3.24 VC-dimension of union of concepts. Let A and B be two sets of functions mapping from...
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3.24 VC-dimension of union of concepts. Let A and B be two sets of functions mapping from X into f0; 1g, and assume that both A and B have nite VCdimension, with VCdim(A) = dA and VCdim(B) = dB. Let C = A [ B be the union of A and B.
(a) Prove that for all m, C(m) A(m) + B(m).
(b) Use Sauer's lemma to show that for m dA + dB + 2, C(m) < 2m; and give a bound on the VC-dimension of C.
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Foundations Of Machine Learning
ISBN: 9780262351362
2nd Edition
Authors: Mehryar Mohri, Afshin Rostamizadeh
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