All Questions

I would like to upper bound the VC dimension of the function class $ F$ defined as follows: $$ F := \left\{ (x,t) \mapsto \mathbb{1} \left( c_Q\min_{q \in Q} {\|x-q \|}_1 - t > 0 \right) \; | \; Q ...

Write $n$ iid draws of $(x,y)$ as $(x^n, y^n)$. Fix $R\in (0,H(x))$. What is the min of $n^{-1}H(y^n|f(x^n))$ over maps $f$ with range $\lbrace 1,\dots,\exp nR\}$, taking $n\to \infty$?

Given $x$ and $y$ in $\mathbb{R}$, and let $\mathcal{H} = \{ h \mid \mathbb{R} \to \mathbb{N} \}$ be a family of hash functions where $ h(x) = \left\lfloor x + \sum^C_{i=1} U_i \right\rfloor$ for some ...