Last modified: Thu Oct 6 17:07:38 EDT 2005 by Dean Foster

Statistical Data mining: Wavelets


Problem: curve fitting

Where to put the knots?

Competitors to splines

Fourier can't fit jumps

Splines can be approximated by wavelets

Theorem: (DJ94) R(SW,f) < a + b log(n)R(PP,f)

Bonferroni can approximate best wavelet

Theorem: (DJ94) R(Bonferroni,f) < (1 + 2 log(n)) * (sigma2 + R(SW,f))

Can anything beat Bonferroni?

Theorem: (DJ94) For some n: R(anything,f) > (2 - epsilon) log(n)R(SW,f)