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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Elementary principles of machine learning

A modeller fits polynomial regressions of increasing degree to the same training data. The training error falls steadily with degree, but the error on a separate validation set falls and then rises sharply for high degrees. Which conclusion is most appropriate?

The high-degree models are overfitting, so a lower-degree model near the validation-error minimum should be chosen. Training error always falls with flexibility, but rising validation error shows the model is fitting noise, meaning high variance and low bias, so it generalises badly.

  1. AHigh-degree models are overfitting, so a lower-degree model near the validation minimum should be chosenCorrect
  2. BHigh-degree models are underfitting, so the degree should be raised further
  3. CThe validation set is biased, so the lowest training error model should be chosen
  4. DThe model has high bias at high degree and low variance
  5. The pattern shows the response is categorical and classification should be used

Explanation

Falling training error with rising validation error is the signature of overfitting: the flexible model is fitting noise. High degree means low bias and high variance, which rules out option 4. Choosing the degree at the validation minimum balances the bias-variance trade-off.

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