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A Formal Approach to Finding Explanations for Database Queries

Sudeepa RoyDan Suciu

University of Washington, Seattle

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We need to understand “Big Data”

ref. Big data whitepaper, Jagadish et al., 2011-12

D1

D2

D3

Data Analysis System

1. Acquire Data 2. Prepare Data 3. Store in DB

Clean Extract Feature Integrate

5. Plot Graphs6. Ask Questions! 4. Run Queries

Do you have an

explanation?

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• Why is there a peak for #sigmod papers from industry during 2000-06,

while #academia papers kept increasing?

• Why is #SIGMOD papers #PODS papers in UK?

Sample Questions

Dataset: Pre-processed DBLP + Affiliation dataDisclaimer: Not all authors have affiliation info

Explanations by our approach at the end

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“What was the cause of the observation?”• Not simple association or correlation• e.g. People having headache drink coffee Does coffee cause headache? Does headache lead to drinking coffee?

Ideal goal: Why Causality

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• Has been studied for many years (Hume1748)• Extensive study in AI over the last decade by Judea Pearl using the notion of intervention:

X is a cause of Y, if removal of X also removes Y keeping other conditions unchanged

• Needs controlled experiments • Not always possible with a database

But, causality is hard…

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Realistic Database-y goal: Why Explanation

Causality ExplanationControlled Experiment Input database and observed query outputs

Causal Paths PK-FK constraints and their generalization

Intervention Remove input tuples,query output should change

Top Causes Top explanations will change the outputin the expected direction to a greater extent

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Previous/Related Work• Causality in databases

– Meliou et al.’10, Meliou et al.’11

• Explanations in databases– Explaining outliers in aggregate queries: Wu-Madden’13– Specific applications (Map-Reduce, Access log, User Rating,…): e.g. Khoussainova et al.’12, Fabbri et al.’12, Das et al.’11

• Other related topics– Provenance, deletion propagation: e.g. Green et al.’07, Buneman et al.’01– Missing answer/Why-Not: e.g. Herschel et al.’09, Huang et al.’10, Chapman-Jagadish’09– Finding causal structure/data mining: e.g. Silverstein et al.’00– OLAP: e.g. Sarawagi-Sathe’01

• Informally use intervention• Explanation = predicate• Mostly single table, no join

• Pearl’s notion of causality and intervention• Causal structure from input to output by lineage• Cause = Individual input tuples, not predicates• No inherent causal structure in input data

Upcoming VLDB 2014 Tutorial“Causality and Explanations in Databases”Alexandra Meliou, Sudeepa Roy, Dan Suciu

This work:• Formal framework of explanations (= predicates) and theoretical analysis – causal structure within input data independent of

queries or user questions– allow multiple tables and joins

• Optimizations and Evaluation– find top explanations using data cube

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Outline

• Framework

• Causal Paths and Intervention

• Computing Intervention

• Optimization: Ranking Explanations by Data Cube

• Evaluation

• Future Work

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Input and Output

Run Group-By Queries and Plot

Toy DBLP database Output Plot

User question • Numerical expression E• Direction: high/low

E = (q1/q3) / (q2/q4)Direction = high

Why is q1/q3 q2/q4

e.g. q1

select count(distinct x.pubid)from Author x, Authored y, Publication zwhere x.id = y.id and y.pubid = z.pubid and z.venue = ’SIGMOD’ and 2000 <= z.year and z.year <= 2004 and x.domain = ’com’

These values will vary for q2, q3, q4

Input

Explanation(s) ф : Predicate on attributese.g.[name = ‘JG’][name = ‘JG’] [inst = ‘C.edu’][name = ‘JG’] [year = 2007]Note: attr from multiple tables

Output

E should change when database is “intervened “with

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Causal Paths by Foreign Key Constraints

• Causal path X Y: removing X removes Y• Analogy in DB: Foreign key constraints and cascade delete semantics

Author(id, name, inst, dom)

Authored(id, pubid)

Publication(pubid, year, venue)

Standard F.K.(cascade delete)

Back and Forth F.K.(cascade delete

+reverse cascade delete)ForwardReverse

Intuition: • An author can exist if one of her papers is deleted• A paper cannot exist if any of its co-authors is deleted

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Causal Paths and InterventionCandidate explanation ф : [name = ‘RR’]

ReverseForward

Intervention ф : Tuples T0 that satisfy ф + Tuples reachable from T0

Given ф, computation of ф requires a recursive query

Multiple tables

require universal

table

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Objective: top-k explanations• Consider user question: Why is E = (q1/q2)/(q3/q4) low,

Find top-k explanations ф w.r.t a score ф = E(D - ф)

The obvious approach: Two sources of complexity

1. For all possible predicates ф– Compute the intervention ф for ф

– Delete tuples in ф from D

– Evaluate q1, q2, q3, q4 on D – ф

– Compute E(D - ф)

2. Find top explanations with highest scores E(D - ф) (top-k)

Recursion

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Computing ф by a Recursive Program

Properties:1. Program has a unique least fixpoint which can be

obtained in poly-time (n = |D| steps)

2. Program is not monotone in database, • i.e., if D D’, not necessarily (D) (D’)• Therefore not expressible in datalog• But expressible in datalog + negation

Delete from universal table

tuples |= ф Cascade delete

Reverse Cascade delete

ф is fixed

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Convergence Depends on Schema

• Convergence in ≤ 4 steps

S

R T

• Convergence requiresn - 1 steps

Can be generalized

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Finding Top-k Explanations with Data CubeFor all possible predicates ф

– Compute the intervention ф for ф

– …..

#Possible predicates is huge

Running FOR LOOP is expensive

Running RECURSION is expensive

Optimization: OLAP data cube

why (q1*q4)/(q2*q3) high?

Suppose we want predicates on attributes [name, inst, venue] as explanations

group by name, inst, venuewith cube

name, inst, venue

e.g. Cube for q1e.g. Query for q1

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name Inst venue q1() - - - 1

RR - - 1

- M.com - 1

……..

q1: com, 2000-04 name Inst venue q2()

- - - 1

CM - - 1

- I.com - 1

……..

q2: com, 2007-11

name Inst venue q3()

- - - 1

JG - - 1

- C.Edu - 1

……..

q3: edu, 2000-04 name Inst venue q4()

- - - 1

JG - - 1

- C.Edu - 1

……..

q4: edu, 2007-11

Sketch of Algorithm with Data Cube

name Inst year E(D - D )

- - - JG - -RR - -- C.edu

1. (Outer)-join the cubes + compute score

Score• All computation done by DBMS

• But,− Cube Algorithm matches theory for some

inputs (e.g. single table, DBLP examples)

− For other inputs it is a heuristic (recursion is necessary)

2. Run Top-K

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Experiment 1: Data Cube Optimization vs. Iterative Algo

Natality Dataset 2010: (from National Center for Health Statistics (NCHS)). Single table with 233 attributes, ~4M entries, 2.89GB size.

More experiments in the paper

Data size vs. time

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Experiment 2: Scalability of the Data Cube Optimization

No. of attributes

E1E2

E1E2

E1 E2

# Aggregate queries in the User Question 2 4

# Data Cubes computed 2 4

# Joins of the Data Cubes to compute final table 1 3

Why (q1/q2) low Why (q1/q2)/(q3/q4) low

Data size vs. time(Max) No. of attributes in explanation predicates vs. time

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Qualitative Evaluation (DBLP)

Q. Why is there a peak for #sigmod papers from industry during 2000-06, while #academia papers kept increasing?

Intuition:1. If we remove these industrial labs and their senior researchers, the

peak during 2000-04 is more flattened2. If we remove these universities with relatively new but highly prolificdb groups, the curve for academia is less increasing

Hard due to lack of gold standard

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Qualitative Evaluation (DBLP)

Intuition:If we remove these leading theoretical DB researchers or their universities/cities,

the bar for UK will look different.

e.g. for UK, Originally: PODS = 62%, SIGMOD = 38%Removing all publications by Libkin: PODS = 46%, SIGMOD = 54%

Q. Why is #SIGMOD papers #PODS papers in UK?

P = 32, S = 3 P = 24, S = 1 P = 9, S = 0

P = 15, S = 2

source: DBLP

Not top expl.:Wenfei FanPeter Buneman…..

P = 15, S = 12

P = 6, S = 12

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Current/Future Work• Optimize for arbitrary SPJUA queries and schemas

– Go beyond data cube

• Model increasing/decreasing trend by linear regression (E = slope)• Ranking algorithm: simple, meaningful, diverse explanations• Prototype with a GUI

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Thank you

Questions?