Non-Linear Least-Squares Regression Algorithm

A Non-Linear Least-Squares Regression Algorithm is a least-squares regression algorithm that is a non-linear regression algorithm which can be applied by a non-linear least squares system (that can solve nonlinear least squares optimization).

• • …
• Counter-Example(s):
  • Linear Least Squares.
• See: Sum-of-Squares, Non-Linear Regression, Nonlinear Regression.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/non-linear_least_squares Retrieved:2014-6-28.
  • '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 non-linear 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.

1994

• (Hagan & Menhaj, 1994) ⇒ Martin T. Hagan, and Mohammad B. Menhaj. (1994). “Training Feedforward Networks with the Marquardt Algorithm.” In: IEEE Transactions on Neural Networks Journal, 5(6). doi:10.1109/72.329697
  • QUOTE: The Marquardt algorithm for nonlinear least squares is presented and is incorporated into the backpropagation algorithm for training feedforward neural networks. The algorithm is tested on several function approximation problems, and is compared with a conjugate gradient algorithm and a variable learning rate algorithm.

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