Editing Open Problems:85
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|source=focs17 | |source=focs17 | ||
|who=Ryan O'Donnell | |who=Ryan O'Donnell | ||
+ | |title=Sample Stretching | ||
}} | }} | ||
Let $p$ be an unknown (discrete) probability distribution over a discrete domain $\Omega$ (e.g., $\Omega=[n]$) and $k\in\mathbb{N}$. As usual, $\operatorname{d}_{\rm TV}$ denotes the total variation distance. | Let $p$ be an unknown (discrete) probability distribution over a discrete domain $\Omega$ (e.g., $\Omega=[n]$) and $k\in\mathbb{N}$. As usual, $\operatorname{d}_{\rm TV}$ denotes the total variation distance. | ||
β | What is the minimum value of $\varepsilon\in(0,1]$ such that there exists an algorithm | + | What is the minimum value of $\varepsilon\in(0,1]$ such that there exists an algorithm which, on input $k$ i.i.d. samples from $p$, outputs $k+1$ i.i.d. samples from some $p'$ such that $\operatorname{d}_{\rm TV}(p,p')\leq \varepsilon$? |
β | ''Note:'' this is of a similar spirit as [[Open_Problems:69|Open Problem 69]] and the setting of sampling correctors | + | ''Note:'' this is of a similar spirit as [[Open_Problems:69|Open Problem 69]], and the setting of sampling correctors/improvers {{cite|CanonneGR-16}}. |