looking for "optimal weighting" algorithm

[Duncan Smith]

"Alex Martelli" <aleaxit at yahoo.com> wrote in message
news:b73ql8011te at enews4.newsguy.com...
> 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
>

Alex,
        I'm not sure exactly which algorithm it is that you've seen before.
But linear discriminant analysis and logistic regression would give you
functions of that form.  Is there any reason you couldn't use a Naive Bayes
classifier?  You could always drop the naive bit and use a Bayesian network
;-).  Then there's a number of tree-based classifiers (eg Chow-Liu).

Duncan