Loess

This is a pure Julia loess implementation, based on the fast kd-tree based approximation described in the original Cleveland, et al papers[1,2,3], implemented in the netlib loess C/Fortran code, and used by many, including in R's loess function.

Synopsis

Loess exports two functions: loess and predict, that train and apply the model, respectively.

using Loess

xs = 10 .* rand(100)
ys = sin.(xs) .+ 0.5 * rand(100)

model = loess(xs, ys)

us = range(extrema(xs)...; step = 0.1)
vs = predict(model, us)

using Gadfly
p = plot(x=xs, y=ys, Geom.point, Guide.xlabel("x"), Guide.ylabel("y"),
         layer(Geom.line, x=us, y=vs))
draw(SVG("loess.svg", 6inch, 3inch), p)

There's also a shortcut in Gadfly to draw these plots:

plot(x=xs, y=ys, Geom.point, Geom.smooth, Guide.xlabel("x"), Guide.ylabel("y"))

Status

Multivariate regression is not yet fully implemented, but most of the parts are already there, and wouldn't require too much additional work.

References

[1] Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American statistical association, 74(368), 829-836. DOI: 10.1080/01621459.1979.10481038

[2] Cleveland, W. S., & Devlin, S. J. (1988). Locally weighted regression: an approach to regression analysis by local fitting. Journal of the American statistical association, 83(403), 596-610. DOI: 10.1080/01621459.1988.10478639

[3] Cleveland, W. S., & Grosse, E. (1991). Computational methods for local regression. Statistics and computing, 1(1), 47-62. DOI: 10.1007/BF01890836