Calculate the ALC or predictive entropy statistic at the X locations, or ALC at new XX predictive locations
Description
Uses analytic integration (at the leaves) to calculate the (regression) ALC statistic, or calculates the predictive (class) entropy at the input (X) locations; or calculate ALC at new predictive locations either analytically or numerically
Usage
1 2 3 4 5 6 7 8 
Arguments
object 
a 
rect 
for 
categ 
A vector of logicals of length 
approx 
a scalar logical that, when 
XX 
a design 
Xref 

probs 
weights for the reference locations to be used in a Monte Carlo approximation; usually these weights are class probabilities for response surfaces under constraints 
verb 
a positive scalar integer indicating how many predictive locations
(iterations) after which a progress statement should be
printed to the console; a (default) value of 
Details
This function is most useful for selecting object$X
locations to remove from the analysis, perhaps in an online inference
setting. See retire.dynaTree
for more details. The
output is the same as using predict.dynaTree
using XX = object$X
, alc = "rect"
, and Xref =
rect
entropyX
only apples to classification models
(object$model != "class"
), and alcX
applies (only)
to the other, regression, models
The alc
function is more generic and allows ALC calculations
at new, predictive, XX
locations. This functionality used
to be part of the predict.dynaTree
function, but were
separated out for computational reasons. The previous version was
Monte Carlobased (using Xref
) whereas the new version
also allows analytic calculation (now the default, via rect
)
Value
The entire object
is returned with a new entry called
alcX
containing a vector of length nrow(X)
with
the ALC values, or entropyX
containing the entropy values,
or alc
if general ALC calculations at new XX
locations
Author(s)
Robert B. Gramacy rbgramacy@chicagobooth.edu,
Matt Taddy taddy@chicagobooth.edu, and
Christoforos Anagnostopoulos christoforos.anagnostopoulos06@imperial.ac.uk
References
Taddy, M.A., Gramacy, R.B., and Polson, N. (2011). “Dynamic trees for learning and design” Journal of the American Statistical Association, 106(493), pp. 109123; arXiv:0912.1586
Anagnostopoulos, C., Gramacy. R.B. (2013) “InformationTheoretic Data Discarding for Dynamic Trees on Data Streams.” Entropy, 15(12), 55105535; arXiv:1201.5568
http://bobby.gramacy.com/r_packages/dynaTree/
See Also
dynaTree
, predict.dynaTree
, and
retire.dynaTree
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33  ## fit the model to the parabola data
n < 100
Xp < runif(n,3,3)
Yp < Xp + Xp^2 + rnorm(n, 0, .2)
rect < c(3,3)
out < dynaTree(Xp, Yp, model="linear", icept="augmented")
## calculate the alcX
out < alcX(out, rect=rect)
## to compare to analytic
out < alc(out, XX=out$X[,1], rect=rect)
## plot comparison between alcX and predictALC
plot(out$X[,1], out$alcX)
o < order(out$X[,2])
lines(out$X[o,1], out$alc[o], col=2, lty=2)
## now compare to approximate analytic
## (which writes over out$alc)
out < alc(out, XX=out$X[,1], rect=rect, approx=TRUE)
lines(out$X[o,1], out$alc[o], col=3, lty=3)
## clean up
deletecloud(out)
## similarly with entropyX for classification models
## see demo("design") for more iterations and
## design under other active learning heuristics
## like ALC, and EI for optimization; also see
## demo("online") for an online learning example where
## ALC is used for retirement
