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Fitting multidimensional data using gradient penalties and the sparse grid combination technique

机译:使用梯度罚分和稀疏网格组合技术拟合多维数据

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摘要

Sparse grids, combined with gradient penalties provide an attractive tool for regularised least squares fitting. It has earlier been found that the combination technique, which builds a sparse grid function using a linear combination of approximations on partial grids, is here not as effective as it is in the case of elliptic partial differential equations. We argue that this is due to the irregular and random data distribution, as well as the proportion of the number of data to the grid resolution. These effects are investigated both in theory and experiments. As part of this investigation we also show how overfitting arises when the mesh size goes to zero. We conclude with a study of modified "optimal" combination coefficients who prevent the amplification of the sampling noise present while using the original combination coefficients. [PUBLICATION ABSTRACT]
机译:稀疏网格与梯度惩罚相结合,为进行正则最小二乘拟合提供了一种有吸引力的工具。早先已经发现,使用对部分网格的近似线性组合来建立稀疏网格函数的组合技术在此不像在椭圆形偏微分方程的情况下那样有效。我们认为这是由于数据分布不规则和随机,以及数据数量与网格分辨率的比例所致。在理论和实验上都对这些影响进行了研究。作为这项研究的一部分,我们还显示了当网格大小变为零时,如何产生过度拟合。我们以修改后的“最佳”组合系数为研究结尾,这些组合系数可防止使用原始组合系数时出现的采样噪声放大。 [出版物摘要]

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