论文标题
蒙特卡洛立方体建筑
Monte Carlo Cubature Construction
论文作者
论文摘要
在数值集成中，立方体方法是有效的，尤其是当可以通过已知的测试函数（例如多项式）对积分进行良好的评估时。但是，群岛的构建公式通常尚不清楚，现有示例仅代表整数的特定域，例如超振管和球体。在这项研究中，我们表明，只要我们有一个I.I.D.来自该度量的采样器和给定测试函数的平均值。此外，即使没有足够的措施的事先信息，该提出的方法也可以作为数据压缩的手段。
In numerical integration, cubature methods are effective, especially when the integrands can be well-approximated by known test functions, such as polynomials. However, the construction of cubature formulas has not generally been known, and existing examples only represent the particular domains of integrands, such as hypercubes and spheres. In this study, we show that cubature formulas can be constructed for probability measures provided that we have an i.i.d. sampler from the measure and the mean values of given test functions. Moreover, the proposed method also works as a means of data compression, even if sufficient prior information of the measure is not available.
