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unit 2/07_Naive_Bayes.md

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+# Naive Bayes Classifier
+
+**Naive Bayes** is a classification algorithm based on **Bayes' Theorem**.
+
+## Why "Naive"?
+It is called "Naive" because it makes a simple assumption:
+- **Assumption**: All features (predictors) are **independent** of each other.
+- **Reality**: This is rarely true in real life, but the model still works surprisingly well.
+
+## Bayes' Theorem
+It calculates the probability of an event based on prior knowledge.
+
+**Formula**:
+`P(A|B) = (P(B|A) * P(A)) / P(B)`
+
+- **P(A|B)**: **Posterior Probability** (Probability of class A given predictor B).
+- **P(B|A)**: **Likelihood** (Probability of predictor B given class A).
+- **P(A)**: **Prior Probability** (Probability of class A being true overall).
+- **P(B)**: **Evidence** (Probability of predictor B occurring).
+
+## Example: Spam Filtering
+We want to label an email as **Spam** or **Ham** (Not Spam).
+
+1. **Prior**: How common is spam overall? (e.g., 15% of emails are spam).
+2. **Likelihood**: If an email is spam, how likely is it to contain the word "Money"?
+3. **Evidence**: How common is the word "Money" in all emails?
+4. **Posterior**: Given the email has "Money", what is the probability it is Spam?
+
+We calculate this for all words and pick the class with the highest probability.