The Square Root Rule for Adaptive Importance Sampling
The Square Root Rule for Adaptive Importance Sampling
复制标题
自适应重要性采样的平方根规则
DOI：
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发表时间：
2019
影响因子：
0.9
通讯作者：
Yi Zhou
中科院分区：
文献类型：
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作者：
A. Owen;Yi Zhou
在自适应重要性采样和其他情况下，我们有K > 1个公共量μ的无偏和不相关估计μ^k。最优无偏线性组合的权重与它们的方差成反比，但这些权重是未知的，难以估计。一个简单的确定性平方根规则基于Var（μ^k）‡ k-1/2的工作模型，给出了μ的无偏估计，该估计在广泛的替代方差模式下几乎是最优的。我们证明，如果Var（μ^k）<$k-y对于一个未知的速率参数y∈[0，1]，那么平方根规则产生的最优方差率与一个常数太大，最多9/8，对于任何0 <$y <$1和任何数量的K估计。数值计算表明，规则是类似的一些其他模式的稳健性与温和减少的方差随着k的增加。
In adaptive importance sampling and other contexts, we have K > 1 unbiased and uncorrelated estimates μ^k of a common quantity μ. The optimal unbiased linear combination weights them inversely to their variances, but those weights are unknown and hard to estimate. A simple deterministic square root rule based on a working model that Var(μ^k) ∝ k−1/2 gives an unbiased estimate of μ that is nearly optimal under a wide range of alternative variance patterns. We show that if Var(μ^k)∝ k−y for an unknown rate parameter y∈[0,1], then the square root rule yields the optimal variance rate with a constant that is too large by at most 9/8 for any 0 ⩽ y⩽ 1 and any number K of estimates. Numerical work shows that rule is similarly robust to some other patterns with mildly decreasing variance as k increases.