MS Thesis Defense Rohit Raghunathan August 19 th , 2011 Committee Members Dr. Subbarao Kambhampti (Chair) Dr. Joohyun

1. An Investigation of the cost and accuracy tradeoffs of Supplanting AFDs with Bayes Network in Query Processing in the Presence of Incompleteness in Autonomous Databases MS Thesis Defense RohitRaghunathan August 19th, 2011 Committee Members Dr. Subbarao Kambhampti (Chair) Dr. Joohyung Lee Dr. Huan Liu

2. Overview of the talk • Introduction to Incomplete Autonomous Databases • Overview of QPIAD and shortcomings of AFD-based approaches • Our approach: Bayes network based imputation and query rewriting

3. Overview of the talk • Introduction to Incomplete Autonomous Databases • Overview of QPIAD and shortcomings of AFD-based approaches • Our approach: Bayes network based imputation and query rewriting

4. Introduction to Web databases • Many websites allow user query through a form based interface and are supported by backend databases • Consider used cars selling websites such as Cars.com, Yahoo! autos, etc

5. Incompleteness in Web databases • Web databases are often input by lay individuals without any curation. For e.g. Cars.com, Yahoo! Autos • Web databases are being populated using automated information extraction techniques which are inherently imperfect • Incomplete/Uncertain tuple: A tuple in which one or more of its attributes have a missing value

6. Problem Statement • Many entities corresponding to tuples with missing values might be relevant to the user query • Traditional query processing does not retrieve such tuples Q: Make = Honda

7. Dimensions of the problem • Single vs Multiple missing values • Multiple missing values requires capturing the correlations between them • Imputation vs Query Rewriting • Imputation can look at all available evidence • Query Rewriting requires finding the smallest number of evidences • Looking at all evidences -> reduces throughput • Looking at very few evidences -> reduction in precision • Need to find middle ground User Q: Model = A8 Rewritten Query Make = Audi ^ Body = Sedan

8. Overview of the talk • Introduction to Incomplete Autonomous Databases • Overview of QPIAD and shortcomings of AFD-based approaches • Our approach: Bayes network based imputation and query rewriting

9. Approximate Functional Dependencies (AFDs) • AFDs are Functional Dependencies that hold on all but a small fraction of the database Model  Body : 0.75 Make Body : 0.75 Model  Make : 1.0 • An AFD is of the form XA • where X is a set of attributes and A is a single attribute • An attribute can have multiple rules

10. Overview of QPIAD Q: Body = Sedan • QPIAD uses AFDs and Naïve Bayes Classifiers to retrieve relevant uncertain answers • When mediator has access privileges to modify the underlying data source • Missing values can be completed by a simple classification task. (Imputation) • After which Traditional query processing will suffice • When mediators do not have such privileges • Generate a set of rewritten queries and issue it to the autonomous database (Query Rewriting) Issuing Q1 : Model = Tl Q2 : Model = 745 will retrieve relevant incomplete answers T2 and T4. • QPIAD uses only the highest confidence AFD of each attribute for imputation and Query Rewriting • Techniques for combining multiple AFDs shown to be ineffective Relevant incomplete answers Model  Body : 0.75

11. Shortcomings of AFD-based approaches • Principles of locality and detachment do not hold for uncertain reasoning • Model  Body (0.7) • This intuitively means that model of a car determines the body of a car with a probability of 0.7 when no other evidence is available. • When other evidences are present, there is no easy way to combine the probabilities

12. Shortcomings of AFD-based approaches • Imputing the missing values in T2 using a single AFD; ignore influence from other attributes • Imputing missing values in T1 ignores the correlations between the attributes Model and Year • Imputing missing values in T6 will get AFDs into cycles • Model  Make Make Model

13. Overview of the talk • Introduction to Incomplete Autonomous Databases • Overview of QPIAD and shortcomings of AFD-based approaches • Our approach: Bayes network based imputation and query rewriting • Introduction • Learning Bayes network models from data • Imputation • Single and multiple missing values • Varying levels of incompleteness in test data • Query Rewriting • Bayes network based rewriting • Comparison of Bayes network based rewriting and AFDs

14. Overview of the talk • Introduction to Incomplete Autonomous Databases • Overview of QPIAD and shortcomings of AFD-based approaches • Our approach: Bayes network based imputation and query rewriting • Introduction • Learning Bayes network models from data • Imputation • Single and multiple missing values • Varying levels of incompleteness in test data • Query Rewriting • Bayes network based rewriting • Comparison of Bayes network based rewriting and AFDs

15. Bayes network Year • A Bayes network is a DAG representing the probabilistic dependencies between attributes • It is a compact representation of the full joint distribution • Therefore influence from all variables are accounted • It represents the generative model of the autonomous database Model Mileage Make Body CPDs model the strength of the probabilistic dependencies

16. Challenges in using Bayes networks for handling incompleteness in Autonomous databases • Learning and inference with Bayes networks is computationally harder than AFDs • Learning the topology and parameters from data involves searching over search the space of topologies • But can be done offline • Inference in a general Bayes network is intractable. • But can use approximate inference Question: Can we get benefits of exact inference while containing costs?

17. Overview of the talk • Introduction to Incomplete Autonomous Databases • Overview of QPIAD and shortcomings of AFD-based approaches • Our approach: Bayes network based imputation and query rewriting • Introduction • Learning Bayes network models from data • Imputation • Single and multiple missing values • Varying levels of incompleteness in test data • Query Rewriting • Bayes network based rewriting • Comparison of Bayes network based rewriting and AFDs

18. Learning a Bayes network model • Structure & Parameter Learning From Data • Challenge: Involves searching over topologies • Use Banjo Software Package as black-box. • Experiments show learned topology is robust w.r.t • Sample size(5-20%) – same topology • Search time(5-30 minutes) – same topology • Max parent count (2-4) – same topology; significantly higher networks examined in case of 2.

19. Inference in Bayes networks • Exact Techniques • NP-hard, in the general case. Therefore, do not scale well with increase in incompleteness • Junction Tree (fastest; but inapplicable when query variables do not form a clique) • Variable Elimination • Approximate Techniques (Scales well; retaining accuracy of exact methods) • Gibbs Sampling • Using Infer.net package allows us to use Expectation Propagation inference

20. Overview of the talk • Introduction to Incomplete Autonomous Databases • Overview of QPIAD and shortcomings of AFD-based approaches • Our approach: Bayes network based imputation and query rewriting • Introduction • Learning Bayes network models from data • Imputation • Single and multiple missing values • Varying levels of incompleteness in test data • Query Rewriting • Bayes network based rewriting • Comparison of Bayes network based rewriting and AFDs

21. Imputation • Experimental Setup • Test Databases: Cars.com database containing 8K tuples and Adult Database from UCI repository containing 15K tuples • Bayes net inference • Exact inference: Junction Tree, Variable Elimination • Approximate inference: Gibbs Sampling

22. Imputation • Remove all the values for the attribute being predicted • Substitute missing value with most likely value • AFD-approach • Use only highest confidence AFD (Use all attributes if confidence is low, e.g., mileage(Cars)). Called Hybrid-one by authors of QPIAD. • Bayes net • Infer the posterior distribution of missing attribute, given evidences of the other attributes in the tuple

23. Overview of the talk • Introduction to Incomplete Autonomous Databases • Overview of QPIAD and shortcomings of AFD-based approaches • Our approach: Bayes network based imputation and query rewriting • Introduction • Learning Bayes network models from data • Imputation • Single and multiple missing values • Varying levels of incompleteness in test data • Query Rewriting • Bayes network based rewriting • Comparison of Bayes network based rewriting and AFDs

24. Imputation- single missing attribute • Significant difference for attributes Model and Year. • AFDs using only the highest confidence rule, and ignore others. • Attempts at combining evidences from multiple rules have been ineffective. • Bayes nets systematically combines all evidences.

25. Imputation- multiple missing attributes • AFD-approach • Predict each missing value independently • Can get in cycles • Bayes net • Computes the Joint distribution over the missing attributes. Make  Model Model  Make

26. Imputation- multiple missing attributes • When missing attributes are correlated, they often get into cycles • Only 9 out of 20 combinations could be predicted when 3 attributes are missing • AFD accuracies are lower as they use a single rule independently for prediction • BNs systematically combine evidences from multiple sources and capture correlations by finding the joint distribution • When attributes are D-separated and involve attributes which have similar prediction accuracies for both methods, there is no difference in accuracy Year Mileage Model Price Make Body

27. Overview of the talk • Introduction to Incomplete Autonomous Databases • Overview of QPIAD and shortcomings of AFD-based approaches • Our approach: Bayes network based imputation and query rewriting • Introduction • Learning Bayes network models from data • Imputation • Single and multiple missing values • Varying levels of incompleteness in test data • Query Rewriting • Bayes network based rewriting • Comparison of Bayes network based rewriting and AFDs

28. Imputation- Increase in incompleteness in test data • Evidence for predicting missing values reduces with increase in incompleteness • AFD-approach • Chain missing values in determining set of AFD • Bayes net • No change. Just compute posterior distribution of the attributes to be imputed given the evidence. Q: Model = 745 AFDs: Make, Body  Model Year  Body

29. Imputation- Increase in incompleteness in test data

30. Time Taken For Imputation BN-Gibbs retains the accuracy edge of BN-Exact while containing costs

31. Overview of the talk • Introduction to Incomplete Autonomous Databases • Overview of QPIAD and shortcomings of AFD-based approaches • Our approach: Bayes network based imputation and query rewriting • Introduction • Learning Bayes network models from data • Imputation • Single and multiple missing values • Varying levels of incompleteness in test data • Query Rewriting • Bayes network based rewriting • Comparison of Bayes network based rewriting and AFDs

32. Query Rewriting • When mediators do not have access privileges, missing values cannot be substituted as in the case of imputation. • Need to generate and send “rewritten” queries to retrieve relevant uncertain answers.

33. Query Rewriting– Single-attribute queries Q: Body = Sedan Relevant incomplete answers CERTAIN ANSWERS (BASE RESULT SET) Can retrieve T2 with Q’1: Model = Tl T4 with Q’2: Model = 745

34. Generating Rewritten Queries CERTAIN ANSWERS (BASE RESULT SET) Year Bayes Networks ATTRIBUTES: ALL ATTRIBUTES IN MARKOV BLANKET (BN-ALL-MB) Q’1: Model = 745 Q’2: Model = Tl AFDs ATTRIBUTES: DETERMINING SET OF AFD Model  Body : 0.9 Q’1: Model = 745 Q’2: Model = Tl Model Mileage Body Make Given evidence of all attributes in MARKOV BLANKET, an attribute is independent of ALL other attributes Q: Body = Sedan

35. Ranking Rewritten queries • All queries may not be equally good in retrieving relevant answers • “tl” model cars are more likely to be sedans than a car with “745” model • Rank queries based on their expected precision (ExpPrec) ExpPrec(Q) = P(Am=vm|ti) where tiεПMB(Am)(RS(Q)) for Bayes nets where tiεПdtrSet(Am)(RS(Q)) for AFDs Q1’: Model = ‘tl’. ExpPrec(Q1’)= P(Body=Sedan|Model=tl) = 1 Q2’= Model = ‘745’. ExpPrec(Q2’)= P(Body=Sedan|Model=745) = 0.6 AFDs Use Naïve Bayes Classifiers Bayes Networks Inference in bayes network

36. Ranking Rewritten Queries- only K queries • When database or network resources are limited, the mediator can choose to issue the top-Kqueries to get the most relevant uncertain answers • It is important to carefully trade precision with throughput • Use F-measure metric (idea borrowed from QPIAD) P – expected precision (e.g. P(Model=745|Make =BMW) ) R – expected recall R = expected precision * expected selectivity expected selectivity = Sample Selectivity * Sample Ratio Sample Ratio estimated from cardinalities result sets from sample and original database =0 – only precision

37. Experimental Setup • Test databases: Cars database consisting of 55K tuples and Adult database consisting of 15K tuples • Training set 15% of the database. • Test data split in two halves- • One half contains no incompleteness and is used to return the base result set • In the other half all query-constrained attributes are made null • A copy of test data is used as the ground truth to compute precision and recall • This is an aggressive setup since most databases have <50% incompleteness

38. BN-All-MB vs AFD BN-All-MB: P(Make=bmw|model= 330) AFD: P(Make=bmw|model=330) Q: Make • When size of determining set > 1 Expected Precision values represented of AFDs (represented by NBCs) are inaccurate • Actual precision is lower for AFDs because their expected precisions are inaccurate

39. Shortcoming of BN-All-MB Year • Throughput of queries reduces drastically as markov blanket size increases • Use F-measure based ranking to increase recall When almost all queries have very low throughput there is simply no way to increase recall Model Mileage Body Make Q: Model = 745 Q’1: MakeᴧBodyᴧYear Q’2: MakeᴧBodyᴧYear Q’3: MakeᴧBodyᴧYear

40. BN-Beam (Single-attribute queries) Q: Model = 745 Year Mileage Model Candidate Attribute Set = {Year, Make, Body} Body Make

41. Best rewritten queries of size 1 BN-Beam Year Body At Level L all (partial) queries have ≤ L attributes constrained Pick Top-K queries at each level based on F-measure metric Issue to database in the increasing order of expected precision P – expected precision (e.g. P(Model=745|Make =BMW) ) R – expected recall R = expected precision * expected selectivity Expected selectivity = Sample Selectivity * Sample Ratio Sample Ratio estimated from cardinalities result sets from sample and original database

42. BN-Beam vs BN-All-MB Recall Plot Results for Top-10 queries for user query Year = 2002 Precision Plot • Increasing α does not increase recall of BN-All-MB • BN-Beam increases recall without a catastrophic reduction in precision

43. Multi-attribute queries • Contribution to QPIAD • Aim: To retrieve relevant uncertain answers with multiple-missing values on query-constrained attributes.

44. Multi-attribute queries QPIAD BN-Beam Base result set • Q: Make = BMW ʌ Mileage = 40000 • Base result set = T5, T6 • QPIAD retrieves T1 and T2. • BN-Beam can also retrieve T3 and T4. • Candidate attribute set: union of attributes in the markov blanket of all constrained attributes • All other steps same as single-attribute query case

45. Comparison over multi-attribute queries • Two AFD approaches • AFD-All-Attributes: Creates a conjunctive query by joining all attributes in the determining set of the AFDs of the constrained attributes. Consider AFDs Model  Make Year  Mileage Q: Make = BMW ʌ Mileage = 40000 Expected Precision = Product of individual query’s expected precision Q’1: Model=745ᴧYear=2001 Q’2: Model=645ᴧYear=2001 Q’3: Model=745ᴧYear=2002 Q’4: Model=645ᴧYear=2002

46. BN-BeamvsAFD-All-Attributes Results for top-10 queries Q: Make ^ Mileage Precision of BN-Beam is competitive with AFD-All Attributes Recall of BN-Beam is higher • AFD-All-Attributes does not consider the joint distribution between the query-constrained attributes. • Leads to low throughput or even empty queries

47. Comparison of multi-attribute queries • AFD-Highest-Confidence: Uses only the AFD of the highest confidence constrained attribute for rewriting Q: Make = Dodge ᴧ Year = 2004 IGNORE all attributes other than Make AFD : Model  Make Q’1: Model=ram Q’2: Model= intrepid

48. BN-BeamvsAFD-Highest-Confidence Results for top-10 queries Q:Make ʌ Year (Car database) AFD-Highest-Confidence increases recall but NOT WITHOUT a CATASTROPHIC drop in precision

49. Summary • A comparison of cost and accuracy tradeoffs of using Bayes network models and AFDs for handling incompleteness in autonomous databases • Bayes nets have a significant edge over AFDs when missing values are on highly correlated attributes and at higher levels of incompleteness in test data. • Presented two approaches- BN-All-MB and BN-Beam for generating rewritten queries using Bayes networks. We showed that BN-Beam is able to retrieve tuples with higher recall than BN-All-MB. We compared Bayes network based rewriting with AFD based rewriting and found the former to retrieve results with higher precision and recall

50. Deviations From the Thesis Draft • CAVEAT: I found two bugs in my code (Query Rewriting section) • Corrected one bug (related to BN-based rewriting) • Will correct the other one (related to AFD-based rewriting) after the defense THANK YOU QUESTIONS?