dichotomy

• 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

VCD:

Paper:

On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities

definition of VCD:

https://en.wikipedia.org/wiki/Vapnik%E2%80%93Chervonenkis_dimension