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Re: computing this probability
Posted:
Nov 6, 2012 1:20 PM


On 06/11/2012 12:20 PM, Anja wrote: > Hi everyone, > > I am doing some discrete optimisation in my problem and I obtain some marginal probabilities as the following expression: > > P(x) = exp(E(x)) / (exp(E(x)) + exp(E(y)) + exp(E(z)) + ...) > > Where E(v) is the energy that the system takes for some configuration v. > > Now, my issue is that these energy values can take very large numbers and hence this P(x) expression affectively becomes 0. If I scale all the energy values by say E(x), so that the expression becomes > > P(x) = exp(1) / (exp(1) + exp(E(y)/E(x)) + exp(E(z)/E(x)) + ...) then usually these numbers get too close and the probability takes a value very close to 1 and does not say anything useful.
Hold it. Your algebra seems all messed up. You should scale by exp(E(x)), and then your expression turns into
P(x) = 1 / (1 + exp(E(x)  E(y)) + exp(E(x)  E(z)) + ...)
However, with your given numbers this is a value too close to 1 to distinguish it in any meaningful way. I suspect that you have other errors as well.
> Can someone suggest how I can scale this data in a way, so that it becomes easy to calculate and the probabilities are still something useful. > > As an example, in the last problem, the values were something like: > > E(x) = 17247 > E(y) = 20425 > E(z) = 26487 > > What would be ideal is if I could somehow scale everything so that the probabilities also make sense. > > If I scale everything by E(x), I get probabilities of 0.4 for the most likely configuration but if I scale by 02.*E(x), then the probability for the most likely configuration jumps to 0.68... So it is really tricky... > > Thanks, > Anja >



