Local Regression Algorithm
A Local Regression Algorithm is a supervised regression algorithm that ...
- Contect:
- It can range from being a Parametric Local Regression Algorithm to being a Non-Parametric Local Regression Algorithm.
- It can be implemented by a Local Regression System (to solve a local regression task).
- Example(s):
- See: Scattergram, Non-Parametric Regression, k-Nearest Neighbor Algorithm, Least Squares Regression, Non-Linear Regression.
References
2018
- (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Local_regression Retrieved:2018-3-30.
- LOESS and LOWESS (locally weighted scatterplot smoothing) are two strongly related non-parametric regression methods that combine multiple regression models in a k-nearest-neighbor-based meta-model. “LOESS" is a later generalization of LOWESS; although it is not a true acronym, it may be understood as standing for "LOcal regrESSion". [1]
LOESS and LOWESS thus build on "classical" methods, such as linear and nonlinear least squares regression. They address situations in which the classical procedures do not perform well or cannot be effectively applied without undue labor. LOESS combines much of the simplicity of linear least squares regression with the flexibility of nonlinear regression. It does this by fitting simple models to localized subsets of the data to build up a function that describes the deterministic part of the variation in the data, point by point. In fact, one of the chief attractions of this method is that the data analyst is not required to specify a global function of any form to fit a model to the data, only to fit segments of the data.
The trade-off for these features is increased computation. Because it is so computationally intensive, LOESS would have been practically impossible to use in the era when least squares regression was being developed. Most other modern methods for process modeling are similar to LOESS in this respect. These methods have been consciously designed to use our current computational ability to the fullest possible advantage to achieve goals not easily achieved by traditional approaches.
A smooth curve through a set of data points obtained with this statistical technique is called a Loess Curve, particularly when each smoothed value is given by a weighted quadratic least squares regression over the span of values of the y-axis scattergram criterion variable. When each smoothed value is given by a weighted linear least squares regression over the span, this is known as a Lowess curve ; however, some authorities treat Lowess and Loess as synonyms.
- LOESS and LOWESS (locally weighted scatterplot smoothing) are two strongly related non-parametric regression methods that combine multiple regression models in a k-nearest-neighbor-based meta-model. “LOESS" is a later generalization of LOWESS; although it is not a true acronym, it may be understood as standing for "LOcal regrESSion". [1]
2017
- https://www.statsdirect.com/help/nonparametric_methods/loess.htm
- QUOTE: … It is called local regression because the fitting at say point x is weighted toward the data nearest to x. The distance from x that is considered near to it is controlled by the span setting, α.When α is less than 1 it represents the proportion of the data that is considered to be neighbouring x, and the weighting that is used is proportional to 1-(distance/maximum distance)^3)^3, which is known as tricubic ...