Gottlieb, Lee-AdKontorovich, AryehMossel, Elchanan2023-05-232023-05-232012-05-282016-06-30https://repository.upenn.edu/handle/20.500.14332/47997We bound the number of nearly orthogonal vectors with fixed VC-dimension over {−1,1}n. Our bounds are of interest in machine learning and empirical process theory and improve previous bounds by Haussler. The bounds are based on a simple projection argument and they generalize to other product spaces. Along the way we derive tight bounds on the sum of binomial coefficients in terms of the entropy function.© 2012. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.VC dimensionpacking numberorthogonalStatistics and ProbabilityArticle