Agnostic Learning (不可知学习)

不可知学习)"/>

Agnostic Learning (不可知学习)

Agnostic Learning (不可知学习)

Computational Learning Theory (Cont.)

The Vapnik-Chervonenkis(VC) dimension

- Shattering a set of instances
- VC dimension- Definition and several examples

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) = ?