| Learning complexity vs. communication complexity (2006) | |||||||||||||||
Abstract | |||||||||||||||
| This paper has two main focal points. We first consider an important class of machine learning algorithms- large margin classifiers (Support Vector Machines belong to this class). The notion of margin complexity quantifies the extent to which a given class of functions can be learned by large margin classifiers. We prove that up to a small multiplicative constant, margin complexity is equal to the inverse of discrepancy. This establishes a strong tie between seemingly very different notions from two distinct areas. In the same way that matrix rigidity is related to rank, we introduce the notion of rigidity of margin complexity. We prove that sign matrices with small margin complexity rigidity are very rare. This leads to the question of proving lower bounds on the rigidity of margin complexity. Quite surprisingly, this question turns out to be closely related to basic open problems in communication complexity, e.g., whether PSPACE can be separated from the polynomial hierarchy in communication complexity. 1 | |||||||||||||||
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