Question

Suppose the VC dimension of a hypothesis space is 4. Which of the following are true?
A) No sets of 4 points can be shattered by the hypothesis space.
B) Atleast one set of 4 points can be shattered by the hypothesis space.
C) All sets of 4 points can be shattered by the hypothesis space.
D) No set of 5 points can be shattered by the hypothesis space.

Answer 1

Explanation:

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Answer 2

Option A)  No sets of 4 points can be shattered by the hypothesis space.

Suppose the VC dimension of a hypothesis space is 4

• The biggest finite subset of instance space X that can be broken by the hypothesis space H is measured by its VC dimension, or VC(H). The size of the greatest finite subset of X that H can shatter is the VC dimension of hypothesis space H over instance space X.
• Even if it might be unable to shatter some sets of size 3, the VC dimension of H in this case is 3. According to the definition of the VC dimension, all that is required to demonstrate that VC(H) is at least d is that H can shatter at least one set of size d.
• A set of size 0 can be easily broken by any non-empty class, hence the VC dimension is non-negative. Additionally, if H has just one hypothesis, a constant function, the VC dimension is equal to zero.

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