Decision Tree From Scratch

Decision Tree is the most powerful and popular tool for classification and prediction. A Decision tree is a flowchart like a tree structure, wherein each internal node denotes a test on an attribute, each branch represents an outcome of the test, and each leaf node (terminal node) holds a class label.

Source: GeeksforGeeks

For the conceptual overview of Decision Trees, refer — Decision Trees for Dummies

We shall now go through the code walkthrough for the implementation of a decision tree:

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, threshold=None, left=None, right=None, *, value=None):
        self.feature = feature
        self.threshold = threshold
        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=100, 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, best_thresh = self._best_criteria(X, y, feat_idxs)
        
        #grow the children that result from the split
        left_idxs, right_idxs = self._split(X[:, best_feat], best_thresh)
        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, best_thresh, left, right)

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

                if gain > best_gain:
                    best_gain = gain
                    split_idx = feat_idx
                    split_thresh = threshold

        return split_idx, split_thresh

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

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

        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, split_thresh):
        left_idxs = np.argwhere(X_column <= split_thresh).flatten()
        right_idxs = np.argwhere(X_column > split_thresh).flatten()
        return left_idxs, right_idxs

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

        if x[node.feature] <= node.threshold:
            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]
        return most_common

from sklearn import datasets
from sklearn.model_selection import train_test_split

def accuracy(y_true, y_pred):   
    accuracy = np.sum(y_true == y_pred)/len(y_true)   
    return accuracy

data = datasets.load_breast_cancer()

X = data.data
y = data.target

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.20, random_state=123)

clf = DecisionTree(max_depth = 10)
clf.fit(X_train, y_train)

y_pred1 = clf.predict(X_train)
acc1 = accuracy(y_train, y_pred1)
print("Training Accuracy: ", acc1)

Out:
Training Accuracy: 1.0

y_pred2 = clf.predict(X_test) 
acc2 = accuracy(y_test, y_pred)
print("Testing Accuracy: ", acc2)

Out:
Testing Accuracy: 0.9649122807017544

For complete implementation code:

tanvipenumudy/Winter-Internship-Internity

To contact, or for further queries, feel free to drop a mail at — [email protected]

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