From: "Mauricio Fernández" <batsman.geo@...>
Date: 2003-04-20T16:05:25+09:00
Subject: Re: Biased weighted random?

On Sat, Apr 19, 2003 at 05:33:39AM +0900, Chris Pine wrote:
[...]
> targets = normalize([2,1,1])
> weights = targets.dup
> probs   = realProbVector(weights)
> 
> 50.times do
>   weights.each_with_index do |x,idx|
>     weights[idx] += targets[idx] - probs[idx]
>   end
>   weights = normalize(weights)
>   probs = realProbVector(weights)
> end

I have been thinking about this for a while and even though I understand
the subjacent idea, I am not sure this is guaranteed to work at all.
I have the feeling the problem cannot be solved generally with just the
weights vector (which generate a single transition matrix according to
the algorithm in realProbVector), and I would expect some cases to be
solvable only with the whole transition matrix (*). Cannot really prove
the latter, but it is obvious that this way (weights only) we're giving
away several degrees of freedom that could come handy later :)

(*) One would expect in such cases that the weights never converge or
directly diverge to huge numbers, as Hal experienced. But I don't think I
can actually prove that the family of solutions generated w/ a transition
matrix is bigger than that w/ only the weights, unless I find one
example :-) 

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