• Dichotomy in a sense can be interpreted as neglecting synonyms while keeping antonyms
  • VC dimension is a replacement for Union bound to minimize the upper bound when we are moving toward generalization.
  • VC dimension in principal is a replacement of growth function with M in Hoeffding Inequality.
  • For a binary classification, VC dimensions introduce the breaking point K which is N when the following situation happens:

Then we call N is the VC dimension of H

  • In step 1 the growth function is the maximum number of dichotomy set
  • In step 2 the growth function can be even just a breaking point we report that it exists. In this case there is no need to report the total dichotomies are 2^N while the total dichotomies due to that restriction (breaking point) collapse to the binomial.
  • Binomial function of N is interpreted as a good upper bound when we can guarantee the learning is possible



definition of VCD:


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