Decision Tree Optimizer

Discrete Math · Axiom Academy

REAL WORLD Decision Tree Optimizer Build optimal decision trees for medical diagnosis using information theory. Minimize questions while maximizing accuracy. The Medical Diagnosis Challenge Imagine you're a doctor seeing a patient with general symptoms. You need to diagnose their condition, but each test or question takes time and resources. How do you ask the fewest questions while still reaching an accurate diagnosis? A patient presents with general fatigue. Possible conditions: Thyroid disorder (25% probability) Sleep disorder (25% probability) Vitamin deficiency (20% probability) You could ask questions randomly, but that's inefficient. Instead, we'll use information theory to build an optimal decision tree that asks the most informative questions first. The key concept is entropy — a measure of uncertainty. The higher the entropy, the more uncertain we are. Our goal is to reduce entropy as quickly as possible by asking questions that give us the most information. Key Insight: The best question to ask is the one that reduces entropy the most. This is called information gain . Which Question Should We Ask First? Let's compare three possible questions and calculate their information gain : "Do you have pale skin?" has the highest information gain because it helps distinguish anemia from other conditions most effectively. Discovery Question: Why does asking about pale skin provide more information than asking about snoring? Building the Optimal Decision Tree

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