John’s walk
John’s walk
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约翰的步行
DOI：
--
复制
发表时间：
2018
影响因子：
1.2
通讯作者：
Hariharan Narayanan
中科院分区：
文献类型：
--
作者：
Adam Gustafson;Hariharan Narayanan
摘要我们提出了一个仿生不变的随机步道，用于从凸体中绘制均匀的随机样品
$ MATHCAL {K}子集Mathbb {r}^n $
使用最大体积的椭圆形，即John's Ellipsoids进行提案分布。
$ MATHCAL {K} $
在当前点。
$ {widetilde {o}}！左（n^7
ight）$
步骤，日志因素隐藏在
$ {widetilde {o}} $
仅取决于与温暖的开始和所需的总变化距离相关的常数。
$ MATHCAL {K} $
包含x，
$ left | log frac {| p-x |} {| q-x |}
ight | $
在上面由n中的多项式界定。
Abstract We present an affine-invariant random walk for drawing uniform random samples from a convex body
$mathcal{K} subset mathbb{R}^n$
that uses maximum-volume inscribed ellipsoids, known as John’s ellipsoids, for the proposal distribution. Our algorithm makes steps using uniform sampling from the John’s ellipsoid of the symmetrization of
$mathcal{K}$
at the current point. We show that from a warm start, the random walk mixes in
${widetilde{O}}!left(n^7
ight)$
steps, where the log factors hidden in the
${widetilde{O}}$
depend only on constants associated with the warm start and desired total variation distance to uniformity. We also prove polynomial mixing bounds starting from any fixed point x such that for any chord pq of
$mathcal{K}$
containing x,
$left|log frac{|p-x|}{|q-x|}
ight|$
is bounded above by a polynomial in n.
较强的自一致性和抽样能力
DOI：
10.1145/3357713.3384272
发表时间：
2020
期刊：
ACM Symposium on the Theory of Computing
影响因子：
--
作者：
Laddha, Aditi;Lee, Yin Tat;Vempala, Santosh
通讯作者：
Vempala, Santosh