Quick Start Guide: Optimal Classification Trees

In this example we will use Optimal Classification Trees (OCT) on the banknote authentication dataset. First we load in the data and split into training and test datasets:

using CSV, DataFrames
df = CSV.read("data_banknote_authentication.txt", DataFrame,
              header=[:variance, :skewness, :curtosis, :entropy, :class])

1372×5 DataFrame
  Row │ variance  skewness   curtosis   entropy   class
      │ Float64   Float64    Float64    Float64   Int64
──────┼─────────────────────────────────────────────────
    1 │  3.6216     8.6661   -2.8073    -0.44699      0
    2 │  4.5459     8.1674   -2.4586    -1.4621       0
    3 │  3.866     -2.6383    1.9242     0.10645      0
    4 │  3.4566     9.5228   -4.0112    -3.5944       0
    5 │  0.32924   -4.4552    4.5718    -0.9888       0
    6 │  4.3684     9.6718   -3.9606    -3.1625       0
    7 │  3.5912     3.0129    0.72888    0.56421      0
    8 │  2.0922    -6.81      8.4636    -0.60216      0
  ⋮   │    ⋮          ⋮          ⋮         ⋮        ⋮
 1366 │ -4.5046    -5.8126   10.8867    -0.52846      1
 1367 │ -2.41       3.7433   -0.40215   -1.2953       1
 1368 │  0.40614    1.3492   -1.4501    -0.55949      1
 1369 │ -1.3887    -4.8773    6.4774     0.34179      1
 1370 │ -3.7503   -13.4586   17.5932    -2.7771       1
 1371 │ -3.5637    -8.3827   12.393     -1.2823       1
 1372 │ -2.5419    -0.65804   2.6842     1.1952       1
                                       1357 rows omitted

X = df[:, 1:4]
y = df[:, 5]
(train_X, train_y), (test_X, test_y) = IAI.split_data(:classification, X, y,
                                                      seed=1)

Optimal Classification Trees

We will use a GridSearch to fit an OptimalTreeClassifier:

grid = IAI.GridSearch(
    IAI.OptimalTreeClassifier(
        random_seed=1,
    ),
    max_depth=1:5,
)
IAI.fit!(grid, train_X, train_y)
IAI.get_learner(grid)

We can make predictions on new data using predict:

IAI.predict(grid, test_X)

412-element Array{Int64,1}:
 0
 0
 0
 0
 0
 0
 0
 0
 0
 1
 ⋮
 1
 1
 1
 1
 1
 1
 1
 1
 1

We can evaluate the quality of the tree using score with any of the supported loss functions. For example, the misclassification on the training set:

IAI.score(grid, train_X, train_y, criterion=:misclassification)

0.9989583333333333

Or the AUC on the test set:

IAI.score(grid, test_X, test_y, criterion=:auc)

0.990956164841196

We can also plot the ROC curve on the test set:

IAI.ROCCurve(grid, test_X, test_y, positive_label=1)

Optimal Classification Trees with Hyperplanes

To use Optimal Classification Trees with hyperplane splits (OCT-H), you should set the hyperplane_config parameter:

grid = IAI.GridSearch(
    IAI.OptimalTreeClassifier(
        random_seed=1,
        max_depth=2,
        hyperplane_config=(sparsity=:all,)
    ),
)
IAI.fit!(grid, train_X, train_y)
IAI.get_learner(grid)

Now we can find the performance on the test set with hyperplanes:

IAI.score(grid, test_X, test_y, criterion=:auc)

0.9972677595628415

It seems that a very small tree with a hyperplane splits is able to model this dataset perfectly.