adapreg: Adaptive Regression
In diffusionMap: Diffusion Map

Description Usage Arguments Details Value References See Also Examples

View source: R/adapreg.R

Non-parametric adaptive regression method for diffusion map basis.

1 2	adapreg(D, y, mmax = min(50, length(y)), fold = NULL, nfolds = 10, nrep = 5)

`D`	n-by-n pairwise distance matrix for a data set with n points, or alternatively output from the dist() function
`y`	vector of responses to model
`mmax`	maximum model size to consider
`fold`	vector of integers of size n specifying the k-fold cross-validation allocation. Default does nfolds-fold CV by sample(1:nfolds,length(y),replace=T)
`nfolds`	number of folds to do CV. If fold is supplied, nfolds is ignored
`nrep`	number of times optimization algorithm is run (with random initializations). Higher nrep allows algorithm to avoid getting stuck in local minima

Fits an adaptive regression model leaving as free parameters both the diffusion map localness parameter, epsilon, and the size of the regression model, m. The adaptive regression model is the expansion of the response function on the first m diffusion map basis functions.

This routine searches for the optimal (epsilon,m) by minimizing the cross-validation risk (CV MSE) of the regression estimate. The function uses optimize() to search over an appropriate range of epsilon and calls the function adapreg.m() to find the optimal m for each epsilon.

Default uses 10-fold cross-validation to choose the optimal model size. User may also supply a vector of fold allocations. For instance, sample(1:10,length(y),replace=T) does 10-fold CV while 1:length(y) performs leave-one-out CV.

The returned value is a list with components

`mincvrisk`	minimum cross-validation risk for the adaptive regression model for the given epsilon
`mopt`	size of the optimal regression model. If mopt == mmax, it is advised to increase mmax.
`epsopt`	optimal value of epsilon used in diffusion map construction
`y.hat`	predictions of the response, y-hat, for the optimal model
`coeff`	coefficients of the optimal model

Richards, J. W., Freeman, P. E., Lee, A. B., and Schafer, C. M., (2009), ApJ, 691, 32

diffuse(),adapreg.m()

library(scatterplot3d)
## trig function on circle
t=seq(-pi,pi,.01)
x=cbind(cos(t),sin(t))
y = cos(3*t) + rnorm(length(t),0,.1)
tcol = topo.colors(32)
colvec = floor((y-min(y))/(max(y)-min(y))*32); colvec[colvec==0] = 1
scatterplot3d(x[,1],x[,2],y,color=tcol[colvec],pch=20,
  main="Cosine function supported on circle",angle=55,
  cex.main=2,col.axis="gray",cex.symbols=2,cex.lab=2,
  xlab=expression("x"[1]),ylab=expression("x"[2]),zlab="y")

D = as.matrix(dist(x))
# do 10-fold cross-validation to optimize (epsilon, m):
AR = adapreg(D,y, mmax=5,nfolds=2,nrep=2)
print(paste("optimal model size:",AR$mopt,"; optimal epsilon:",
  round(AR$epsopt,4),"; min. CV risk:",round(AR$mincvrisk,5)))
plot(y,AR$y.hat,ylab=expression(hat("y")),cex.lab=1.5,cex.main=1.5,
  main="Predictions")
abline(0,1,col=2,lwd=2)

[1] "Doing 2-fold cross-validation"
[1] "Finding optimal model for epsilon= 0.1034"
Performing eigendecomposition
Computing Diffusion Coordinates
Elapsed time: 0.274 seconds
[1] "Finding optimal model for epsilon= 0.1673"
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Elapsed time: 0.24 seconds
[1] "Finding optimal model for epsilon= 0.2068"
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Elapsed time: 0.142 seconds
[1] "Finding optimal model for epsilon= 0.2427"
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Elapsed time: 0.148 seconds
[1] "Finding optimal model for epsilon= 0.229"
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Elapsed time: 0.136 seconds
[1] "Finding optimal model for epsilon= 0.2506"
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Elapsed time: 0.145 seconds
[1] "Finding optimal model for epsilon= 0.2583"
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[1] "Finding optimal model for epsilon= 0.2672"
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[1] "Finding optimal model for epsilon= 0.2638"
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Elapsed time: 0.141 seconds
[1] "Finding optimal model for epsilon= 0.2686"
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Elapsed time: 0.148 seconds
[1] "Finding optimal model for epsilon= 0.2694"
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Elapsed time: 0.07 seconds
[1] "Finding optimal model for epsilon= 0.2694"
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[1] "Finding optimal model for epsilon= 0.2693"
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Elapsed time: 0.066 seconds
[1] "Finding optimal model for epsilon= 0.2694"
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Elapsed time: 0.145 seconds
[1] "Finding optimal model for epsilon= 0.0638"
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Elapsed time: 0.154 seconds
[1] "Finding optimal model for epsilon= 0.1032"
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[1] "Finding optimal model for epsilon= 0.1276"
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[1] "Finding optimal model for epsilon= 0.1542"
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[1] "Finding optimal model for epsilon= 0.1441"
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[1] "Finding optimal model for epsilon= 0.1591"
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[1] "Finding optimal model for epsilon= 0.1579"
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[1] "Finding optimal model for epsilon= 0.1568"
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[1] "Finding optimal model for epsilon= 0.1577"
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[1] "Finding optimal model for epsilon= 0.1583"
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[1] "Finding optimal model for epsilon= 0.158"
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[1] "Finding optimal model for epsilon= 0.1582"
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[1] "Finding optimal model for epsilon= 0.1582"
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[1] "Finding optimal model for epsilon= 0.1583"
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Elapsed time: 0.141 seconds
[1] "Finding optimal model for epsilon= 0.1582"
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Elapsed time: 0.065 seconds
[1] "Finding optimal model for epsilon= 0.2694"
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Elapsed time: 0.14 seconds
[1] "optimal model size: 5 ; optimal epsilon: 0.2694 ; min. CV risk: 0.01051"