Why are Nonlinear Fits to Data so Challenging?

被引:141
作者
Transtrum, Mark K. [1 ]
Machta, Benjamin B. [1 ]
Sethna, James P. [1 ]
机构
[1] Cornell Univ, Lab Atom & Solid State Phys, Ithaca, NY 14853 USA
关键词
ALGORITHMS;
D O I
10.1103/PhysRevLett.104.060201
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to changes in parameters, and one is left to make adjustments by hand. We explain this difficulty by interpreting the fitting process as a generalized interpolation procedure. By considering the manifold of all model predictions in data space, we find that cross sections have a hierarchy of widths and are typically very narrow. Algorithms become stuck as they move near the boundaries. We observe that the model manifold, in addition to being tightly bounded, has low extrinsic curvature, leading to the use of geodesics in the fitting process. We improve the convergence of the Levenberg-Marquardt algorithm by adding geodesic acceleration to the usual step.
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收藏
页数:4
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