Can this be rearranged to solve?

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In summary, the conversation discusses the possibility of rearranging or inverting an equation to solve for p(1X | Y). The notation and context of the problem are unclear, but it appears to be related to a Bayesian network and AHP questionnaire. It is mentioned that the equation involves an mxm matrix and two column vectors and that it cannot be uniquely solved due to insufficient information.
  • #1
jeff91
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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.

1wk =p(1X | Y)⋅ wk

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

where 1 ≤ k ≤ m
 
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  • #2
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?
 
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  • #3
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.
 
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  • #4
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
 
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  • #5
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.
1596886909421.png

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.
 
  • #6
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 1wk and wk.
 
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Related to Can this be rearranged to solve?

1. Can any equation or problem be rearranged to find a solution?

Yes, in most cases, equations and problems can be rearranged in different ways to find a solution. However, there are some complex equations that may not have a rearranged solution.

2. How do you know when to rearrange an equation or problem?

Rearranging an equation or problem is often necessary when the original form is difficult to solve or does not provide a clear solution. It can also be helpful when trying to isolate a specific variable or factor.

3. What are the steps to rearrange an equation or problem?

The steps for rearranging an equation or problem may vary depending on the specific problem. However, some general steps include identifying the variable or factor to be isolated, using inverse operations to move terms to the opposite side of the equation, and simplifying the equation to find the solution.

4. Is it possible to rearrange an equation or problem in multiple ways?

Yes, there are often multiple ways to rearrange an equation or problem to find a solution. This is especially true for more complex equations or problems that involve multiple variables or factors.

5. Can rearranging an equation or problem change the solution?

Yes, in some cases, rearranging an equation or problem can change the solution. This is because different rearrangements can lead to different equations or problems, which may have different solutions. It is important to check the solution to ensure it is accurate after rearranging an equation or problem.

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