Learning A Real Valued Function

file=./bookps/bayes-linear.epsf,width=2.5in

Consider any real-valued target function 43#43

Training examples 44#44, where 45#45 is noisy training value

• 46#46
• 47#47 is random variable (noise) drawn independently for each 48#48 according to some Gaussian distribution with mean=0

Then the maximum likelihood hypothesis 49#49 is the one that minimizes the sum of squared errors:

50#50