In this Machine Learning from Scratch Tutorial, we are going to implement a Decision Tree algorithm using only built-in Python modules and numpy. We will also learn about the concept and the math behind this popular ML algorithm.

Part 1 will cover the theory, and Part 2 contains the implementation.

All algorithms from this course can be found on GitHub together with example tests.

## Implementation

```
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
```