Editing Open Problems:46
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'''Question:''' Can we construct a distribution with this property such that the matrix-vector product $Ax$ can be evaluated in time $(s+k)\cdot \operatorname{polylog}(d)$ time given an $s$-sparse $x$? | '''Question:''' Can we construct a distribution with this property such that the matrix-vector product $Ax$ can be evaluated in time $(s+k)\cdot \operatorname{polylog}(d)$ time given an $s$-sparse $x$? | ||
β | '''Background:''' Such an algorithm is not known even for $s=d$ (unless $k$ is larger {{cite|AilonL | + | '''Background:''' Such an algorithm is not known even for $s=d$ (unless $k$ is larger {{cite|AilonL-11}}). |
β | '''Question:''' Provide an explicit construction of a distribution with the $(\epsilon, P)$-JL property such that the random | + | '''Question:''' Provide an explicit construction of a distribution with the $(\epsilon, P)$-JL property such that the random variable $A$ can be generated using $O(\log (d/P))$ bits. |