使用rpart（R包）对观测结果对决策树预测的影响

Question

I'm very new to machine learning so I apologize if the answer to this is very obvious.

I'm using a decision tree, using the rpart package, to attempt to predict when a structure fire may result in a fatality using a variety of variables related to that structure fire such as what was the cause, the extent of damage etc.

The chance of a fatality resulting from structure fire is about 1 in 100.

In short I have about 154,000 observations in my training set. I have noticed that when I use the full training set, that the complexity parameter cp has to be reduced all the way down to .0003 .

> rpart(Fatality~.,data=train_val,method="class", control=rpart.control(minsplit=50,minbucket = 1, cp=0.00035))
n= 154181 

node), split, n, loss, yval, (yprob)
      * denotes terminal node

  1) root 154181 1881 0 (0.987800053 0.012199947)  
    2) losscat=Minor_Loss,Med_Loss 105538  567 0 (0.994627528 0.005372472) *
    3) losscat=Major_Loss,Total_Loss 48643 1314 0 (0.972986863 0.027013137)  
      6) HUM_FAC_1=3,6,N, 46102 1070 0 (0.976790595 0.023209405) *
      7) HUM_FAC_1=1,2,4,5,7 2541  244 0 (0.903974813 0.096025187)  
       14) AREA_ORIG=21,24,26,47,72,74,75,76,Other 1846  126 0 (0.931744312 0.068255688)  
         28) CAUSE_CODE=1,2,5,6,7,8,9,10,12,14,15 1105   45 0 (0.959276018 0.040723982) *
         29) CAUSE_CODE=3,4,11,13,16 741   81 0 (0.890688259 0.109311741)  
           58) FIRST_IGN=10,12,15,17,18,Other,UU 690   68 0 (0.901449275 0.098550725) *
           59) FIRST_IGN=00,21,76,81 51   13 0 (0.745098039 0.254901961)  
            118) INC_TYPE=111,121 48   10 0 (0.791666667 0.208333333) *
            119) INC_TYPE=112,120 3    0 1 (0.000000000 1.000000000) *
       15) AREA_ORIG=14,UU 695  118 0 (0.830215827 0.169784173)  
         30) CAUSE_CODE=1,2,4,7,8,10,11,12,13,14,15,16 607   86 0 (0.858319605 0.141680395) *
         31) CAUSE_CODE=3,5,6,9 88   32 0 (0.636363636 0.363636364)  
           62) HUM_FAC_1=1,2 77   24 0 (0.688311688 0.311688312) *
           63) HUM_FAC_1=4,5,7 11    3 1 (0.272727273 0.727272727) *

However, when I just grab the first 10,000 observations (no meaningful order) I can now run with a cp of .01

> rpart(Fatality~., data = test, method = "class", 
+       control=rpart.control(minsplit=10,minbucket = 1, cp=0.01))
n= 10000 

node), split, n, loss, yval, (yprob)
      * denotes terminal node

  1) root 10000 112 0 (0.988800000 0.011200000)  
    2) losscat=Minor_Loss,Med_Loss 6889  26 0 (0.996225867 0.003774133) *
    3) losscat=Major_Loss,Total_Loss 3111  86 0 (0.972356156 0.027643844)  
      6) HUM_FAC_1=3,7,N 2860  66 0 (0.976923077 0.023076923) *
      7) HUM_FAC_1=1,2,4,5,6 251  20 0 (0.920318725 0.079681275)  
       14) CAUSE_CODE=1,3,4,6,7,8,9,10,11,14,15 146   3 0 (0.979452055 0.020547945) *
       15) CAUSE_CODE=5,13,16 105  17 0 (0.838095238 0.161904762)  
         30) weekday=Friday,Monday,Saturday,Tuesday,Wednesday 73   6 0 (0.917808219 0.082191781) *
         31) weekday=Sunday,Thursday 32  11 0 (0.656250000 0.343750000)  
           62) AREA_ORIG=21,26,47,Other 17   2 0 (0.882352941 0.117647059) *
           63) AREA_ORIG=14,24,UU 15   6 1 (0.400000000 0.600000000)  
            126) month=2,6,7,9 7   1 0 (0.857142857 0.142857143) *
            127) month=1,4,10,12 8   0 1 (0.000000000 1.000000000) *

1. Why is it that a greater number of observations is resulting in me having to reduce complexity? Intuitively I would think it should be opposite.
2. Is having to reduce cp to .003 "bad"?
3. Generally, is there any other advice for improving the effectiveness of a decision tree, especially when predicting something that has such low probability in the first place?

Answer 1

1. cp , from what I read, is a parameter that is used to decide when to stop adding more leaves to the tree (for a node to be considered for another split, the improvement of the relative error by allowing a new split must by more than that cp threshold). Thus, the lower the number, the more leaves it can add. More observations implies that there is an opportunity to lower the threshold, I'm not sure I understand that you "have to" reduce cp ... but I could be wrong. If this is a very rare event and your data doesn't lend itself to showing significant improvement in the early stages of the model, it may require that you "increase the sensitivity" by lowering the cp ... but you probably know your data better than me.
2. If you're modeling a rare event, no. If it's not a rare event, the lower your cp the more likely you are to overfit to the bias of your sample. I don't think that minbucket=1 ever leads to a model that is interpretable, either... for similar reasons.
3. Decision Trees, to me, don't make very much sense beyond 3-4 levels unless you really believe that these hard cuts truly create criteria that justify a final "bucket"/node or a prediction (eg if I wanted to bucket you into something financial like a loan or insurance product that fits your risk profile, and my actuaries made hard cuts to split the prospects). After you've split your data 3-4 times, producing a minimum of 8-16 nodes at the bottom of your tree, you've essentially built a model that could be thought of as 3rd or 4th order interactions of independent categorical variables. If you put 20 statisticians (not econo-missed's) in a room and ask them about the number of times they've seen significant 3rd or 4th order interactions in a model, they'd probably scratch their heads. Have you tried any other methods? Or started with dimension reduction? More importantly, what inferences are you trying to make about the data?