 
Summary: Fitting Algebraic Curves to Noisy Data
Sanjeev Arora #
Princeton University
arora@cs.princeton.edu
Subhash Khot +
Princeton University
khot@cs.princeton.edu
April 7, 2002
Abstract
Motivated by applications in vision and pattern de
tection, we introduce the following problem. We
are given pairs of datapoints (x 1 , y 1 ), (x 2 , y 2 ),
. . . , (xm , ym ), a noise parameter # > 0, a degree
bound d, and a threshold # > 0. We desire ``every''
degree d polynomial h satisfying
h(x i ) # [y i  #, y i + #]
for at least # fraction of i's.
We assume by rescaling the data that each
x i , y i # [1, 1].
If # = 0, this is just the list decoding problem
