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An overview of probabilistic soft logic, a language for templating hinge-loss Markov random fields.

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- 1. Probabilistic Soft Logic: An Overview Lise Getoor, Stephen Bach, Bert Huang University of Maryland, College Park http://psl.umiacs.umd.edu Additional Contributors: Matthias Broecheler, Shobeir Fakhraei, Angelika Kimmig, London, Alex Memory, Hui Miao, Lily Mihalkova, Eric Norris, Jay Pujara, Theo Rekatsinas, Arti Rames
- 2. Probabilistic Soft Logic (PSL) Declarative language based on logics to express collective probabilistic inference problems Predicate = relationship or property Atom = (continuous) random variable Rule = capture dependency or constraint Set = define aggregates PSL Program = Rules + Input DB
- 3. Probabilistic Soft Logic (PSL) Declarative language based on logics to express collective probabilistic inference problems Predicate = relationship or property Atom = (continuous) random variable Rule = capture dependency or constraint Set = define aggregates PSL Program = Rules + Input DB
- 4. Probabilistic Soft Logic Entity Resolution Entities - People References Attributes - Name Relationships - Friendship Goal: Identify references that denote the same person A B John Smith J. Smith name name C E D F G H friend friend = =
- 5. Probabilistic Soft Logic Entity Resolution References, names, friendships Use rules to express evidence - ‘’If two people have similar names, they are probably the same’’ - ‘’If two people have similar friends, they are probably the same’’ - ‘’If A=B and B=C, then A and C must also denote the same person’’ A B John Smith J. Smith name name C E D F G H friend friend = =
- 6. Probabilistic Soft Logic Entity Resolution References, names, friendships Use rules to express evidence - ‘’If two people have similar names, they are probably the same’’ - ‘’If two people have similar friends, they are probably the same’’ - ‘’If A=B and B=C, then A and C must also denote the same person’’ A B John Smith J. Smith name name C E D F G H friend friend = = A.name ≈{str_sim} B.name => A≈B : 0.8
- 7. Probabilistic Soft Logic Entity Resolution References, names, friendships Use rules to express evidence - ‘’If two people have similar names, they are probably the same’’ - ‘’If two people have similar friends, they are probably the same’’ - ‘’If A=B and B=C, then A and C must also denote the same person’’ A B John Smith J. Smith name name C E D F G H friend friend = = {A.friends} ≈{} {B.friends} => A≈B : 0.6
- 8. Probabilistic Soft Logic Entity Resolution References, names, friendships Use rules to express evidence - ‘’If two people have similar names, they are probably the same’’ - ‘’If two people have similar friends, they are probably the same’’ - ‘’If A=B and B=C, then A and C must also denote the same person’’ A B John Smith J. Smith name name C E D F G H friend friend = = A≈B ^ B≈C => A≈C : ∞
- 9. Probabilistic Soft Logic Link Prediction Entities - People, Emails Attributes - Words in emails Relationships - communication, work relationship Goal: Identify work relationships - Supervisor, subordinate, colleague
- 10. Probabilistic Soft Logic Link Prediction People, emails, words, communication, relations Use rules to express evidence - “If email content suggests type X, it is of type X” - “If A sends deadline emails to B, then A is the supervisor of B” - “If A is the supervisor of B, and A is the supervisor of C, then B and C are colleagues”
- 11. Probabilistic Soft Logic Link Prediction People, emails, words, communication, relations Use rules to express evidence - “If email content suggests type X, it is of type X” - “If A sends deadline emails to B, then A is the supervisor of B” - “If A is the supervisor of B, and A is the supervisor of C, then B and C are colleagues” complete by due
- 12. Probabilistic Soft Logic Link Prediction People, emails, words, communication, relations Use rules to express evidence - “If email content suggests type X, it is of type X” - “If A sends deadline emails to B, then A is the supervisor of B” - “If A is the supervisor of B, and A is the supervisor of C, then B and C are colleagues”
- 13. Probabilistic Soft Logic Link Prediction People, emails, words, communication, relations Use rules to express evidence - “If email content suggests type X, it is of type X” - “If A sends deadline emails to B, then A is the supervisor of B” - “If A is the supervisor of B, and A is the supervisor of C, then B and C are colleagues”
- 14. Probabilistic Soft Logic Node Labeling ?
- 15. Probabilistic Soft Logic Voter Opinion Modeling ? $$ Tweet Status update
- 16. Probabilistic Soft Logic Voter Opinion Modeling spouse spouse colleague colleague spouse friend friend friend friend
- 17. Probabilistic Soft Logic Voter Opinion Modeling vote(A,P) ∧ spouse(B,A) vote(B,P) : 0.8 vote(A,P) ∧ friend(B,A) vote(B,P) : 0.3 spouse spouse colleague colleague spouse friend friend friend friend
- 18. Probabilistic Soft Logic Multiple Ontologies 18 Organization Employees Developer Staff CustomersService & Products Hardware IT Services Sales PersonSoftware work forprovides buys helps interacts sells todevelops Company Employee Technician Accountant CustomerProducts & Services Hardware Consulting SalesSoftware Dev works fordevelop buys helps interacts with sells
- 19. Probabilistic Soft Logic Ontology Alignment 19 Organization Employees Developer Staff CustomersService & Products Hardware IT Services Sales PersonSoftware work forprovides buys helps interacts sells todevelops Company Employee Technician Accountant CustomerProducts & Services Hardware Consulting SalesSoftware Dev works fordevelop buys helps interacts with sells
- 20. Probabilistic Soft Logic Ontology Alignment 20 Organization Employees Developer Staff CustomersService & Products Hardware IT Services Sales PersonSoftware work forprovides buys helps interacts sells todevelops Company Employee Technician Accountant CustomerProducts & Services Hardware Consulting SalesSoftware Dev works fordevelop buys helps interacts with sells Match, Don’t Match?
- 21. Probabilistic Soft Logic Ontology Alignment 21 Organization Employees Developer Staff CustomersService & Products Hardware IT Services Sales PersonSoftware work forprovides buys helps interacts sells todevelops Company Employee Technician Accountant CustomerProducts & Services Hardware Consulting SalesSoftware Dev works fordevelop buys helps interacts with sells Similar to what extent?
- 22. Probabilistic Soft Logic Logic Foundation
- 23. Probabilistic Soft Logic Rules Atoms are real valued - Interpretation I, atom A: I(A) [0,1] - We will omit the interpretation and write A [0,1] ∨, ∧ are combination functions - T-norms: [0,1]n →[0,1] H1 ∨... Hm ← B1 ∧ B2 ∧ ... Bn Ground Atoms [Broecheler, et al., UAI ‘1
- 24. Probabilistic Soft Logic Rules Combination functions (Lukasiewicz T-norm) A ∨ B = min(1, A + B) A ∧ B = max(0, A + B – 1) H1 ∨... Hm ← B1 ∧ B2 ∧ ... Bn [Broecheler, et al., UAI ‘1
- 25. Probabilistic Soft Logic Satisfaction Establish Satisfaction - ∨ (H1,..,Hm) ← ∧ (B1,..,Bn) H1 ∨... Hm ← B1 ∧ B2 ∧ ... Bn H1 ← B1:0.7 ∧ B2:0.8 [Broecheler, et al., UAI ‘1 ≥0.5
- 26. Probabilistic Soft Logic Distance to Satisfaction Distance to Satisfaction - max( ∧ (B1,..,Bn) - ∨ (H1,..,Hm) , 0) H1 ∨... Hm ← B1 ∧ B2 ∧ ... Bn H1:0.7 ← B1:0.7 ∧ B2:0.8 H1:0.2 ← B1:0.7 ∧ B2:0.8 0.0 0.3 [Broecheler, et al., UAI ‘1
- 27. Probabilistic Soft Logic W: H1 ∨... Hm ← B1 ∧ B2 ∧ ... Bn Rule Weights Weighted Distance to Satisfaction - d(R,I) = W max( ∧ (B1,..,Bn) - ∨ (H1,..,Hm) , 0) [Broecheler, et al., UAI ‘1
- 28. Probabilistic Soft Logic Let’s Review Given a data set and a PSL program, we can construct a set of ground rules. Some of the atoms have fixed truth values and some have unknown truth values. For every assignment of truth values to the unknown atoms, we get a set of weighted distances from satisfaction. How to decide which is best?
- 29. Probabilistic Soft Logic Probabilistic Foundation
- 30. Probabilistic Soft Logic Probabilistic Model Probability density over interpretation I Normalization constant Set of ground rules Distance exponent in {1, 2} Rule’s weight Rule’s distance to satisfaction
- 31. Probabilistic Soft Logic Hinge-loss Markov Random Fields Subject to arbitrary linear constraints PSL models ground out to HL-MRFs Log-concave!
- 32. Probabilistic Soft Logic MPE Inference
- 33. Probabilistic Soft Logic Inferring Most Probable Explanations Objective: Convex optimization Decomposition-based inference algorithm using the ADMM framework
- 34. Probabilistic Soft Logic Alternating Direction Method of Multipliers • We perform inference using the alternating direction method of multipliers (ADMM) • Inference with ADMM is fast, scalable, and straightforward • Optimize subproblems (ground rules) independently, in parallel • Auxiliary variables enforce consensus across subproblems [Bach et al., NIPS ’12]
- 35. Probabilistic Soft Logic Inference Algorithm Initialize local copies of variables and Lagrange multipliers Begin inference iterations Simple updates solve subproblems for each potential... ...and each constraint Average to update global variables and clip to [0,1] [Bach, et al., Under revie
- 36. Probabilistic Soft Logic ADMM Scalability 0 100 200 300 400 500 600 125000 225000 325000 Timeinseconds Number of potential functions and constraints ADMM Interior-point method [Bach, et al., NIPS ‘12]
- 37. Probabilistic Soft Logic ADMM Scalability [Bach, et al., Under revie
- 38. Probabilistic Soft Logic Distributed MPE Inference: MapReduce Implementation z1z1 zq zqz1 z2z2 zp sub problem local variable copy Mapper z1 z2z1 z1 z2 zq zq zp Reducer update global component load global variable X as side data Job Bootstrap HDFS or HBase read/write subproblem write new global variable read global variable X Hui Miao, Xiangyang Liu
- 39. Probabilistic Soft Logic Distributed MPE Inference: GraphLab Implementation . . . . . . . . . . . . sub problem node global variable component gather get z apply update y update x scatter notify z gather get local z,y apply update z scatter unless converge notify X update i update i+1 Hui Miao, Xiangyang Liu
- 40. Probabilistic Soft Logic Weight Learning
- 41. Probabilistic Soft Logic Weight Learning Learn from training data No need to hand-code rule-weights Various methods: - approximate maximum likelihood [Broecheler et al., UAI ’10] - maximum pseudolikelihood - large-margin estimation [Bach, et al., UAI ’13]
- 42. Probabilistic Soft Logic Weight Learning State-of-the-art supervised-learning performance on - Collective classification - Social-trust prediction - Preference prediction - Image reconstruction [Bach, et al., UAI ’13]
- 43. Probabilistic Soft Logic Foundations Summary
- 44. Probabilistic Soft Logic Foundations Summary Design probabilistic models using declarative language - Syntax based on first-order logic Inference of most-probable explanation is fast convex optimization (ADMM) Learning algorithms for training rule weights from labeled data
- 45. Probabilistic Soft Logic PSL Applications
- 46. Probabilistic Soft Logic Document Classification 2 2 2 2 2A B A or B? A or B? A or B? Given a networked collection of documents Observe some labels Predict remaining labels using link direction inferred class label [Bach, et al., UAI ’13]
- 47. Probabilistic Soft Logic Computer Vision Applications Low-level vision: - image reconstruction High-level vision: - activity recognition in videos
- 48. Probabilistic Soft Logic Image Reconstruction RMSE reconstruction error [Bach, et al., UAI ’13]
- 49. Probabilistic Soft Logic Activity Recognition in Videos crossing waiting queueing walking talking dancing jogging [London, et al., Under revi
- 50. Probabilistic Soft Logic Results on Activity Recognition Recall matrix between different activity types Accuracy metrics compared against baseline features [London, et al., Under revi
- 51. Probabilistic Soft Logic Social Trust Prediction Competing models from social psychology of strong ties - Structural balance [Granovetter ’73] - Social status [Cosmides et al., ’92] Leskovec, Huttenlocher, & Kleinberg, [2010]: effects of both models present in online social networks
- 52. Probabilistic Soft Logic Structural Balance vs. Social Status Structural balance: strong ties are governed by tendency toward balanced triads - e.g., the enemy of my enemy... Social status: strong ties indicate unidirectional respect, “looking up to”, expertise status - e.g., patient-nurse-doctor, advisor-advisee
- 53. Probabilistic Soft Logic Structural Balance in PSL [Huang, et al., SBP ‘1
- 54. Probabilistic Soft Logic Structural Balance in PSL [Huang, et al., SBP ‘1
- 55. Probabilistic Soft Logic Social Status in PSL [Huang, et al., SBP ‘1
- 56. Probabilistic Soft Logic Social Status in PSL [Huang, et al., SBP ‘1
- 57. Probabilistic Soft Logic Experiments User-user trust ratings from two different online social networks Observe some ratings, predict held-out Eight-fold cross validation on two data sets: - FilmTrust - movie review network, trust ratings from 1-10 - Epinions - product review network, trust / distrust ratings {-1, 1} [Huang, et al., SBP ‘1
- 58. Probabilistic Soft Logic Compared Methods TidalTrust: graph-based propagation of trust - Predict trust via breadth-first search to combine closest known relationships EigenTrust: spectral method for trust - Predict trustworthiness of nodes based on eigenvalue centrality of weighted trust network Average baseline: predict average trust score for all relationships [Huang, et al., SBP ‘1
- 59. Probabilistic Soft Logic FilmTrust Experiment Normalize [1,10] rating to [0,1] Prune network to largest connected-component 1,754 users, 2,055 relationships Compare mean average error, Spearman’s rank coefficient, and Kendall-tau distance * measured on only non-default predictions • PSL-Status and PSL-Balance disagree on 514 relationships [Huang, et al., SBP ‘1
- 60. Probabilistic Soft Logic Epinions Experiment Snowball sample of 2,000 users from Epinions data set 8,675 trust scores normalized to {0,1} Measure area under precision-recall curve for distrust edges (rarer class) [Huang, et al., SBP ‘1
- 61. Probabilistic Soft Logic Knowledge Graph Identification Problem: Collectively reason about noisy, inter-related fact extractions Task: NELL fact-promotion (web-scale IE) - Millions of extractions, with entity ambiguity and confidence scores - Rich ontology: Domain, Range, Inverse, Mutex, Subsumption Goal: Determine which facts to include in NELL’s knowledge base Jay Pujara, Hui Miao, William Cohen
- 62. Probabilistic Soft Logic PSL Rules Candidate Extractions: - CandRel_CMC(E1,E2,R) => Rel(E1,E2,R) - CandLbl_Morph(E1,L) => Lbl(E1,L) Entity Resolution: - SameEntity(E1,E2) & Lbl(E1,L) => Lbl(E2,L) - SameEntity(E1,E2) & Rel(E1,X,R) => Rel(E2,X,R) Ontological Rules: - Domain(R,L) & Rel(E1,E2,R) => Lbl(E1,L) - Mut(L1,L2) & Lbl(E,L1) => ~Lbl(E,L2)
- 63. Probabilistic Soft Logic Results Data: Iteration 165 of NELL - 1.2M extractions - 68K ontological constraints - 14K labeled instances (Jiang, 2012) - NELL & MLN baselines (Jiang, 2012) F1 Precision Recall AUC-PR NELL .673 .801 .580 .765 MLN .836 .837 .836 .899 PSL .841 .773 .922 .882
- 64. Probabilistic Soft Logic Schema Matching Correspondences between source and target schemas Matching rules - ‘’If two concepts are the same, they should have similar subconcepts’’ - ‘’If the domains of two attributes are similar, they may be the same’’ Organization Customers Service & Products provides buys Company Customer Products & Services develop buys Portfolios includes develop(A, B) <= provides(A, B) Company(A) <= Organization(A) Products&Services(B) <= Service&Products(B)
- 65. Probabilistic Soft Logic Schema Mapping Input: Schema matches Output: S-T query pairs (TGD) for exchange or mediation Mapping rules - “Every matched attribute should participate in some TGD.” - “The solutions to the queries in TGDs should be similar.” Organization Customers Service & Products provides buys Company Customer Products & Services develop buys Portfolios includes ∃Portfolio P, develop(A, P) ∧ includes(P, B) <= provides(A, B) . . . Alex Memory, Angelika Kimmig
- 66. Probabilistic Soft Logic Learning Latent Groups Can we better understand political discourse in social media by learning groups of similar people? Case study: 2012 Venezuelan Presidential Election Incumbent: Hugo Chávez Challenger: Henrique Capriles Left: This photograph was produced by Agência Brasil, a public Brazilian news agency. This file is licensed under the Creative Commons Attribution 3.0 Brazil license. Right: This photograph was produced by Wilfredor. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. [Bach, et al., Under revi
- 67. Probabilistic Soft Logic Learning Latent Groups South American tweets collected from 48-hour window around election. Selected 20 top users Candidates, campaigns, media, and most retweeted 1,678 regular users interacted with at least one top user and used at least one hashtag in another tweet Those regular users had 8,784 interactions with non-top users [Bach, et al., Under revi
- 68. Probabilistic Soft Logic Learning Latent Groups [Bach, et al., Under revi
- 69. Probabilistic Soft Logic Learning Latent Groups [Bach, et al., Under revi
- 70. Probabilistic Soft Logic Learning Latent Groups [Bach, et al., Under revi
- 71. Probabilistic Soft Logic Learning Latent Groups [Bach, et al., Under revi
- 72. Probabilistic Soft Logic Other LINQS Projects Drug-target interaction: Shobeir Fakhraei MOOC user-role prediction and expert identification: Arti Ramesh Semantic-role labeling: Arti Ramesh and Alex Memory Optimal source selection for data integration: Theo Rekatsinas Learning theory in non-I.I.D. settings: Ben London, Bert Huang Collective stability [London et al, ICML13] Scalable graph analysis using GraphLab: Hui Miao, Walaa Eldin Moustafa Uncertain graph models: Walaa Eldin Moustafa
- 73. Probabilistic Soft Logic Conclusion
- 74. Probabilistic Soft Logic Conclusion PSL: expressive framework for structured problems scalable Much ongoing work, including incorporating hidden variables and structure learning, distributing Very interested in applying it to a variety of domains, especially in computational social science We encourage you to try it! http://psl.umiacs.umd.edu
- 75. Probabilistic Soft Logic psl.umiacs.umd.edu

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