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Overview of Relational Markov Networks

Overview of Relational Markov Networks. Colin Evans. Relational Schema. Relational Data – an Instantiation. Problem. How do we find an optimal assignment of labels I .y to a set of variables I .x in a specific instantiation I ?

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Overview of Relational Markov Networks

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  1. Overview of Relational Markov Networks Colin Evans

  2. Relational Schema

  3. Relational Data – an Instantiation

  4. Problem • How do we find an optimal assignment of labels I.y to a set of variables I.x in a specific instantiation I? • We need an objective function p(I.y|I.x) that indicates the quality of an assignment of labels. • The objective function should take into account the relational structure of the data.

  5. Relational Clique Templates • A template C is an algorithm for selecting a subset of nodes requiring labels – essentially a logical query. • “Find all label attributes A, B with pages C, D where C hasLabel A and D hasLabel B and C linksTo D” • A specific subset is called a clique, I.xc. • An potential function fc(I.yc|I.xc) where I.yc is a subset of I.y is associated with the template. • An example potential function for the above template: • A=B → 1 • A≠B → 0

  6. Markov Networks • Given a set of templates C and a set of cliques C(I), we can construct a Markov Network by connecting each of the cliques.

  7. Markov Networks • Given a Markov Network, we have the following JPD:

  8. Potential Functions • A weight wc associated with each clique template C is inserted to balance the contribution of each potential function. • These weights need to be learned.

  9. How do we learn the weights? • Gradient Descent • Perceptron Learning • Other optimization methods

  10. How do we find an optimal labeling? • Modeling the relationships of the cliques as a Markov Network and use the sum-product algorithm. • Problem: sum-product is only proven to converge on trees.

  11. Other Issues • How does this method work if you have a large body of “correctly” labeled relational data and only wish to apply a small number of labels? • Email classification is a good example of this. • Complexity of assigning a label goes down, but we still use relationships to determine the label. • Could one template “dominate” in a specific data set? Does there need to be a factor which normalizes the contribution of a template if it produces too many cliques? • How do you test the “usefulness” of a template?

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