An n-dimensional Rosenbrock distribution for Markov chain Monte Carlo testing
An n-dimensional Rosenbrock distribution for Markov chain Monte Carlo testing
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DOI：
10.1111/sjos.12532
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发表时间：
2021-05-12
影响因子：
1
通讯作者：
Nadarajah, Saralees
中科院分区：
文献类型：
--
作者：
Pagani, Filippo;Wiegand, Martin;Nadarajah, Saralees
Rosenbrock函数是数值优化中的一个普遍存在的基准问题，并且已经提出了变体来测试马尔可夫链蒙特卡罗算法在具有弯曲和狭窄形状的分布上的性能。在这项工作中，我们讨论了Rosenbrock分布及其目前的n维扩展的优点和局限性。然后，我们提出了一个新的扩展到任意尺寸称为混合Rosenbrock分布，它解决了所有的限制，影响当前的扩展。混合Rosenbrock分布由条件正态核组成，以保留原始Rosenbrock核的关键特征的方式排列。此外，由于其结构，混合Rosenbrock分布是分析上易于处理的，并具有几个理想的属性，使其成为一个很好的测试模型的计算算法。我们的结论与数值实验表明，常用的马尔可夫链蒙特卡罗算法可能无法探索密度与弯曲的相关结构，重申这类密度的可靠的基准问题的重要性。
The Rosenbrock function is a ubiquitous benchmark problem in numerical optimization, and variants have been proposed to test the performance of Markov chain Monte Carlo algorithms on distributions with a curved and narrow shape. In this work we discuss the Rosenbrock distribution and the advantages and limitations of its current n-dimensional extensions. We then propose a new extension to arbitrary dimensions called the Hybrid Rosenbrock distribution, which addresses all the limitations that affect the current extensions. The Hybrid Rosenbrock distribution is composed of conditional normal kernels arranged in such a way that preserves the key features of the original Rosenbrock kernel. Moreover, due to its structure, the Hybrid Rosenbrock distribution is analytically tractable, and possesses several desirable properties which make it an excellent test model for computational algorithms. We conclude with numerical experiments that show how commonly used Markov chain Monte Carlo algorithms may fail to explore densities with curved correlation structure, restating the importance of a reliable benchmark problem for this class of densities.