Core Idea

• Correlation captures linear association.
• Independence means full probabilistic non-influence.

Key Point

• Independence implies zero correlation (under finite variance), but not the reverse.

Why This Matters for ML

• Feature engineering and model assumptions often confuse correlation with independence.
• Spurious correlations can mislead interpretation and degrade robustness.
• Independence assumptions appear in simplified models and require careful validation.
• This distinction helps prevent incorrect causal or predictive conclusions.