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Distribution and Histogram (DisH) Learning
Machine learning has made incredible advances in the last couple of decades. Notwithstanding, a lot of this progress has been limited to basic point-estimation tasks. That is, a large bulk of attention has been geared at solving problems that take in a static finite vector and map it to another static finite vector. However, we do not navigate through life in a series of point-estimation problems, mapping x to y. Instead, we find broad patterns and gather a far-sighted understanding of data by considering collections of points like sets, sequences, and distributions. Thus, contrary to what various billionaires, celebrity theoretical physicists, and sci-fi classics would lead you to believe, true machine intelligence is fairly out of reach currently. In order to bridge this gap, this thesis develops algorithms that understand data at an aggregate, holistic level.
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