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Probabilistic Estimation of Vapnik-Chervonenkis Dimension

We present an idea of probabilistic estimation of Vapnik-Chervonenkis dimension given a set of indicator functions. The idea is embedded in two algorithms we propose — named A and A′. Both algorithms are based on an approach that can be described as expand or divide and conquer. Also, algorithms are parametrized by probabilistic constraints expressed in a form of (e,δ)-precision. The precision implies how often and by how much the estimate can deviate from the true VC-dimension. Analysis of convergence and computational complexity for proposed algorithms is also presented.