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.x c. An potential function f c (I.y c |I.x c ) where I.y c 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 w c 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?