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POGraph theory - learn cost function to find optimal path
 

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  1. POGraph theory - learn cost function to find optimal path
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    <p>This is a supervised learning problem.</p> <p>I have a directed acyclic graph (DAG). Each edge has a vector of features X, and each node (vertex) has a label 0 or 1. The task is to find a cost function w(X), so that the shortest path between any pair of nodes has the highest ratio of 1s to 0s (minimum classification error).</p> <p>The solution must generalize well. I tried logistic regression, and the learned logistic function predicts fairly well the label of a node giving the features of a incoming edge. However, the graph's topology is not taken into account by that approach, so the solution in the whole graph is non-optimal. In other words, the logistic function is not a good weight function given the problem setup above.</p> <p>Although my problem setup is not the typical binary classification problem setup, here is a good intro to it: <a href="http://en.wikipedia.org/wiki/Supervised_learning#How_supervised_learning_algorithms_work">http://en.wikipedia.org/wiki/Supervised_learning#How_supervised_learning_algorithms_work</a></p> <p>Here are some more details:</p> <ol> <li>Each feature vector X is a d-dimensional list of real numbers. </li> <li>Each edge has a vector of features. That is, given the set of edges E = {e1, e2, .. en} and set of feature vectors F = {X1, X2 ... Xn}, then edge ei is associated to vector Xi.</li> <li>It is possible to come up with a function f(X), so that f(Xi) gives the likelihood that edge ei points to a node labeled with a 1. An example of such function is the one I mentioned above, found through logistic regression. However, as I mentioned above, such function is non-optimal. </li> </ol> <p>SO THE QUESTION IS: Given the graph, a starting node and an finish node, how do I learn the optimal cost function w(X), so that the ratio of nodes 1s to 0s is maximized (minimum classification error)?</p>
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    1. COCan you possibly elaborate on what you tried and what you mean by "it doesn't work"?
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    2. COThe graph seems to only have two nodes i.e. node for label 0 and node for label 1 ?! However, those nodes are sepearate and that means that there is no actual graph? Would you elaborate more on your model and selected graph representation?
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    3. CO@carlosdc. Ok, I elaborated on my logistic regression approach, which didn't work on my toy data. Thanks.
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