Fast and comprehensive fitting of complex mathematical models to massive amounts of empirical data
Fast and comprehensive fitting of complex mathematical models to massive amounts of empirical data
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DOI：
10.1016/j.chemolab.2011.04.009
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发表时间：
2012-08-01
影响因子：
3.9
通讯作者：
Martens, Harald
中科院分区：
文献类型：
--
作者：
Isaeva, Julia;Saebo, Solve;Martens, Harald
由Isaeva等人提出的用非线性函数参数化大量观测曲线的新方法在这里被应用于噪声数据，并在计算速度、易用性和估计精度方面进行了测试。该方法采用传统的最小二乘最小化拟合残差。但在算法上，它用快速、非迭代的线性投影取代了传统的、耗时的迭代爬坡（例如，单纯形优化）。每个非线性函数通过其多元元模型（其行为的低维双线性主成分分析模型）进行模拟，并通过简单的投影和数据库查找产生参数估计。为了建立一个通用的、快速的线曲率建模系统，我们选择了38个不同的数学函数，其中大多数是非线性的，因为它们能够给出s型曲线。对每个模型，通过设计的计算机模拟建立其行为库，并估计其多元元模型。然后，将新的曲线拟合方法与传统的单纯形优化方法进行比较，通过将人工但有噪声的曲线拟合到38个曲线函数中，以确定正确的函数类型和参数值。最后，将该方法应用于异方差噪声，并对蛋白质组学二维凝胶电泳（2DGE）图像显影时移监测的bbb170,000条s形曲线进行了参数化。新方法给出了至少与单纯形优化一样精确的参数估计，并且对于均方差和异方差噪声都能很好地工作。与单纯形优化相比，该方法将非线性模型的参数估计速度提高了约24倍。此外，根据定义，它避免了不得不选择起始值和以局部最优解结束的问题。它减少了非线性模型规范的主观选择问题，可能存在错误的选择。(C) 2011 Elsevier B.V.版权所有
The new method for parameterising a high number of observed curves in terms of nonlinear functions, presented by Isaeva et al. is here applied to noisy data and tested with respect to computational speed, ease of use and estimation precision. The method employs conventional least squares minimisation of the lack-of-fit residuals. But algorithmically it replaces traditional, time-consuming iterative hill-climbing (e.g., simplex optimisation) by a fast, non-iterative linear projection. Each nonlinear function is emulated by its multivariate metamodel (a low-dimensional bi-linear principal component analysis model of its behaviour), and yields parameter estimates by a simple projection plus a data base look-up.For setting up a generic, fast modelling system for line curvature, a set of 38 widely different mathematical functions - most of them nonlinear - were selected for their ability to give sigmoid curves. For each model, its behavioural repertoire was established by designed computer simulation, and its multivariate metamodel was estimated. Then the new curve fitting approach was compared to conventional simplex optimisation, by fitting artificial, but noisy curves to the 38 curve-functions, in order to identify the correct function type and parameter values. Finally, the new method was adapted to heteroscedastic noise and employed for parameterisation of > 170,000 sigmoid curves from time lapse monitoring of proteomic 2D Gel Electrophoresis (2DGE) image development.The new method gave at least as precise parameter estimates as the simplex optimisation and worked well both for homoscedastic and heteroscedastic noise. It speeded up the parameter estimation in the nonlinear models by a factor of about 24 compared to the simplex optimisation.Moreover, per definition it avoids the problems of having to select starting values and ending up in locally optimal solutions. And it reduced the problem of subjective, possibly erroneous choice of nonlinear model specification. (C) 2011 Elsevier B.V. All rights reserved.