formalizes a variety of potential transformations and embeds them within a principled learning framework. This makes it possible to handle real scenarios where data transforms, translates, changes nonlinearly and effectively creates many difficulties fortraditional tools. The set of interesting transformations the proposal considers also includes permutations. Handling permutation allows algorithms to learn when each data-point in the dataset is a collection of tuples whose ordering is arbitrary. For example, adigital color image can be represented as a bag of pixels whose ordering is arbitrary. This project then develops the necessary algorithms for invariance to permutations, re-orderings, translations, and many other transformations affecting data in practice.The proposal makes use of and extends state-of-the-art techniques in the machine learning field including Bayesian networks, kernel methods and convex programming. Primary applications include face recognition and surveillance. To recognize human face identity from video, the proposed algorithms compensate for possible transformations as faces translate, deform and rotate in real images. Standardized and challenging face recognition datasets are used for evaluation. The representation learning methods also facilitate machine learning in general, promising potential impact in other applied fields where data undergoes transformations including computational vision, speech, timeseries analysis and bio-informatics.