Bias and Variance

Bias and variance describe two ways an estimate can go wrong.

Bias is systematic error.

Variance is sensitivity to the particular sample.

biased: consistently offhigh variance: unstable
Bias is systematic error; variance is sensitivity to the sample.

Working Intuition

A biased estimator tends to miss in the same direction.

A high-variance estimator may sometimes be close and sometimes be far, depending on which data it saw.

Bias is about the center of many attempts. Variance is about how spread out those attempts are.

An estimator can have both problems. It can be consistently off and unstable.

This is why one train-validation split is only a clue. To see bias and variance clearly, imagine repeating the experiment with new samples from the same population.

In ML

An underfit model often has high bias. It is too simple to represent the pattern.

An overfit model often has high variance. It reacts too much to the training sample.

If training error is high and validation error is high, the model may be too limited. If training error is low but validation error is high, the model may be reacting too much to the training sample.

MATH-C10-T05-001Exercise: High bias clue

A model performs poorly on both training data and validation data.

Enter 1 if this suggests high bias more than high variance.

Compute it first, then check your number.

Hint

If it cannot fit even the training data well, it is probably too limited.

Solution

Enter 1. Poor training and validation performance often suggests high bias or underfitting.

MATH-C10-T05-002Exercise: High variance clue

A model performs very well on training data but poorly on validation data.

Does this suggest high variance more than high bias?

Answer it first, then check.

Hint

The model fits the training sample but does not transfer well.

Solution

Yes. Strong training performance with poor validation performance often suggests high variance or overfitting.

MATH-C10-T05-003Exercise: Systematic miss

Which word names systematic error: bias or variance?

Answer it first, then check.

Hint

Bias is about consistently missing in the same direction.

Solution

Bias names systematic error. It is about the center of many attempts missing in a consistent direction.

MATH-C10-T05-004Exercise: Sample sensitivity

Which word names sensitivity to the particular sample: bias or variance?

Answer it first, then check.

Hint

Variance is about spread across attempts.

Solution

Variance names sensitivity to the particular sample. It is about how much the estimate moves across repeated samples.

MATH-C10-T05-005Exercise: Repeated experiments

Enter 1 if bias and variance are easiest to understand by imagining many repeated samples, not just one result.

Compute it first, then check your number.

Hint

One result cannot show the center and spread of many attempts.

Solution

Enter 1. Bias and variance describe how estimates behave across repeated samples or repeated training runs.

Before Moving On

Bias and variance are not insults. They are lenses for reading model behavior.