The VC-dimension based error bounds are ridiculously pessimistic in practice- but tight in the ‘distributionindependent’ framework
Hedged prediction technology gives individual error estimates (confidences) on predictions that are in practice much better
Based on Kolmogorov complexity, make a prediction that makes the current history + prediction as ‘random’ as possible
Based on non-conformance measure, predict continuation of (x1,y1), (x2,y2), … (xk,yk), (x(k+1), Y) that makes (x(k+1),Y) as ‘conforming’ as possible.
Lagrange multipliers measure ‘force’ between point and constraint -- ideal as non-conformance measure 3% wrongly classified-- confidence of classifier is 97% for point outside margin
NOTE: Under exchangeability hypothesis
P-values from Lagrange Multipliers
Lagrange multipliers measure ‘force’ between point and constraint -- ideal as non-conformance measure 7% support vectors:
Giving ‘corridor’ as prediction set has confidence 93%.
NOTE: Under exchangeability hypothesis, ie not for time series.
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