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The VC dimension (for Vapnik–Chervonenkis dimension) is a measure of the capacity (complexity, expressive power, richness, or flexibility) of a statistical classification algorithm, defined as the cardinality of the largest set of points that the algorithm can shatter.

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What is the VC dimension of the hypothesis class $H=\left\{f_{\theta_{1}, \theta_{2}}: R^{2}...

The VC-dimension of your hypothesis class $\mathcal H$ is 2. To see this, we begin by showing that $\mathcal H$ shatters any 2-element set $\{(a_1 a_2), (b_1, b_2)\}$ of real numbers where all compone …
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