Improved maximum entropy analysis with an extended search space
Improved maximum entropy analysis with an extended search space
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DOI：
10.1016/j.jcp.2012.12.023
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发表时间：
2011-10
期刊：
影响因子：
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通讯作者：
A. Rothkopf
中科院分区：
文献类型：
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作者：
A. Rothkopf
最大熵方法（MEM）的标准实现遵循Bryan [1]，并部署了奇异值分解（SVD）来先验地限制底层解空间的维度。在这里，我们提出的参数的基础上的形状的SVD基函数和模拟数据分析的数值证据，这表明，正确的贝叶斯解决方案是不是在一般恢复与这种方法。作为补救措施，我们建议系统地扩展搜索基础，这将最终恢复完整的解决方案空间和正确的解决方案。为了充分解决使用指数阻尼内核的问题，我们提供了一个开源实现，使用C/C++语言，该语言利用在运行时可调的高精度算术[2]。LBFGS算法包含在代码中，以便在不需要求助于特定搜索空间限制的情况下解决问题。
The standard implementation of the Maximum Entropy Method (MEM) follows Bryan [1] and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the shape of the SVD basis functions and numerical evidence from a mock data analysis, which show that the correct Bayesian solution is not in general recovered with this approach. As a remedy we propose to extend the search basis systematically, which will eventually recover the full solution space and the correct solution. In order to adequately approach problems where an exponentially damped kernel is used, we provide an open-source implementation, using the C/C++ language that utilizes high precision arithmetic adjustable at run-time [2]. The LBFGS algorithm is included in the code in order to attack problems without the need to resort to a particular search space restriction.