**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Nonlinear regression

Summary

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.
In nonlinear regression, a statistical model of the form,
relates a vector of independent variables, , and its associated observed dependent variables, . The function is nonlinear in the components of the vector of parameters , but otherwise arbitrary. For example, the Michaelis–Menten model for enzyme kinetics has two parameters and one independent variable, related by by:
This function is nonlinear because it cannot be expressed as a linear combination of the two s.
Systematic error may be present in the independent variables 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.
Other examples of nonlinear functions include exponential functions, logarithmic functions, trigonometric functions, power functions, Gaussian function, and Lorentz distributions. Some functions, such as the exponential or logarithmic functions, can be transformed so that they are linear. When so transformed, standard linear regression can be performed but must be applied with caution. See Linearization§Transformation, below, for more details.
In general, there is no closed-form expression for the best-fitting parameters, as there is in linear regression. Usually numerical optimization algorithms are applied to determine the best-fitting parameters. Again in contrast to linear regression, there may be many local minima of the function to be optimized and even the global minimum may produce a biased estimate. In practice, estimated values of the parameters are used, in conjunction with the optimization algorithm, to attempt to find the global minimum of a sum of squares.
For details concerning nonlinear data modeling see least squares and non-linear least squares.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people (2)

Related units

No results

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related MOOCs

No results

Related publications (4)

Related concepts (10)

Related courses (61)

Related lectures (635)

Loading

Loading

Loading

CS-401: Applied data analysis

This course teaches the basic techniques, methodologies, and practical skills required to draw meaningful insights from a variety of data, with the help of the most acclaimed software tools in the dat

MATH-408: Regression methods

General graduate course on regression methods

FIN-403: Econometrics

The course covers basic econometric models and methods that are routinely applied to obtain inference results in economic and financial applications.

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

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. In nonlinear regression, a statistical model of the form, relates a vector of independent variables, , and its associated observed dependent variables, . The function is nonlinear in the components of the vector of parameters , but otherwise arbitrary.

Ordinary least squares

In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable.

Neural Networks: Multilayer Learning

Covers the fundamentals of multilayer neural networks and deep learning, including back-propagation and network architectures like LeNet, AlexNet, and VGG-16.

Multilayer Neural Networks: Deep Learning

Covers the fundamentals of multilayer neural networks and deep learning.

Generative Models: Self-Attention and Transformers

Covers generative models with a focus on self-attention and transformers, discussing sampling methods and empirical means.

This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods

Adjustable robust minimization problems where the objective or constraints depend in a convex way on the adjustable variables are generally difficult to solve. In this paper, we reformulate the origin

Sophie Myriam Hautphenne, Katharine Felicity Turner

We consider a class of continuous-time branching processes called Markovian binary trees (MBTs), in which the individuals lifetime and reproduction epochs are modelled using a transient Markovian arri