Oregon State University – CS539 PRMs Learning Probabilistic Models of Link Structure Getoor, Friedman, Koller, Taskar

Oregon State University – CS539 PRMs Example Application: WebKB  Classify web page as course, student, professor, project, none using… Words on the web page Links from other web pages (and the class of those pages, recursively) Words in the “anchor text” from the other page anchor text.  Web pages obtained from Cornell, Texas, Washington, and Wisconsin

Oregon State University – CS539 PRMs Example Application: CORA  Classify documents according to topic (7 levels) using… words in the document papers cited by the document papers citing the document

Oregon State University – CS539 PRMs Standard PRM  parents(Doc.class) = {MODE(Doc.citers.class),MODE(Doc.cited.clas s)} Document class words Document class words Document class words Document class words Document class words Document class words Document class words Document class words citers cited MODE

Oregon State University – CS539 PRMs Problem: The Citation Structure is Fixed  The existence (or non-existence) of a link cannot serve as evidence  Individually-linked papers only influence the class through the MODE.

Oregon State University – CS539 PRMs Possible Solution: Link Uncertainty  Model the existence of links as random variables  Create a Link instance for each pair of possibly-linked objects

Oregon State University – CS539 PRMs Unrolled Network Document class words Document class words Document class words Cites Exists Cites Exists Cites Exists

Oregon State University – CS539 PRMs Getoor’s Diagram  Entity classes (Paper)  Relation classes (Cites)  Technically, every instance has an Exists variable which is true for all Entity instances.

Oregon State University – CS539 PRMs Semantics  P is the basic CPT  P* will be the equivalent unrolled CPT  Require that an object does not exist if any of the objects it points to do not exist

Oregon State University – CS539 PRMs WebKB Network

Oregon State University – CS539 PRMs Experimental Results  Cora and WebKB

Oregon State University – CS539 PRMs WebKB with various features

Oregon State University – CS539 PRMs A Second Approach: Reference Uncertainty  Treat reference attributes as random variables Each reference attribute takes as value an object of the indicated class  Citation Citing: reference attribute, value is a Paper Cited: reference attribute, value is a Paper

Oregon State University – CS539 PRMs Problems  How many citation objects exist? Consequently, how many reference random variables exist?  How do we represent P(Citation.cites | …)? Citation.cites could take on thousands of possible values. Huge conditional probability table Costly inference at run time

Oregon State University – CS539 PRMs Solutions Problem 1: How many citations?  Fix the number of Citation objects  This gives the “object skeleton”

Oregon State University – CS539 PRMs Problem 2: Too many potential values for a reference attribute  Attach to each reference attribute a set of partition attributes The reference attribute chooses a partition A Paper is then chosen uniformly at random from the partition Citation Citing Cited Paper Theory Paper Graphics Paper Learning

Oregon State University – CS539 PRMs Representing Constraints Between Citing and Cited Papers Parents(Cites.Cited) = {Cites.Citing.Topic}

Oregon State University – CS539 PRMs Details  Each reference attribute  has a selector attribute S  that chooses the partition. Citation Paper Learning Paper Theory Paper Graphics Paper S citing Citing S cited Cited

Oregon State University – CS539 PRMs Class-level Dependency Graph  Five types of edges Type I: edges within a single object Type II: edges between objects Type III: edges from every reference attribute along any reference paths Type IV: edges from every partition attribute to the selector attributes that use those partition attributes to choose a partition Type V: edge from selector attributes to their corresponding reference attributes

Oregon State University – CS539 PRMs Movie Theater Example  Type I: Genre  Popularity  Type II: Shows.Movie.Genre  Shows.Profit Shows.Theater.Type  S Movie  Type III: Move  Profit; Theater  S movie  Type IV: Genre  S Movie  Type V: S Theater  Theater; S Movie  Movie

Oregon State University – CS539 PRMs Unrolled Graph?  The Unrolled Graph can have a huge number of edges  Is learning and inference really feasible?

Oregon State University – CS539 PRMs Homework Exercise  Construct the dependency graph for the citation example  Construct an unrolled network for a reference uncertainty example