Agnostic Learning (不可知学习)

Agnostic Learning (不可知学习)

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Computational Learning Theory (Cont.)

The Vapnik-Chervonenkis(VC) dimension

- Shattering a set of instances
- VC dimension

    - Definition and several examples

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The Vapnik-Chervonenkis(VC) dimension

  • An unbiased hypothesis spaceis one that shatters the instance space X.
  • Sometimes X cannotbe shattered by H, but a large subset of it can.
  • Definition: The Vapnik-ChervonenkisDimensionVC(H)of hypothesis space Hdefined over instance space X
  • is the size of the largestfinite subset of X shattered by H.
  • if arbitrarily large finite sets of X can be shattered by H, then VC(H)≡∞
  • If we find ONE set of instances of size d that can be shattered, then VC(H) d.
  • To show that VC(H)

VC Dim. Examples (1)

  • Example 1:
    • Instance space X: the set of real numbers
      X = R
    • H is the set of intervals on the real number axis.
    • Form of H is: a < x < b
    • VC(H) = ?
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