Regression Tree

data("Boston", package = "MASS")
# set the p-value of the permutation test to 0.01
htt_boston <- HTT(medv ~ . , data = Boston, controls = htt_control(pt = 0.01))
htt_boston

#      Hypothesis Testing Tree 
# 
# node, split, n, pvalue
# * denotes terminal node
# 
# [1] root   (n = 506, pvalue = 0)
# |  [2] rm<=7.437   (n = 476, pvalue = 0)
# |  |  [4] lstat<=15   (n = 314, pvalue = 0)
# |  |  |  [6] rm<=6.797   (n = 256, pvalue = 0)
# |  |  |  |  [8] lstat<=4.615   (n = 10) *
# |  |  |  |  [9] lstat>4.615   (n = 246, pvalue = 0)
# |  |  |  |  |  [12] rm<=6.543   (n = 212, pvalue = 0)
# |  |  |  |  |  |  [14] lstat<=7.57   (n = 42) *
# |  |  |  |  |  |  [15] lstat>7.57   (n = 170) *
# |  |  |  |  |  [13] rm>6.543   (n = 34) *
# |  |  |  [7] rm>6.797   (n = 58) *
# |  |  [5] lstat>15   (n = 162, pvalue = 0)
# |  |  |  [10] crim<=0.65402   (n = 46) *
# |  |  |  [11] crim>0.65402   (n = 116, pvalue = 0)
# |  |  |  |  [16] crim<=11.36915   (n = 77) *
# |  |  |  |  [17] crim>11.36915   (n = 39) *
# |  [3] rm>7.437   (n = 30) *

# print the split information
htt_boston$frame

#    node parent leftChild rightChild  statistic pval    split     var isleaf   n
# 1     1      0         2          3 2258.92680 0.00    7.437      rm      0 506
# 2     2      1         4          5 1126.14057 0.00       15   lstat      0 476
# 3     3      1        NA         NA   54.73540   NA   <leaf> ptratio      1  30
# 4     4      2         6          7  750.08329 0.00    6.797      rm      0 314
# 5     5      2        10         11  201.23810 0.00  0.65402    crim      0 162
# 6     6      4         8          9  284.52923 0.00    4.615   lstat      0 256
# 7     7      4        NA         NA   54.33706   NA   <leaf>   lstat      1  58
# 8     8      6        NA         NA    0.00000   NA   <leaf>    <NA>      1  10
# 9     9      6        12         13  188.93990 0.00    6.543      rm      0 246
# 10   10      5        NA         NA   73.70296   NA   <leaf>     dis      1  46
# 11   11      5        16         17  115.47482 0.00 11.36915    crim      0 116
# 12   12      9        14         15  126.15810 0.00     7.57   lstat      0 212
# 13   13      9        NA         NA   20.83679   NA   <leaf>     nox      1  34
# 14   14     12        NA         NA   12.63760   NA   <leaf>     dis      1  42
# 15   15     12        NA         NA   66.02809   NA   <leaf>    crim      1 170
# 16   16     11        NA         NA   32.28858   NA   <leaf>   lstat      1  77
# 17   17     11        NA         NA   76.00906 0.02   <leaf>     nox      1  39
#        yval
# 1  22.53281
# 2  21.11071
# 3  45.09667
# 4  24.45924
# 5  14.62037
# 6  22.73242
# 7  32.08103
# 8  33.13000
# 9  22.30976
# 10 18.32826
# 11 13.15000
# 12 21.68821
# 13 26.18529
# 14 23.95000
# 15 21.12941
# 16 14.35195
# 17 10.77692

# Visualize HTT
plot(htt_boston)

Classification Tree

htt_iris <- HTT(Species ~., data = iris, controls = htt_control(pt = 0.01))
plot(htt_iris, layout = "tree")

# prediction 
table(predict(htt_iris), iris[, 5])

#             
#              setosa versicolor virginica
#   setosa         50          0         0
#   versicolor      0         49         5
#   virginica       0          1        45

Multivariate regression Tree

data("ENB")
set.seed(1)
idx = sample(1:nrow(ENB), floor(nrow(ENB)*0.8))
train = ENB[idx, ]
test = ENB[-idx, ]
htt_enb = HTT(cbind(Y1, Y2) ~ . , data = train, controls = htt_control(pt = 0.05, R = 99))
# prediction
pred = predict(htt_enb, newdata = test)
test_y = test[, 9:10]
# MAE
colMeans(abs(pred - test_y))

#        Y1        Y2 
# 0.4808483 1.2228675

# MSE
colMeans(abs(pred - test_y)^2)

#       Y1       Y2 
# 1.039948 3.594125