looking for "optimal weighting" algorithm

Alex Martelli aleaxit at yahoo.com
Thu Apr 10 09:13:11 EDT 2003


I _know_ there's a decent algorithm to solve the following problem,
but I don't recall its name and thus can't rapidly google for the 
details... can somebody help?


The problem: I need to design a "decision criterion" to classify
"observations".  For each observation I measure the values of a
number N of features, x1, x2, ... xN; the desired design criterion
is a set of weights w1, w2, ... wN such that for any observation I 
will then just compute a weighted sum
  S = w1*x1 + w2*x2 + ... + wN*xN
and classify the observation as Black if S<=1, White if S>1.  To
train my classifier I have a large corpus of observations already
made and annotated with "ground-truth" data about whether each
given observation should have been classified as B or W, and an
error-cost value for each kind of classification (Ebw is the cost
of erroneously classifying a feature as W when it should be B,
Ewb is that of classifying it as B when it should be W).  So,
what's the algorithm to estimate the weights given the corpus of
observation and ground-truth data, and the error-costs?

Responses welcome either here or directly to my mailbox -- if I
do get responses to my mailbox, I'll eventually summarize here --
as a bonus, I promise to make available a Python implementation of 
whatever algorithm I end up with, if one's not already around...;-).


TIA,

Alex





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