Bias vs. Variance

Bias

  • Symptom
    $ J_{cv}(\theta) -1 $ and $ J_{train}(\theta) $ are high.
  • Prescription
  1. Getting additional features
  2. Adding polynomial features ($x_{1}^{2}, x_{2}^{2}, x_1x_2, etc $)
  3. Decreasing $\lambda $

Variance

  • Symptom
    $ J_{cv}(\theta) \gg J_{train}(\theta) $ and $J_{train}(\theta) $ is low.

  • Prescription

    1. Getting more training samples
    2. Getting rid of some features
    3. Increasing $\lambda$

Regularization

Very big $\lambda \rightarrow $ Bias(underfiiting)
very small $\lambda \rightarrow $ Variance(overfilling)

$\lambda $ selection : use the same training set and select the lambda that leads to the smallest CV Error and to check the Test Error.

Learning Curve

  • High Bias
    $J_{train}(\theta) $ is close to $J_{cv}(\theta) $.

Getting more data is useless!

  • High Variance
    There is a gap between $J_{train}(\theta) $ and $J_{cv}(\theta) $.

Getting more data may give a better result.

Neural networks and overfitting

  • Using “large” neural network with good regularization to address overfiting is usually better than “small” neural network, but the computation cost is more expensive.

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