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Tuffy Scaling up Statistical Inference in Markov Logic using an RDBMS

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1 Tuffy Scaling up Statistical Inference in Markov Logic using an RDBMS
Feng Niu, Chris Ré, AnHai Doan, and Jude Shavlik University of Wisconsin-Madison

2 Tuffy scales up Markov Logic by orders of magnitude using an RDBMS
One Slide Summary Machine Reading is a DARPA program to capture knowledge expressed in free-form text Similar challenges in enterprise applications We use Markov Logic, a language that allows rules that are likely – but not certain – to be correct Markov Logic yields high quality, but current implementations are confined to small scales Tuffy scales up Markov Logic by orders of magnitude using an RDBMS

3 Outline Markov Logic Tuffy the System Data model Query language
Inference = grounding then search Tuffy the System Scaling up grounding with RDBMS Scaling up search with partitioning

4 A Familiar Data Model Datalog? EDB IDB Markov Logic program
Datalog + Weights ≈ Markov Logic Relations with known facts Relations to be predicted EDB IDB

5 * [Richardson & Domingos 2006]
Markov Logic* Syntax: a set of weighted logical rules Weights: cost for rule violation Semantics: a distribution over possible worlds Each possible world 𝐼 incurs total cost cost(𝐼) Pr[𝐼] ∝⁡ exp⁡(−cost(𝐼)) Thus most likely world has lowest cost 3 wrote(s,t) ∧ advisedBy(s,p)  wrote(p,t) // students’ papers tend to be co-authored by advisors exponential models * [Richardson & Domingos 2006]

6 Markov Logic by Example
Rules 3 wrote(s,t) ∧ advisedBy(s,p)  wrote(p,t) // students’ papers tend to be co-authored by advisors 5 advisedBy(s,p) ∧ advisedBy(s,q)  p = q // students tend to have at most one advisor ∞ advisedBy(s,p)  professor(p) // advisors must be professors EDB IDB Evidence wrote(Tom, Paper1) wrote(Tom, Paper2) wrote(Jerry, Paper1) professor(John) … Query advisedBy(?, ?) // who advises whom

7 Inference Rules Inference Query Relations Evidence Relations MAP
regular tuples Marginal tuple probabilities

8 Inference Rules Query Relations Grounding Search Evidence Relations
Find tuples that are relevant (to the query) Find tuples that are true (in most likely world)

9 How to Perform Inference
Step 1: Grounding Instantiate the rules wrote(s, t) ∧ advisedBy(s, p)  wrote(p, t) 3 wrote(Tom, P1) ∧ advisedBy(Tom, Jerry)  wrote (Jerry, P1) 3 wrote(Tom, P1) ∧ advisedBy(Tom, Chuck)  wrote (Chuck, P1) 3 wrote(Chuck, P1) ∧ advisedBy(Chuck, Jerry)  wrote (Jerry, P1) 3 wrote(Chuck, P2) ∧ advisedBy(Chuck, Jerry)  wrote (Jerry, P2) … Grounding

10 How to Perform Inference
Step 1: Grounding Instantiated rules  Markov Random Field (MRF) A graphical structure of correlations 3 wrote(Tom, P1) ∧ advisedBy(Tom, Jerry)  wrote (Jerry, P1) 3 wrote(Tom, P1) ∧ advisedBy(Tom, Chuck)  wrote (Chuck, P1) 3 wrote(Chuck, P1) ∧ advisedBy(Chuck, Jerry)  wrote (Jerry, P1) 3 wrote(Chuck, P2) ∧ advisedBy(Chuck, Jerry)  wrote (Jerry, P2) … Nodes: Truth values of tuples Edges: Instantiated rules

11 How to Perform Inference
Step 2: Search Problem: Find most likely state of the MRF (NP-hard) Algorithm: WalkSAT*, random walk with heuristics Remember lowest-cost world ever seen advisee advisor Tom Jerry Chuck Search False True * [Kautz et al. 2006]

12 Outline Markov Logic Tuffy the System Data model Query language
Inference = grounding then search Tuffy the System Scaling up grounding with RDBMS Scaling up search with partitioning

13 Challenge 1: Scaling Grounding
Previous approaches Store all data in RAM Top-down evaluation [Singla and Domingos 2006] [Shavlik and Natarajan 2009] RAM size quickly becomes bottleneck Even when runnable, grounding takes long time

14 3 wrote(s, t) ∧ advisedBy(s, p)  wrote(p, t)
Grounding in Alchemy* Prolog-style top-down grounding with C++ loops Hand-coded pruning, reordering strategies 3 wrote(s, t) ∧ advisedBy(s, p)  wrote(p, t) For each person s: For each paper t: If !wrote(s, t) then continue For each person p: If wrote(p, t) then continue Emit grounding using <s, t, p> Grounding sometimes accounts for over 90% of Alchemy’s run time [*] reference system from UWash

15 Grounding in Tuffy Encode grounding as SQL queries
Executed and optimized by RDBMS

16 Grounding Performance
Tuffy achieves orders of magnitude speed-up Relational Classification Entity Resolution Alchemy [C++] 68 min 420 min Tuffy [Java + PostgreSQL] 1 min 3 min Evidence tuples 430K 676 Query tuples 10K 16K Rules 15 3.8K Yes, join algorithms & optimizer are the key!

17 Challenge 2: Scaling Search
Grounding Search

18 Challenge 2: Scaling Search
First attempt: pure RDBMS, search also in SQL No-go: millions of random accesses Obvious fix: hybrid architecture RDBMS RAM Grounding Search Alchemy Tuffy-DB Tuffy Problem: stuck if |MRF | > |RAM|!

19 Partition to Scale up Search
Observation MRF sometimes have multiple components Solution Partition graph into components Process in turn

20 Effect of Partitioning
Pro Con (?) Motivated by scalability Willing to sacrifice quality Scalability Parallelism What’s the effect on quality?

21 Partitioning Hurts Quality?
Alchemy took over 1 hr. Quality similar to Tuffy-no-part Relational Classification Goal: lower the cost quickly Partitioning can actually improve quality!

22 Partitioning (Actually) Improves Quality
Reason: Tuffy Tuffy-no-part WalkSATiteration cost1 cost2 cost1 + cost2 1 5 20 25 min

23 Partitioning (Actually) Improves Quality
Reason: Tuffy Tuffy-no-part WalkSATiteration cost1 cost2 cost1 + cost2 1 5 20 25 2 10 30 min

24 Partitioning (Actually) Improves Quality
Reason: Tuffy Tuffy-no-part WalkSATiteration cost1 cost2 cost1 + cost2 1 5 20 25 2 10 30 3 min cost[Tuffy] = 10 cost[Tuffy-no-part] = 25

25 Partitioning (Actually) Improves Quality
Theorem (roughly): Under certain technical conditions, component-wise partitioning reduces expected time to hit an optimal state by (2 ^ #components) steps. 100 components  100 years of gap!

26 In the paper: cost-based trade-off model
Further Partitioning Partition one component further into pieces Graph Scalability Quality Sparse / Dense In the paper: cost-based trade-off model

27 Conclusion Markov Logic is a powerful framework for statistical inference But existing implementations do not scale Tuffy scales up Markov Logic inference RDBMS query processing is perfect fit for grounding Partitioning improves search scalability and quality Try it out!

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