Multiple importance sampling revisited: breaking the bounds
Multiple importance sampling revisited: breaking the bounds
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DOI：
10.1186/s13634-018-0531-2
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发表时间：
2018-02-27
影响因子：
1.9
通讯作者：
Szirmay-Kalos, Laszlo
中科院分区：
文献类型：
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作者：
Sbert, Mateu;Havran, Vlastimil;Szirmay-Kalos, Laszlo
我们重新研究了多重重要抽样（MIS）估计，并研究了Veach论文中建立的具有等样本数的平衡启发式估计的效率改进的界。我们修改了这个证明，并得出结论，不存在这样的界限，因此寻找新的估计量是有意义的，它可以改进具有等样本计数的平衡启发式估计量。接下来，我们研究了最近引入的非平衡启发式MIS估计器，该估计器在样本数量相等的情况下比平衡启发式估计器更好，并在方差和效率方面对其进行了改进。然后，我们获得了一个同样可证明的更好的单样本平衡启发式估计器，最后，我们引入了一个启发式的样本计数，当单个技术有偏差时可以使用。总而言之，我们提出了三种新的采样策略，以提高使用非相等样本计数的平衡启发式的方差和效率。我们的方案需要预先了解几个量，但这些量可以通过自适应的方式获得。结果还表明，通过仔细检查估计量的方差和性质，可以在将来发现更好的估计量。我们提出的例子支持我们的理论发现。
We revisit the multiple importance sampling (MIS) estimator and investigate the bound on the efficiency improvement over balance heuristic estimator with equal count of samples established in Veach's thesis. We revise the proof for this and come to the conclusion that there is no such bound and henceforth it makes sense to look for new estimators that improve on balance heuristic estimator with equal count of samples. Next, we examine a recently introduced non-balance heuristic MIS estimator that is provably better than balance heuristic with equal count of samples, and we improve it both in variance and efficiency. We then obtain an equally provably better one-sample balance heuristic estimator, and finally, we introduce a heuristic for the count of samples that can be used when the individual techniques are biased. All in all, we present three new sampling strategies to improve on both variance and efficiency on the balance heuristic using non-equal count of samples.Our scheme requires the previous knowledge of several quantities, but those can be obtained in an adaptive way. The results also show that by a careful examination of the variance and properties of the estimators, even better estimators could be discovered in the future. We present examples that support our theoretical findings.