Learning to Rank Typed Graph Walks: Local and Global Approaches

1. Learning to Rank Typed Graph Walks:Local and Global Approaches Language Technologies Institute and Machine Learning Department School of Computer Science Carnegie Mellon University Einat Minkov and William W. Cohen

2. Did I forget to invite anyone for this meeting?

3. Did I forget to invite anyone for this meeting? What is Jason’s personalemail address ?

4. Did I forget to invite anyone for this meeting? What is Jason’s personalemail address ? Who is “Mike” who is mentioned in this email?

5. CALO Has Subject Term Sent To William graph proposal CMU 6/17/07 6/18/07 einat@cs.cmu.edu

6. Q: “what are Jason’s email aliases?” Sent To Has terminverse einat@cs.cmu.edu “Jason” einat Sent-to Msg18 Msg5 Msg 2 JasonErnst Sent toEmail Sent fromEmail Alias jernst@cs.cmu.edu jernst@andrew.cmu.edu Similar to

7. Search via lazy random graph walks • An extended similarity measure via graph walks:

8. Search via lazy random graph walks • An extended similarity measure via graph walks: • Propagate “similarity” from start nodes through edges in the graph – accumulating evidence of similarity over multiple connecting paths.

9. Search via lazy random graph walks • An extended similarity measure via graph walks: • Propagate “similarity” from start nodes through edges in the graph – accumulating evidence of similarity over multiple connecting paths. • Fixed probability of halting the walk at every step – i.e., shorter connecting paths have greater importance (exponential decay)

10. Search via lazy random graph walks • An extended similarity measure via graph walks: • Propagate “similarity” from start nodes through edges in the graph – accumulating evidence of similarity over multiple connecting paths. • Fixed probability of halting the walk at every step – i.e., shorter connecting paths have greater importance (exponential decay) • Finite graph walk, applied through sparse matrix multiplication (estimated via sampling for large graphs)

11. Search via lazy random graph walks • An extended similarity measure via graph walks: • Propagate “similarity” from start nodes through edges in the graph – accumulating evidence of similarity over multiple connecting paths. • Fixed probability of halting the walk at every step – i.e., shorter connecting paths have greater importance (exponential decay) • Finite graph walk, applied through sparse matrix multiplication (estimated via sampling for large graphs) • The result is a list of nodes, sorted by “similarity” to an input node distribution (final nodeprobabilities).

12. The graph • Graph nodes are typed. • Graph edges - directed and typed (adhering to the graph schema) • Multiple relations may hold between two given nodes. • Every edge type is assigned a fixed weight.

13. A query language:Q: { , } Graph walks Returns a list of nodes (of type ) ranked by the graph walk probs. The graph Nodes Node type Edge label Edge weight graph walk controlled by edge weights Θ , walk length K and stay probabilityγ The probability of reaching y from x in one step:the sum of edge weights from x to y, out of the total outgoing weight from x. The transition matrix assumes a stay probability at the current node at every time step.

14. Tasks Person namedisambiguation [ term “andy”file msgId ] “person” Threading What are the adjacent messages in this thread? A proxi for finding generally related messages. [ file msgId ] “email-file” [ term Jason ] Alias finding What are the email-addresses of Jason ?... “email-address”

15. Learning to RankTyped Graph Walks

16. Learning settings Task T (query class) … Query q Query a Query b + Rel. answers a + Rel. answers b + Rel. answers q GRAPH WALK node rank 1 node rank 2 node rank 3 node rank 4 … node rank 10 node rank 11 node rank 12 … node rank 50 node rank 1 node rank 2 node rank 3 node rank 4 … node rank 10 node rank 11 node rank 12 … node rank 50 node rank 1 node rank 2 node rank 3 node rank 4 … node rank 10 node rank 11 node rank 12 … node rank 50

17. Learning approaches Edge weight tuning: Graph walk Weightupdate Theta*

18. Learning approaches Edge weight tuning: Graph walk Weightupdate Theta* Graph walk task

19. Learning approaches Edge weight tuning: Graph walk Weightupdate Theta* Graph walk task Node re-ordering: Feature generation Updatere-ranker Re-rankingfunction Graph walk

20. Learning approaches Edge weight tuning: Graph walk Weightupdate Theta* Graph walk task Node re-ordering: Feature generation Updatere-ranker Re-rankingfunction Graph walk Graph walk Feature generation Score byre-ranker task

21. Learning approaches • Gradient descent (Chang et-al, 2000) Graphparameters’tuning • Can be adapted from extended PageRank settings to finite graph walks. • Exhaustive local search over edge type (Nie et-al, 05) • Strong assumption of first-order Markov dependencies • Hill climbing error backpropagation (Dilligenti et-al, IJCAI-05) • Gradient descent approximation for partial order preferences (Agarwal et-al, KDD-06) Nodere-ordering • A discriminative learner, using graph-paths describing features. • Re-ranking (Minkov, Cohen and NG, SIGIR-06) • Loses some quantitative data in feature decoding. However, can represent edge sequences.

22. Error Backpropagation following Dilligenti et-al, 2005 Cost function: Weight updates: Where,

23. Re-ranking follows closely on (Collins and Koo, Computational Linguistics, 2005) Scoring function:Adapt weights to minimize (boosted version): , where

24. Path describing Features X1 ‘Edge unigram’was edge type l used in reaching x from Vq? X2 X3 ‘Edge (n-)bigram’ were edge types l1 and l2 traversed (in that order) in reaching x from Vq? X4 X5 K=0 K=1 K=2 ‘Top edge (n-)bigram’ same, where only the top k contributing paths are considered. x2 x1  x3 x4 x1  x3 x4  x2  x3 x2  x3 Paths [x3, k=2]: ‘Source count’ indicates the number of different source nodes in the set of connecting paths.

25. Learning to Rank Typed Graph Walks: Local vs. Globalapproaches

26. Experiments Methods: • Gradient descent: Θ0 ΘG • Reranking: R(Θ0) • Combined: R(ΘG) Tasks &Corpora :

27. The results (MAP) Namedisambiguation * * * + + * * Threading * * * * * * * + + + Alias finding MAP

28. Namedisambiguation Threading Alias finding

29. Our Findings • Re-ranking often preferable due to ‘global’ features: • Models relation sequences. e.g., threading: sent-from  sent-to-inv • Re-ranking rewards nodes for which the set of connecting paths is diverse. • source-count feature informative for complex queries • The approaches are complementary Future work: • Re-ranking: large feature space. • Re-ranking requires decoding at run-time. • Domain specific features

30. Related papers Einat Minkov, William W. Cohen, Andrew Y. NgContextual Search and Name Disambiguation in Email using GraphsSIGIR 2006 Einat Minkov, William W. CohenAn Email and Meeting Assistant using Graph WalksCEAS 2006 Alekh Agarwal, Soumen Chakrabarti Learning Random Walks to Rank Nodes in GraphsICML 2007 Hanghang Tong, Yehuda Koren, and Christos Faloutsos Fast Direction-Aware Proximity for Graph Mining KDD 2007

31. Thanks! Questions?