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Topic: computing this probability
Replies: 2   Last Post: Nov 6, 2012 3:06 PM

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 rt servo Posts: 19 Registered: 2/1/05
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
>

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