A simple program consisting of if-else decisions (decision stumps) based on the features.

• We can create a bunch of decision stumps and define a “score” for each possible rule.
• An intuitive way of thinking about this is as classification accuracy: “if we use this rule, how many examples do we label correctly?”
• We can create a tree using greedy recursive splitting: using a sequence of stumps to fit a tree
• However, accuracy isn’t perfect. Sometimes splitting doesn’t immediately improve accuracy. We can get around this by generally selecting feature test that maximizes information gain
• Entropy of set of data samples is defined as , where is the set of classes represented in and is the empirical distribution of class in .
• Generally, select feature test that maximizes information gain:

## Tradeoffs

Advantages

• Easy to implement
• Interpretable
• Learning is fast, prediction is very fast
• Can elegantly handle a small number of missing values during training Disadvantages
• Had to find optimal set of rules
• Greedy splitting often not accurate, can require very deep trees
• Can only express ‘and’ relations, not OR

## Pseudocode for choosing decision stumps

// time complexity: O(ndk), O(nd) if k=1 (binary classifier)
decision_stump(feature matrix X, and label vector Y):
compute error: number of times y_i does not equal most common value for feature j
for each threshold t:
set y_yes to most common label of objects i satisfying rule (x_ij > t)
set y_no to most common label of objects i satisfying rule (x_ij <= t)
set y_pred[i] to be our preditions for each object i based on the rule
y_pred[i] = y_yes if satisfied, y_no otherwise
compute error e which is the number of objects where y_pred_i != y_i
store the rule (j, t, y_yes, y_no) if it has the lowest error so far
return the best decision stump based on score