Computational Intelligence, SS08
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Homework 15: VC-dimension of disjoint hypothesis classes



[Points: 8; Issued: 2004/03/04; Deadline: 2004/05/19; Tutor: Katharina Seke; Infohour: 2004/05/17, 12:00-13:00, Seminarraum IGI; Einsichtnahme: 2004/06/7, 12:00-13:00, Seminarraum IGI; Download: pdf; ps.gz]





Prove or disprove the following assumption: For every $ n \in \mathbf{N}$ it is true that if $ \mathcal{H}_1\subseteq\mathcal{H}$ and $ \mathcal{H}_2\subseteq\mathcal{H}$ are disjoint hypothesis classes out of the space $ \mathcal{H}$ of all possible hypothesis $ \{0,1\}^n \rightarrow \{0,1\}$, then VC-dim( $ \mathcal{H}_1\cup\mathcal{H}_2$) = VC-dim( $ \mathcal{H}_1$) + VC-dim( $ \mathcal{H}_2$).