Calculate the ALC or predictive entropy statistic at the X locations, or ALC at new XX predictive locations
Calculate the ALC or predictive entropy statistic at the X locations, or ALC at new XX predictive locations
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
## S3 method for class 'dynaTree'alcX(object, rect =NULL, categ =NULL, approx =FALSE, verb =0)## S3 method for class 'dynaTree'entropyX(object, verb =0)## S3 method for class 'dynaTree'alc(object, XX, rect =NULL, categ =NULL, approx =FALSE, Xref =NULL, probs =NULL, verb =0)
Arguments
object: a "dynaTree"-class object built by dynaTree
rect: for alcX, a matrix with two columns and ncol(object$X) rows describing the bounding rectangle for the ALC integration; the default that is used when rect = NULL is the bounding rectangle obtained by applying range to each column of object$X (taking care to remove the first/intercept column of object$X if icept = "augmented"; only applies to regression models (object$model != "class"); for alc, rect
must be a scalar logical: see Xref below
categ: A vector of logicals of length ncol(object$X) indicating which, if any, dimensions of the input space should be treated as categorical; this input is used to help with the analytic integrals from a rect-based calculation, which means it should not specified along with Xref; the default categ
argument is NULL meaning that the categorical inputs are derived from object$X in a sensible way
approx: a scalar logical that, when TRUE, causes the number of data points in a node/leaf to be used as a proxy for its area in the analytic calculations
XX: a design matrix of predictive locations (where ncol(XX) == ncol(X); only used by alc
Xref: Xref input can be optionally used to specify a grid of reference locations for the numerical ALC calculation - a matrix with ncol(X) columns. If NULL, the default, then the XX is taken as both candidate and reference locations.
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 verb = 0 is quiet
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$model != "class"), and alcX applies (only) to the other, regression, models
The alc function is more generic and allows ALC calculations at new, predictive, XX locations. This functionality used to be part of the predict.dynaTree function, but were separated out for computational reasons. The previous version was Monte Carlo-based (using Xref) whereas the new version also allows analytic calculation (now the default, via rect)
Returns
The entire object is returned with a new entry called alcX containing a vector of length nrow(X) with the ALC values, or entropyX containing the entropy values, or alc if general ALC calculations at new XX locations
References
Taddy, M.A., Gramacy, R.B., and Polson, N. (2011). Dynamic trees for learning and design
Journal of the American Statistical Association, 106(493), pp. 109-123; arXiv:0912.1586
Anagnostopoulos, C., Gramacy, R.B. (2013) Information-Theoretic Data Discarding for Dynamic Trees on DataStreams. Entropy, 15(12), 5510-5535; arXiv:1201.5568
## fit the model to the parabola datan <-100Xp <- runif(n,-3,3)Yp <- Xp + Xp^2+ rnorm(n,0,.2)rect <- c(-3,3)out <- dynaTree(Xp, Yp, model="linear", icept="augmented")## calculate the alcXout <- alcX(out, rect=rect)## to compare to analytic out <- alc(out, XX=out$X[,-1], rect=rect)## plot comparison between alcX and predict-ALCplot(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 updeletecloud(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