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Binary scalar products
Let $A, B \subseteq \mathbb{R}^d $ both span $\mathbb{R}^d$ such that $\langle a, b \rangle \in \{0, 1\}$ holds for all $a \in A$, $b \in B$.
Combinatorics Discrete Mathematics
The VC-dimension of k-vertex d-polytopes
In this short note, we show that the VC-dimension of the class of $k$-vertex polytopes in $\mathbb R^d$ is at most $8d^2k\log_2k$, answering an old question of Long and Warmuth.
Optimal Bounds on the VC-dimension
The VC-dimension of a set system is a way to capture its complexity and has been a key parameter studied extensively in machine learning and geometry communities.
When are epsilon-nets small?
In many interesting situations the size of epsilon-nets depends only on $\epsilon$ together with different complexity measures.
