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Old 07-17-2017, 06:20 AM
RicLouRiv RicLouRiv is offline
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Join Date: Jun 2017
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Default Problem 2.19 (c)

I would appreciate some guidance on Problem 2.19 (c).

Using the result of Part (b), I can write:

m_\mathcal{H}(N) \leq \frac{(eN)^D}{\tilde{d}^{\tilde{d}}d_1^{d_1}\cdots d_k^{d_k}},

where D=\tilde{d}+d_1+\cdots+d_k.

If d_{VC} is the dimension, then:

m_\mathcal{H}(d_{VC}) = 2^{d_{VC}} \leq \frac{(e d_{VC})^D}{\tilde{d}^{\tilde{d}}d_1^{d_1}\cdots d_k^{d_k}}

I'm stuck at this point. I don't have a clever way to deal with that denominator...you'd want to re-write it in terms of an inequality involving D, but i don't see how.
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