Non-Linear Model Fitting Algorithm

A Non-Linear Model Fitting Algorithm is a parametric regression algorithm that can be applied by a non-linear regression system (that can solve a non-linear regression task by producing a regressed nonlinear function.

• Context:
  • It can (typically) minimize a Non-Linear Least Squares (to produce a least squares regression line).
  • It can range from being a Univariate Non-Linear Regression Algorithm to being a Multivariate Non-Linear Regression Algorithm.
  • It can range from being a Simple Non-Linear Regression Algorithm to being a Robust Non-Linear Regression Algorithm.
  • It can range from being a Continuous Non-Linear Regression Algorithm to being a Segmented Non-Linear Regression Algorithm.
  • It can range from being an Ordinary Non-Linear Regression Algorithm (such as ordinary nonlinear least squares) to being a Regularized Non-Linear Regression Algorithm.
  • It can (often) be based on a Nonlinear Function Approximation Algorithm.
  • …
• Example(s):
  • a Non-Linear Least-Squares Algorithm.
  • a Non-Linear Regression Feature Selection Algorithm.
  • …
• Counter-Example(s):
  • a Linear Regression Algorithm.
• See: Logistic Regression Algorithm, Hyperbolic Regression Algorithm, Non-Linear Least Squares.

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References

• http://onlineregression.sdsu.edu/onlineregression12.php
• http://onlineregression.sdsu.edu/onlineregression14.php

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/nonlinear_regression Retrieved:2015-4-30.
  • In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations.

2011

• http://en.wikipedia.org/wiki/Nonlinear_regression
  • In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations.

    The data consist of error-free independent variables (explanatory variables), x, and their associated observed dependent variables (response variables), y. Each y is modeled as a random variable with a mean given by a nonlinear function [math]\displaystyle{ f }[/math](x,β). Systematic error may be present but its treatment is outside the scope of regression analysis. If the independent variables are not error-free, this is an errors-in-variables model, also outside this scope.

    For example, the Michaelis–Menten model for enzyme kinetics [math]\displaystyle{ v = \frac{V_\max[\mbox{S}]}{K_m + [\mbox{S}]} }[/math] can be written as [math]\displaystyle{ f(x,\boldsymbol\beta)= \frac{\beta_1 x}{\beta_2 + x} }[/math] where [math]\displaystyle{ \beta_1 }[/math] is the parameter [math]\displaystyle{ V_\max }[/math], [math]\displaystyle{ \beta_2 }[/math] is the parameter [math]\displaystyle{ K_m }[/math] and [S] is the independent variable, x. This function is nonlinear because it cannot be expressed as a linear combination of the [math]\displaystyle{ \beta }[/math]s.

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