Re: [agi] A probabilistic/algorithmic puzzle...

[Jonathan Standley]

a challenge! cool :)  but let me try to put it in less-math terms for myself and others who are not math-types

 

>Let X_i, i=1,...,n, denote a set of discrete random variables

 

X_i is the set of all integers between i and n, initial value for i is 1?

or is i any member of the set X?

or does i function only as a lower bound to set X?

 

 

> Let's say we have a set of N << n^2 conditional probability relationships of
> the form

set N consists of relationships numbering n^2, n is the upper boundary of the set X? 
> P(X_j|X_i)

what does this notation "|" mean ?

does P(X_j|X_i) mean the probability of subset occuring within the set X,   X is bounded by [i,n]?

 

 > where i, j are drawn from {1,...,n}.

does X_i represent the whole set and j is a subset or set X_i?

or is i the lower bound of set X and j is an arbitrary member of set X?

> Let's say we also have a set of M <= n probabilities
 

is this a different n than the upper bound of set x?

> P(X_i)

M = P(X_i)?

if so, it means that M is the chance of set X existing within a larger 'parent' set (ie the novamente system)?

 

> The problem is:
>
> * Infer the rest of the P(X_i|X_j) and P(X_i): the ones that aren't given
>
> * Specifically, infer cases where P(X_i|X_j) differs significantly from
> P(X_i)

 

Is the above asking?  given a set X bounded upper = n, lower = i, and given j, an arbitrary subset of set X in X's  initial state, use the available data to approximate the probability of a hypothetical integer set ( a new value for j) apperaing within X in a future state.  specifically, try to find initial conditions which will lead to a large difference between the chances of X existing and the chances of X that contains j existing at a future state. all of this is assuming that Set X is being acted upon by a specified algorithm or process?
>
> Clearly this is a massively "underdetermined" problem: the given data will
> generally not be enough to uniquely determine the results.  This is what
> makes it interesting!
>
> As I said, we have two solutions for this, one implemented the other just
> designed; so we know the problem is approximately and heuristically solvable
> in a plausible computational timeframe.  But I wonder if there aren't
> radically different solutions from the ones we've come up with...

would you mind trying to put the problem in 'word problem' form?  I do much better with concepts than equations ;)

 

If it;s not worth the effort dont bother :)

 

J Standley