author: niplav, created: 2021-04-19, modified: 2022-02-02, language: english, status: on hold, importance: 2, confidence: likely
Solutions to the textbook “Pattern Recognition and Machine Learning” by Christopher M. Bishop.
(*) Consider the sum-of-squares error function given by (1.2) in which the function is given by the polynomial (1.1). Show that the coefficients that minimizes this error function are given by the solution to the following set of linear equations
where
Here a suffix or denotes the index of a component, whereas denotes raised to the power of .
Recap: formula 1.1 is
and formula 1.2 (the error function) is
Substituting 1.1 into 1.2 gives
Differentiating after then returns
I really should learn multivariable calculus.
(*) Using the definition (1.38) show that satisfies (1.39).