Bias-Variance Tradeoff

Bias-Variance Tradeoff

Bias-Variance Tradeoff is a fundamental concept in machine learning that describes the balance between two sources of error that affect model performance: bias and variance.

What is Bias?

Bias refers to the error introduced by approximating a real-world problem, which may be complex, by a simpler model. A model with high bias pays little attention to the training data and oversimplifies the problem.

• High bias can cause underfitting, where the model misses relevant relations between features and target outputs.

What is Variance?

Variance refers to the error introduced by the model's sensitivity to small fluctuations in the training dataset. A model with high variance learns noise and details from the training data too well.

• High variance can cause overfitting, where the model fits the training data closely but performs poorly on new data.

Understanding the Tradeoff

• A simple model (e.g., linear regression) has high bias and low variance.
• A complex model (e.g., deep neural network) has low bias and high variance.

The goal is to find the right balance:

$\text{Total Error}={\text{Bias}}^2+\text{Variance}+\text{Irreducible Error}$

Minimizing both bias and variance leads to better generalization on unseen data.

Visual Example

Imagine trying to hit a target with arrows:

• High bias: Arrows consistently miss the target in the same direction (systematic error).
• High variance: Arrows scatter widely around the target (inconsistent).
• Ideal model: Arrows cluster tightly on the target.

How to Manage Bias-Variance Tradeoff

• To reduce bias: Use more complex models, add features, train longer.
• To reduce variance: Use simpler models, regularization, more training data, cross-validation.

Techniques Related to Tradeoff

• Regularization reduces variance by adding penalties.
• Cross-validation helps select models with good bias-variance balance.
• Ensemble methods like bagging reduce variance.

Importance

Understanding bias-variance tradeoff helps in:

• Choosing the right model complexity.
• Avoiding overfitting and underfitting.
• Improving prediction accuracy.

Related Pages

• Overfitting
• Underfitting
• Regularization
• Cross Validation
• Model Evaluation Metrics

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