Statistics - Splines

Data System Architecture

About

A spline is a piecewise polynomial model:

Characteristics

Continuity

Splines have the “maximum” amount of continuity over all knots function.




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Third Degree Polynomial
Data Mining - (Global) Polynomial Regression (Degree)

polynomials regression Although polynomials are easy to think of, splines are much better behaved and more local. With polynomial regression, you create new variables that are just transformations...
Step Function Linear Regression
Data Mining - Step Function (piecewise constants)

Step functions, are another way of fitting non-linearities. (especially popular in epidemiology and biostatistics) Continuous variable are cut into discrete sub-ranges and fit a constant model in...
Card Puncher Data Processing
R - Spline

Fitting splines in R is easy: bs(x, ...) for any degree splines (one: linear spline, three: cubic spline and ns(x, ...) for natural cubic splines, in package splines.
Linear Spline
Statistics - (Linear spline|Piecewise linear function)

A linear spline, or piecewise linear function has a degree zero and is: linear in the left and the right. forced to be continuous at the knot. Just like the global polynomials and the piecewise...
Piecewise Polynomial Cubic Spline
Statistics - Cubic spline

Cubic splines is a step cubic piecewise polynomial in the left and the right and continuous at the knot. There's the following constraints: The first derivatives continues at the knot, and the...
Natural Cubic Spline
Statistics - Natural (Cubic) Spline

A natural cubic spline is a cubic spline where two extra constraints have been added at the boundaries (on each end). The goal of this constraints is to avoid as for global cubic polynomial that the tail...
Thomas Bayes
Statistics - Non-linear (effect|function|model)

Non-linear effect The truth is almost never linear but often the linearity assumption is good enough. (Linearity is an approximation) When its not (increasing in complexity): polynomials, step functions,...
Piecewise Cubic Polynomial Non Continu
Statistics - Piecewise polynomials

Piecewise polynomials generalize the idea of piecewise constants. The idea try to get rid of the global polynomial because it's global and not local. Instead of having asingle polynomial over the whole...
Smoothing Spline Df
Statistics - Smoothing (cubic) spline

A smoothing spline is a way of fitting splines without having to worry knots. They are a little bit more challenging mathematically as others splines and approaches the problem from a completely different...



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