73 lines
2.4 KiB
R
73 lines
2.4 KiB
R
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#
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# A hard-core test of losses and priors
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# Simple data set where I know what the answers must be
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#
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library(rpart)
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aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...)
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dummy <- c(3,1,4,1,5,9,2,6,5,3,5,8,9,7,9)/5
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pdata <- data.frame(y=factor(rep(1:3, 5)),
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x1 = 1:15,
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x2 = c(1:6, 1:6, 1:3),
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x3 = (rep(1:3, 5) + dummy)*10)
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pdata$x3[c(1,5,10)] <- NA
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pdata$y[15] <- 1 # make things unbalanced
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set.seed(10)
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pfit <- rpart(y ~ x1 + x2 + x3, pdata,
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cp=0, xval=0, minsplit=5, maxdepth=1,
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parms=list(prior=c(.2, .3, .5),
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loss =matrix(c(0,2,2,2,0,6,1,1,0), 3,3,byrow=T)))
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#
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# See section 12.1 of the report for these numbers
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#
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ntot <- c(6,5,4)
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phat <- c(6,5,4)/15 # observed class probabilities
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prior <- c(.2, .3, .5) # priors
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aprior <- c(4,12,5)/21 # altered priors
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lmat <- matrix(c(0,1,2, 2,0,1, 2,6,0), ncol=3) #loss matrix
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gini <- function(p) 1-sum(p^2)
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loss <- function(n, class) sum(n * lmat[,class])
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phat <- function(n, ntot=c(6,5,4), prior=c(.2, .3, .5)) {
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n*prior/ntot
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}
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# Are the losses correct?
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# Class counts for the two children are (4,4,0) and (2,1,4), when
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# using surrogates
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aeq(pfit$frame$dev/15, c(loss(prior,2), loss(phat(c(4,4,0)),2),
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loss(phat(c(2,1,4)),3)))
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# Node probabilities?
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aeq(pfit$frame$yval2[,8] ,
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c(1, sum(phat(c(4,4,0))), sum(phat(c(2,1,4)))))
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aeq(pfit$frame$yval2[,5:7] , rbind(prior,
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phat(c(4,4,0))/ sum(phat(c(4,4,0))),
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phat(c(2,1,4))/ sum(phat(c(2,1,4)))))
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# Now the node and class probs, under altered priors
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phat2 <- function(n, ntot=c(6,5,4), prior=aprior) {
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n*prior/ntot
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}
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# Use these to create the gini losses, base data, and for the best
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# splits on variables 1, 2, 3
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gfun <- function(n) { #The gini loss for a node, given the counts
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temp <- phat2(n)
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sum(temp) * gini(temp/sum(temp))
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}
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# These are in order x3, x2, x1 (best split to worst)
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# Note that for x3, missing values cause the "parent" to be viewed as
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# having 12 obs instead of 15.
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# Each line is gini(parent) - gini(children)
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aeq(pfit$splits[1:3, 3],
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15* c(gfun(c(4,4,4)) - (gfun(c(3,4,0)) + gfun(c(1,0,4))),
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gfun(c(6,5,4)) - (gfun(c(6,5,2)) + gfun(c(0,0,2))),
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gfun(c(6,5,4)) - (gfun(c(4,4,4)) + gfun(c(2,1,0)))))
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