Probabilistic Ranking of Database Query Results Surajit Chaudhuri, Microsoft Research Gautam Das, Microsoft Research Vagelis Hristidis, Florida International University Gerhard Weikum, MPI Informatik Presented by Weimin He CSE@UTA

Outline Motivation Problem Definition System Architecture Construction of Ranking Function Implementation Experiments Conclusion and open problems 11/21/2018 Weimin He CSE@UTA

Motivating example Realtor DB: Table D=(TID, Price , City, Bedrooms, Bathrooms, LivingArea, SchoolDistrict, View, Pool, Garage, BoatDock) SQL query: Select * From D Where City=Seattle AND View=Waterfront 11/21/2018 Weimin He CSE@UTA

Motivation Many-answers problem Two alternative solutions: Query reformulation Automatic ranking Apply probabilistic model in IR to DB tuple ranking 11/21/2018 Weimin He CSE@UTA

Problem Definition Given a database table D with n tuples {t1, …, tn} over a set of m categorical attributes A = {A1, …, Am} and a query Q: SELECT * FROM D WHERE X1=x1 AND … AND Xs=xs where each Xi is an attribute from A and xi is a value in its domain. The set of attributes X ={X1, …, Xs} is known as the set of attributes specified by the query, while the set Y = A – X is known as the set of unspecified attributes Let be the answer set of Q How to rank tuples in S and return top-k tuples to the user ? 11/21/2018 Weimin He CSE@UTA

System Architecture 11/21/2018 Weimin He CSE@UTA

Intuition for Ranking Function Select * From D Where City=“Seattle” And View=“Waterfront” Score of a Result Tuple t depends on Global Score: Global Importance of Unspecified Attribute Values E.g., Homes with good school districts are globally desirable Conditional Score: Correlations between Specified and Unspecified Attribute Values E.g., Waterfront  BoatDock 11/21/2018 Weimin He CSE@UTA

Probabilistic Model in IR Bayes’ Rule Product Rule Document t, Query Q R: Relevant document set R = D - R: Irrelevant document set 11/21/2018 Weimin He CSE@UTA

Adaptation of PIR to DB Tuple t is considered as a document Partition t into t(X) and t(Y) t(X) and t(Y) are written as X and Y Derive from initial scoring function until final ranking function is obtained 11/21/2018 Weimin He CSE@UTA

Preliminary Derivation 11/21/2018 Weimin He CSE@UTA

Limited Independence Assumptions Given a query Q and a tuple t, the X (and Y) values within themselves are assumed to be independent, though dependencies between the X and Y values are allowed 11/21/2018 Weimin He CSE@UTA

Continuing Derivation 11/21/2018 Weimin He CSE@UTA

Workload-based Estimation of Assume a collection of “past” queries existed in system Workload W is represented as a set of “tuples” Given query Q and specified attribute set X, approximate R as all query “tuples” in W that also request for X All properties of the set of relevant tuple set R can be obtained by only examining the subset of the workload that caontains queries that also request for X 11/21/2018 Weimin He CSE@UTA

Final Ranking Function 11/21/2018 Weimin He CSE@UTA

Pre-computing Atomic Probabilities in Ranking Function Relative frequency in W Relative frequency in D (#of tuples in W that conatains x, y)/total # of tuples in W (#of tuples in D that conatains x, y)/total # of tuples in D 11/21/2018 Weimin He CSE@UTA

Example for Computing Atomic Probabilities Select * From D Where City=“Seattle” And View=“Waterfront” Y={SchoolDistrict, BoatDock, …} D=10,000 W=1000 W{excellent}=10 W{waterfront &yes}=5 p(excellent|W)=10/1000=0.1 p(excellent|D)=10/10,000=0.01 p(waterfront|yes,W)=5/1000=0.005 p(waterfront|yes,D)=5/10,000=0.0005 11/21/2018 Weimin He CSE@UTA

Indexing Atomic Probabilities {AttName, AttVal, Prob} B+ tree index on (AttName, AttVal) {AttName, AttVal, Prob} B+ tree index on (AttName, AttVal) {AttNameLeft, AttValLeft, AttNameRight, AttValRight, Prob} B+ tree index on (AttNameLeft, AttValLeft, AttNameRight, AttValRight) {AttNameLeft, AttValLeft, AttNameRight, AttValRight, Prob} B+ tree index on (AttNameLeft, AttValLeft, AttNameRight, AttValRight) 11/21/2018 Weimin He CSE@UTA

Scan Algorithm Preprocessing - Atomic Probabilities Module Computes and Indexes the Quantities P(y | W), P(y | D), P(x | y, W), and P(x | y, D) for All Distinct Values x and y Execution Select Tuples that Satisfy the Query Scan and Compute Score for Each Result-Tuple Return Top-K Tuples 11/21/2018 Weimin He CSE@UTA

Beyond Scan Algorithm Scan algorithm is Inefficient Many tuples in the answer set Another extreme Pre-compute top-K tuples for all possible queries Still infeasible in practice Trade-off solution Pre-compute ranked lists of tuples for all possible atomic queries At query time, merge ranked lists to get top-K tuples 11/21/2018 Weimin He CSE@UTA

Two kinds of Ranked List CondList Cx {AttName, AttVal, TID, CondScore} B+ tree index on (AttName, AttVal, CondScore) GlobList Gx {AttName, AttVal, TID, GlobScore} B+ tree index on (AttName, AttVal, GlobScore) 11/21/2018 Weimin He CSE@UTA

Index Module 11/21/2018 Weimin He CSE@UTA

List Merge Algorithm 11/21/2018 Weimin He CSE@UTA

Experimental Setup Datasets: MSR HomeAdvisor Seattle (http://houseandhome.msn.com/) Internet Movie Database (http://www.imdb.com) Software and Hardware: Microsoft SQL Server2000 RDBMS P4 2.8-GHz PC, 1 GB RAM C#, Connected to RDBMS through DAO 11/21/2018 Weimin He CSE@UTA

Quality Experiments Conducted on Seattle Homes and Movies tables Collect a workload from users Compare Conditional Ranking Method in the paper with the Global Method [CIDR03] 11/21/2018 Weimin He CSE@UTA

Quality Experiment-Average Precision For each query Qi , generate a set Hi of 30 tuples likely to contain a good mix of relevant and irrelevant tuples Let each user mark 10 tuples in Hi as most relevant to Qi Measure how closely the 10 tuples marked by the user match the 10 tuples returned by each algorithm 11/21/2018 Weimin He CSE@UTA

Quality Experiment- Fraction of Users Preferring Each Algorithm 5 new queries Users were given the top-5 results 11/21/2018 Weimin He CSE@UTA

Performance Experiments Datasets Compare 2 Algorithms: Scan algorithm List Merge algorithm 11/21/2018 Weimin He CSE@UTA

Performance Experiments – Pre-computation Time 11/21/2018 Weimin He CSE@UTA

Performance Experiments – Execution Time 11/21/2018 Weimin He CSE@UTA

Performance Experiments – Execution Time 11/21/2018 Weimin He CSE@UTA

Performance Experiments – Execution Time 11/21/2018 Weimin He CSE@UTA

Conclusion and Open Problems Automatic ranking for many-answers Adaptation of PIR to DB Mutiple-table query Non-categorical attributes 11/21/2018 Weimin He CSE@UTA