The best hypothesis
n Find best function that models given data.
n How to define the best function?
¡ Fidelity to the data – error on existing data: E(h,D)
¡ Simplicity – how complicated is the solution: C(h)
n One measure: how many possible hypotheses for the class?
n Inevitable tradeoff between complexity of
hypothesis and degree of fit to the data
n Minimize α E(h,D)  + (1-α) C(h)
¡ Where α is a tuning parameter