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Table 4 Values of parameters \(\beta \) and \(w\) for various samplings \(\hat{S}\)

From: Parallel coordinate descent methods for big data optimization

sampling \(\hat{S}\) \({{\mathrm{\mathbf {E}}}}[|\hat{S}|]\) \(\beta \) \(w\) ESO monotonic? Follows from
uniform \(\mathbf {E}[|\hat{S}|] \) \(1\) \(\nu \odot L\) No Thm 10
nonoverlapping uniform \(\tfrac{n}{l}\) \(1\) \(\gamma \odot L\) Yes Thm 11
doubly uniform \({{\mathrm{\mathbf {E}}}}[|\hat{S}|]\) \(1+\frac{ (\omega -1)\left( \frac{{{\mathrm{\mathbf {E}}}}[|\hat{S}|^2]}{{{\mathrm{\mathbf {E}}}}[|\hat{S}|]}-1\right) }{\max (1,n-1)}\) \(L\) No Thm 13
\(\tau \)-uniform \(\tau \) \(\min \{\omega ,\tau \}\) \(L\) Yes Thm 10
\(\tau \)-nice \(\tau \) \(1+ \frac{ (\omega -1)(\tau -1)}{\max (1,n-1)}\) \(L\) No Thm 12/13
\((\tau ,p_b)\)-binomial \(\tau p_b\) \(1+ \frac{p_b(\omega -1)(\tau -1)}{\max (1,n-1)}\) \(L\) No Thm 13
serial \(1\) \(1\) \(L\) Yes Thm 11/12/13
fully parallel \(n\) \(\omega \) \(L\) Yes Thm 11/12/13