nignatiadis / SmoothingSplines.jl

Cubic smoothing splines in Julia.

SmoothingSplines

A Julia package for nonparametric regression with Cubic Smoothing Splines. The initial aim is to provide the same functionality as R's smooth.spline function and competitive computational performance. The implementation however is completely independent of the R function and based on the algorithm by Reinsch [1], as described in Chapter 2 of [2].

using SmoothingSplines
using RDatasets
using Gadfly

cars = dataset("datasets","cars")
X = map(Float64,convert(Array,cars[!,:Speed]))
Y = map(Float64,convert(Array,cars[!,:Dist]))

spl = fit(SmoothingSpline, X, Y, 250.0) # λ=250.0
Ypred = predict(spl) # fitted vector
plot(layer(x=X, y=Y, Geom.point),
	layer(x=X, y=Ypred, Geom.line, 	Theme(default_color=colorant"red")))

predict(spl, 20.0) #prediction at arbitrary point

TODO

• Better docs
• conversion between regularization parameter λ and degrees of freedom
• automatic selection of λ (LOOCV, GCV)
• subsampling of design grid for higher efficiency

References

[1] Reinsch, Christian H. "Smoothing by spline functions." Numerische mathematik 10.3 (1967): 177-183.

[2] Green, Peter J., and Bernard W. Silverman. Nonparametric regression and generalized linear models: a roughness penalty approach. CRC Press, 1993.