ML Interview Q Series: How would you describe the procedure of using binary recursive splitting when creating a decision tree?
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Comprehensive Explanation
Binary recursive partitioning in decision trees involves progressively splitting the dataset into subsets (two at each step) based on feature values, aiming to isolate examples that share similar target labels within the same leaf. The process starts from the entire dataset and continues until a stopping criterion is reached. Each split is chosen to best reduce impurity in the target variable.
In each node, a feature is selected to partition the data into two child nodes that yield the most homogeneous subgroups with respect to the target. This choice is often driven by a metric that measures how “pure” each node is. For classification, Gini index and entropy are widely used to quantify impurity. For regression, variance reduction is a common strategy.
Starting with the Entire Training Set
The algorithm begins with a node containing all data points. This node captures the entire input space as one large group. No partition has yet been made, so the impurity in the node is simply the impurity of the full dataset.
Selecting a Splitting Feature and Threshold
The tree-building process searches across available features and potential thresholds (if they are continuous features) or distinct feature categories (if they are categorical). The goal is to find the split that yields child nodes with the lowest average impurity. For classification, two of the most popular measures of impurity are Gini index and entropy.
Here K is the number of classes, and p_k is the fraction of samples belonging to class k in that node.
Again, K is the number of classes, and p_k is the proportion of items in class k within the node.
Both Gini index and entropy quantify how mixed a node is: if all instances belong to a single class, their impurity becomes minimal (0). Splitting aims to lower impurity even further.
Splitting into Two Child Nodes
After evaluating every feature and threshold combination, the algorithm chooses the one that yields the largest impurity decrease in the resulting child nodes. It then splits the node into two branches based on that chosen criterion. For a continuous feature, this often becomes “feature value <= threshold” for one branch and “feature value > threshold” for the other. For categorical features, it might become “feature is in subset of categories” for one branch and “feature is in the remaining categories” for the other branch.
Recursively Continuing the Process
Each of the newly created child nodes now becomes a parent node for the next step. Within each child node, the same procedure is repeated: pick the best feature to split that node, split again, and so on. This recursive procedure continues until the stopping criteria are met, such as reaching a maximum depth, when further splitting does not reduce impurity sufficiently, or when a node has too few samples left.
Stopping Criteria and Leaf Creation
Eventually, the recursion halts. Situations that typically lead to a stop are:
A node has too few samples.
Further splitting does not significantly improve purity.
A preset maximum depth has been reached.
All samples in a node belong to a single class.
When a node no longer splits, it is designated a leaf. In classification, a leaf might predict the majority class within that node. In regression, a leaf might predict the mean value of the target variable within that node.
Common Follow-Up Questions
How do you decide which attribute is the best for a split?
Decision trees typically measure the decrease in impurity after a split. For classification, this can be the Gini index reduction or the information gain derived from entropy reduction. You calculate these impurity metrics for the parent node and then for each proposed split in the child nodes. The attribute that yields the greatest impurity reduction is chosen.
Why choose Gini instead of entropy, or vice versa?
Both Gini index and entropy measure node impurity. They often produce similar results in practice. Gini tends to be computationally simpler, since it does not involve logarithmic operations. Entropy can be more sensitive to changes in small class probabilities. The choice is sometimes a matter of preference or empirical validation on a given dataset.
How do you handle continuous features?
For each continuous feature, you typically sort the unique values and consider splitting points between adjacent sorted values. For every potential threshold t, you compute how well that threshold partitions the data. You then pick the threshold that yields the greatest drop in impurity.
How are missing values handled?
Methods vary. A common approach is to omit records with missing values for that feature when evaluating the split, though that can reduce the effective sample size. Another strategy is to use surrogate splits, where the tree attempts to find another correlated feature to make a split for missing values. Imputing missing values before the tree-building process is also a possibility.
What are the typical stopping criteria to prevent overfitting?
Overfitting can occur if the tree grows too deep or too specific to the training data. Techniques include restricting the maximum depth, requiring a minimum number of samples to further split a node, or imposing a threshold on the maximum permitted impurity reduction at each split. Another method is post-pruning, where the tree is fully grown and then pruned back by removing branches that contribute little improvement.
How do you choose between pre-pruning and post-pruning?
Pre-pruning (early stopping) halts the tree from growing once a predefined condition is met, such as a maximum depth limit or a minimum number of records in a node. Post-pruning grows the tree entirely, then prunes it after evaluating performance on a validation set or using statistical measures like cost complexity pruning. Pre-pruning can be more efficient, but post-pruning often yields a better-performing final model, since it considers a fully expanded tree before deciding which branches to remove.
Why might binary partitioning be preferable?
Binary splits simplify the analysis and interpretability of the decision tree. When features are numerical or continuous, deciding “<= threshold” vs. “> threshold” is often straightforward and easier to visualize. This approach also speeds up the splitting process compared to multi-way splits, as you only have two child nodes at each split to evaluate further.
How do you handle high-cardinality features?
For features that have a large number of categories, splitting them directly might lead to complex branching. You can group categories into subsets before performing a binary partition. Alternatively, applying techniques like target encoding or dimensionality reduction on categorical variables can help reduce the branching complexity.
Are there limitations to recursive partitioning?
Recursive partitioning can overfit if left unchecked, leading to very deep trees that do not generalize well. Decision trees can be sensitive to slight changes in the data, which might result in drastically different splits (high variance). Pruning techniques, minimum node size, and ensemble methods (like Random Forests or Gradient Boosted Trees) can mitigate these issues and improve generalization.
Can you combine decision trees to improve performance?
Yes. Ensemble methods such as Random Forests and Gradient Boosted Trees aggregate multiple decision trees to reduce variance and often improve accuracy. Random Forests train multiple trees on bootstrap samples with random feature subsets at each split, while Gradient Boosted Trees add new weak learners (trees) sequentially to correct the errors of previous ones.
Why not keep splitting until all leaves are pure?
Allowing trees to fully grow can cause overfitting, since the tree starts memorizing the noise in the training data. While it might produce perfect predictions on the training dataset, it often fails on new data. Limiting tree size or using pruning is essential for good generalization.