Non-Linear Least-Squares Regression System

AKA: Nonlinear Least Squares System, Nonlinear Least Squares Optimization System, Nonlinear Least Squares Estimation System.
Example(s)
- scipy.optimize.least_squares , a Scipy Optimization mode that solves a nonlinear least-squares problem with bounds on the variables.
- …
Counter-Example(s)
- Linear Least-Squares System.
See: Least Squares, Nonlinear Regression, Linear Least Squares (Mathematics).

References

(Scipy, 2017) ⇒ The Scipy community (2008-2009). “scipy.optimize.least_squares" https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.htmlLast updated on Jun 10, 2017
- QUOTE: Solve a nonlinear least-squares problem with bounds on the variables.
  Given the residuals f(x) (an m-dimensional real function of n real variables) and the loss function rho(s) (a scalar function), least_squares finds a local minimum of the cost function F(x):

minimize F(x) = 0.5 * sum(rho(f_i(x)**2), i = 0, ..., m - 1) subject to lb <= x <= ub

The purpose of the loss function rho(s) is to reduce the influence of outliers on the solution(...)

(Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Non-linear_least_squares Retrieved:2017-8-13.
- Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m > n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences.