decision_tree_scratch.py

import numpy as np
from collections import Counter


def entropy(y):
    hist = np.bincount(y)
    ps = hist / len(y)
    return -np.sum([p * np.log2(p) for p in ps if p > 0])


class Node:

    def __init__(self, feature=None, left=None, right=None, *, value=None):
        self.feature = feature
        self.left = left
        self.right = right
        self.value = value

    def is_leaf_node(self):
        return self.value is not None


class DecisionTree:

    def __init__(self, min_samples_split=2, max_depth=5, n_feats=None):
        self.min_samples_split = min_samples_split
        self.max_depth = max_depth
        self.n_feats = n_feats
        self.root = None

    def fit(self, X, y):
        self.n_feats = X.shape[1] if not self.n_feats else min(self.n_feats, X.shape[1])
        self.root = self._grow_tree(X, y)

    def predict(self, X):
        return np.array([self._traverse_tree(x, self.root) for x in X])

    def _grow_tree(self, X, y, depth=0):
        n_samples, n_features = X.shape
        n_labels = len(np.unique(y))

        # stopping criteria
        if (depth >= self.max_depth
                or n_labels == 1
                or n_samples < self.min_samples_split):
            leaf_value = self._most_common_label(y)
            return Node(value=leaf_value)

        feat_idxs = np.random.choice(n_features, self.n_feats, replace=False)

        # greedily select the best split according to information gain
        best_feat = self._best_criteria(X, y, feat_idxs)
        
        # grow the children that result from the split
        left_idxs, right_idxs = self._split(X[:, best_feat])
        left = self._grow_tree(X[left_idxs, :], y[left_idxs], depth+1)
        right = self._grow_tree(X[right_idxs, :], y[right_idxs], depth+1)
        return Node(best_feat, left, right)

    def _best_criteria(self, X, y, feat_idxs):
        best_gain = -1
        split_idx = None
        for feat_idx in feat_idxs:
            X_column = X[:, feat_idx]
            gain = self._information_gain(y, X_column)

            if gain > best_gain:
                best_gain = gain
                split_idx = feat_idx

        return split_idx

    def _information_gain(self, y, X_column):
        # parent loss
        parent_entropy = entropy(y)

        # generate split
        left_idxs, right_idxs = self._split(X_column)

        if len(left_idxs) == 0 or len(right_idxs) == 0:
            return 0

        # compute the weighted avg. of the loss for the children
        n = len(y)
        n_l, n_r = len(left_idxs), len(right_idxs)
        e_l, e_r = entropy(y[left_idxs]), entropy(y[right_idxs])
        child_entropy = (n_l / n) * e_l + (n_r / n) * e_r

        # information gain is difference in loss before vs. after split
        ig = parent_entropy - child_entropy
        return ig

    def _split(self, X_column):
        left_idxs = np.argwhere(X_column == 0).flatten()
        right_idxs = np.argwhere(X_column == 1).flatten()
        return left_idxs, right_idxs

    def _traverse_tree(self, x, node):
        if node.is_leaf_node():
            return node.value

        if x[node.feature] == 0:
            return self._traverse_tree(x, node.left)
        return self._traverse_tree(x, node.right)

    def _most_common_label(self, y):
        counter = Counter(y)
        most_common = counter.most_common(1)[0][0]
        # most_common = dict(counter)
        return most_common