Getting More Randomness
نویسنده
چکیده
Theorem 1.1 (Number of Samples for Class with Bounded VC-Dimension) Suppose (X,C) has VC-dimension at most d. Then, suppose S is a subset obtained by sampling from X independently m times. If m ≥ max{ log 2 δ , 8d log 8d }, then with probability at least 1− δ, S is an -net. Using VC-dimension, we can bound the number of effective boolean functions on the random subset S. However, after conditioning on S, there is no more randomness left. We see how we can introduce extra artificial randomness in the analysis in order to make the proof works.
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