Decision Paths: Explanations for Free

Intuition

A decision tree is interpretable by construction: the explanation of a prediction is the list of questions asked on the way to the leaf. "Income ≤ 30k → yes; debt > 5k → yes → reject."

Precise explanation

Represent a tree as nested dicts:

internal node: {"feature": j, "threshold": t, "left": node, "right": node} — go left if $x_j \le t$ (as in ML-21), else right;
leaf: {"value": v}. The path is the sequence of (feature, operator, threshold) conditions satisfied. This is an intrinsic explanation (the model is the explanation), unlike post-hoc methods (XA-06+). Deep trees produce long paths that are no longer easy to read — interpretability depends on size.

flowchart TD A{"income ≤ 30?"} -- yes --> B{"debt ≤ 5?"} A -- no --> L1["approve"] B -- yes --> L2["approve"] B -- no --> L3["reject"]

Worked example

x = {income 25, debt 8}: income ≤ 30 ✓ → debt ≤ 5 ✗ → "reject"; path ["income <= 30", "debt > 5"].

Common mistakes

Inconsistent <= vs < with the training convention.
Losing the right-branch condition (it should read "> t").
Mutating the tree while traversing.

Why this matters

Rule-style explanations are what many regulated domains (credit, healthcare) expect; trees are also used as global surrogates (XA-10).

References

Interpretable Machine Learning (3rd edition) — Christoph Molnar (S024)