在 rpart 中使用 minsplit 和不等权重

Question

当权重不均匀时，如何将权重合并到rpart 的minsplit 标准中？ 我找不到让minsplit 阈值考虑权重的方法，当权重不均匀时，它就会成为一个问题，如下例所示。 我目前的解决方法是将数据扩展为每行都是观察的数据，但这在时间和内存上似乎都是浪费的（而且我怀疑我是否可以将需要使用的真实数据集以扩展形式保存在内存中） ，因此 - 寻求帮助。 在此先感谢您的帮助， -萨尔

以下代码显示了问题所在；前 3 棵树是相同的，但以下两棵树（权重不均匀）结果不同：

## playing with rpart weights
require(rpart)
dev.new()
par(mfrow=c(2,3), xpd=NA) 
data(kyphosis)

fitOriginal <- rpart(Kyphosis ~ Age + Number + Start, data=kyphosis, control=rpart.control(minsplit=15))
plot(fitOriginal)
text(fitOriginal, use.n=TRUE)

# this dataset is the original data repeated 3 times
kyphosisRepeated <- rbind(kyphosis, kyphosis, kyphosis)
fitRepeated <- rpart(Kyphosis ~ Age + Number + Start, data=kyphosisRepeated, control=rpart.control(minsplit=45))
plot(fitRepeated)
text(fitRepeated, use.n=TRUE)

# instead of repeating, use weights
kyphosisWeighted <- kyphosis
kyphosisWeighted$myWeights <- 3
fitWeighted <- rpart(Kyphosis ~ Age + Number + Start, data=kyphosisWeighted, weights=myWeights, 
    control=rpart.control(minsplit=15))        ## minsplit has to be adjusted for weights...
plot(fitWeighted)
text(fitWeighted, use.n=TRUE)

# uneven weights don't works the same way
kyphosisUnevenWeights <- rbind(kyphosis, kyphosis)
kyphosisUnevenWeights$myWeights <- c(rep(1,length.out=nrow(kyphosis)), rep(2,length.out=nrow(kyphosis)))

fitUneven15 <- rpart(Kyphosis ~ Age + Number + Start, data=kyphosisUnevenWeights, weights=myWeights, 
    control=rpart.control(minsplit=15))
plot(fitUneven15)
text(fitUneven15, use.n=TRUE)

fitUneven45 <- rpart(Kyphosis ~ Age + Number + Start, data=kyphosisUnevenWeights, weights=myWeights, 
    control=rpart.control(minsplit=45))
plot(fitUneven45)
text(fitUneven45, use.n=TRUE)

## 30 works, but seems like a special case 
fitUneven30 <- rpart(Kyphosis ~ Age + Number + Start, data=kyphosisUnevenWeights, weights=myWeights, 
    control=rpart.control(minsplit=30))
plot(fitUneven30)
text(fitUneven30, use.n=TRUE)

Answer 1

这里没有问题。如果您使用的数据集是原始数据集的两倍，然后要求 minsplit 是原始 minsplit 的 3 倍，那么您当然会长出一棵较短的树（假设权重之间的相关性保持不变。）请参阅这些修改后的示例，这些示例表明，如果您保持权重相关性相同，并且 minsplit/n 的比率也相同，您将种植相同的树。

## playing with rpart weights
require(rpart)
dev.new()
par(mfrow=c(2,2), xpd=NA) 
data(kyphosis)

# this dataset is the original data repeated 2 times############################################################
# without weights
kyphosisRepeated <- rbind(kyphosis, kyphosis)
fitRepeated <- rpart(Kyphosis ~ Age + Number + Start, data=kyphosisRepeated, control=rpart.control(minsplit=30))
plot(fitRepeated)
text(fitRepeated, use.n=TRUE)

# with weights
kyphosisUnevenWeights <- rbind(kyphosis, kyphosis)
kyphosisUnevenWeights$myWeights <- c(rep(1,length.out=nrow(kyphosis)), rep(2,length.out=nrow(kyphosis)))

fitUneven30 <- rpart(Kyphosis ~ Age + Number + Start, data=kyphosisUnevenWeights, weights=myWeights, 
                     control=rpart.control(minsplit=30))
plot(fitUneven30)
text(fitUneven30, use.n=TRUE)
################################################################################################################

# this dataset is the original data repeated 3 times
# without weights
kyphosisRepeated <- rbind(kyphosis, kyphosis, kyphosis)
fitRepeated <- rpart(Kyphosis ~ Age + Number + Start, data=kyphosisRepeated, control=rpart.control(minsplit=45))
plot(fitRepeated)
text(fitRepeated, use.n=TRUE)

# with weights
kyphosisUnevenWeights <- rbind(kyphosis, kyphosis, kyphosis)
kyphosisUnevenWeights$myWeights <- c(rep(1,length.out=nrow(kyphosis)), rep(2,length.out=nrow(kyphosis)), rep(3,length.out=nrow(kyphosis)))

fitUneven45 <- rpart(Kyphosis ~ Age + Number + Start, data=kyphosisUnevenWeights, weights=myWeights, 
                     control=rpart.control(minsplit=45))
plot(fitUneven45)
text(fitUneven45, use.n=TRUE)

有关RPart 的更多详细信息，请参阅this blog post。