Can this be rearranged to solve?

[jeff91]

Is it possible to rearrange or inverse this to solve for p(₁X | Y)? I haven't done this level of maths for over 15 years and haven't a clue where to start.

₁w_k =p(₁X | Y)⋅ w_k

weight vector of ₁X node in case a is ₁w=[₁w₁, ₁w₂,…, ₁w_m]
weight vector of Y node w=[w₁, w₂,…, w_m]

where 1 ≤ k ≤ m

 

[Stephen Tashi]

I don't understand the notation. Are you asking about solving an equation of the form:

<n-dimensional column vector> = <n by n matrix> < another n-dimensional column vector>

You want to solve for the matrix when given the two column vectors?

 

[mfb]

I don't understand the notation either.
If p(₁X | Y) is a scalar then it's trivial to solve (you have m equations that should all lead to the same scalar, excluding possible lines that are 0=p*0). If it is an mxm matrix then there is not enough information to determine it uniquely.

 

[jedishrfu]

What is the context of your problem? It looks like something related to a neural net where the p(X|Y) is some kind of Baysian probability

 

[jeff91]

Thank you for your replies. I am trying to obtain probabilities to put in a Bayesian network from an AHP questionnaire.
This is the bit from the book I am looking at.

I have the weights as they are outputted from the AHP spreadsheet.
I have only ever done Bayesian networks when I have been supplied with the probabilities.

 

[mfb]

It's an mxm matrix then. No, you can't invert that problem. There are many different matrices that will lead to the same result for given vectors ₁w_k and w_k.