Explain the bias–variance trade off.

Bias–Variance Trade off

The bias–variance trade off is a key concept in machine learning that explains the balance between underfitting and overfitting.

• Bias → Error caused by a model being too simple.
• High bias → Underfitting
• Example: Using a straight line to model a complex pattern.
• **Variance → Error caused by a model being too sensitive to training data**.
• High variance → Overfitting
• Example: A very complex model that memorizes training data.

Var(X)=E(X2)−[E(X)]2

Var(X)=(1.4)2=1.96Var(X)=(\text{1.4})²=\text{1.96}Var(X)=(1.4)2=1.96

σ\sigmaσ

σ\sigmaσ

μ-σ+σVar(X) ≈ 1.96

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Trade off

Model Bias Variance Result Too Simple High Low Underfitting Balanced. Medium Medium **Good Generalization **Too Complex Low High Overfitting.

Key idea: 👉 The goal is to find the optimal balance between bias and variance so the model performs well on both training and unseen data.