Normal Equation Noninvertibility

When implementing the normal equation in octave we want to use the ‘pinv’ function rather than ‘inv.’ The ‘pinv’ function will give you a value of θ even if X^(T)X is not invertible.

  • Redundant features, where two features are very closely related (i.e. they are linearly dependent)
  • Too many features (e.g. m ≤ n). In this case, delete some features or use “regularization” (to be explained in a later lesson).

Solutions to the above problems include deleting a feature that is linearly dependent on another or deleting one or more features when there are too many features.