Relational Retrieval Using a Combination ofPath-Constrained Random Walks

Ni Lao

Joint work with William Cohen

2010.6.22

22

Outline

• Problem definition and related work

• Retrieval Models with PCRW (ECML PKDD 2010)– Path Ranking Algorithm (PRA) – Ext.1: query-independent experts– Ext.2: popular entity experts

• Comparing efficient random walk strategies (KDD 2010)– Sampling– Truncation

33

Scientific Literature• Can be represented as a labeled directed graph

– Typed nodes: documents, terms, metadata– Labeled edges: “authorOf”, “datePublished”

• Can support a family of typed proximity queries– Input: a set of query nodes + expected answer type– Output: a list of nodes of the desired answer type, ordered by proximity to

the query nodes

• Many tasks– ad hoc retrieval

• term nodes documents– gene recommendation (Andrew & Cohen’09)

• User, year gene– Reference (citation) recommendation

• topic paper– Expert finding

• topic user– Collaborator recommendation (Liben-Nowell and Kleinberg)

• Scientist scientist through co-authorship relation

44

Biology Literature Data• Data of this study

– Yeast: 0.2M nodes, 5.5M links– Fly: 0.8M nodes, 3.5M links

• Human labeled task– Literature recommendation: author,yearpaper

• Automatically labeled tasks– Gene recommendation: author, yeargene– Venue recommendation: genes, title wordsjournal– Reference recommendation: title words,yearpaper– Expert-finding: title words, genesauthor

• E.g. the fly graph:

Publication126,813

Author233,229

Write679,903 Gene

516,416Protein414,824

689,812

Cite 1,267,531

Bioentity5,823,376

1,785,626

Physical/Geneticinteractions1,352,820

Downstream/Uptream

Year58

Journal1,801

Transcribe293,285

before

Title Terms102,223

2,060,275

55

Related Works• Keyword search in relational databases –each answer is a tree

connecting all query entities and a target entity– BANKS (Bhalotia et al., 2002; Bhavana et al., 2008), – DBXplorer (Agrawal et al., 2002), – Discover (Hristidis & Papakonstantinou, 2002), – BLINKS (He et al., 2007)

• Similarity measure based on Random Walk with Restart (RWR)– Topic-sensitive Pagerank (Haveliwala, 2002) – Personalized Pagerank (Jeh &. Widom, 2003)– ObjectRank (Balmin et al., 2004), – Personal information management (Minkov & Cohen, 2007)

• Improving RWR model by tuning edge weights– quadratic programming (Tsoi et al., 2003), – simulated annealing (Nie et al., 2005), – back-propagation (Diligenti et al., 2005; Minkov & Cohen, 2007), – limit memory Newton method (Agarwal et al., 2006)

66

The Limitation of RWR models

• One-parameter-per-edge label RWR proximity measures are limited because the context in which an edge label appears is ignored

Path Comments

a(Read)p(Gene)g(_Gen)pDon't read about genes which I

have already read

a(Read)p(Auth)a(_Aut)p Read about my favorite authors

Path Comments

a(_Aut)p(Gene)g(_Gen)p

Read about the genes that I am working on

a(_Aut)p(Aff)af(_Aff)p Don't read paper from my own lab

77

This Work

• A new proximity measures on labeled graphs– Path Constrained Random Walk (PCRW)– a weighted combination of simple “path experts”, each of which

corresponds to a particular labeled path through the graph

• Citation recommendation task as an example – In the TREC-CHEM Prior Art Search Task [11], people found

that instead of directly searching for patents with the query words, it is much more e ective to first find patents with similar fftopic, then aggregate these patents’ citations

– Our model systematically generate many relation paths and learn proper weighting

Weight Path

88

Outline

• Problem definition and related work

• Retrieval Models with PCRW (ECML PKDD 2010)– Path Ranking Algorithm (PRA) – Ext.1: query-independent experts– Ext.2: popular entity experts

• Comparing efficient random walk strategies (KDD 2010)– Sampling– Truncation

99

Definitions

• An Entity-Relation graph G=(T,E,R), is– a set of entities types T={T} – a set of entities E={e}, Each entity is typed with e.T T – a set of typed and ordered relations R={R}

• dom(R):=R.T1, range(R):= R.T2

• Relational Retrieval (RR) Problem – Given a query q=(Eq,Tq)

• where Eq={e'} is a set of seed entities, and Tq is the target entity type – Produce the relevance of each entity e in Tq

• A Relation path P=(R1, …,Rn) – a sequence of relations, with constraint that Ri.T2=Ri+1.T1

– E.g.

10

Path Constrained Random Walk• Recursively define a distributions hi(e), for the path

P=R1R2…RL as

– Where P=R1R2…RL-1. Each entity passes its probability mass evenly to all of this children in a particular relation

• And for the length zero path, it is an even distribution on the query entities

1111

Relation Trees

• Given – a graph G and a query q=(Eq,Tq), Eq={e0},

• Define P(q, L) as the set of relation paths – that start with T, end with Tq, and have length ≤L

• A relation tree of P(q, L) is– The prefix tree of all the paths with each node corresponds to a

distribution hP(e) over the entities

Paper

Paper

Author

Paper

Paper

Paper

Author

Paper

WrittenBy

Write

Cite

Cite

CiteBy

CiteBy

WrittenBy

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Retrieval Based on PCRW

• A model (G, L, θ) ranks IE(Tq) by

• in matrix form s=Aθ– s is a (sparse) column vector of scores – θ is a column vector of weights for the paths P(q,L) – each column of A is the distribution hP(e) of a path P

( , )

( ; , ) ( )P PP q L

score e L h e

P

1313

Parameter Estimation• Given a set of training data

– D={(q(m), A(m), y(m))} m=1…M, y(m)(e)=1/0

• We can define a regularized objective function

• Use average log-likelihood as the objective om(θ)

– P(m) the index set or relevant entities, – N(m) the index set of irrelevant entities

(how to choose them will be discussed later)

1 1 2 21..

( ) ( ) | | | | / 2mm M

O o

1 ( ) 1 ( )( ) | | ln | | ln(1 )m m

m mm m i m i

i P i N

o P p N p

( )

( ) ( ) ( )( )

exp( )( 1| ; )

1 exp( )

T mm m m ii i T m

i

Ap p y q

A

1414

Parameter Estimation

• Selecting the negative entity set Nm

– Few positive entities vs. thousands (or millions) of negative entities?– First sort all the negative entities with an initial model (uniform weight

1.0)– Then take negative entities at the k(k+1)/2-th position,

• The gradient

• Use orthant-wise L-BFGS (Andrew & Gao, 2007) to estimate θ– Efficient– Can deal with L1 regularization

1 ( ) ( ) 1 ( ) ( )( )| | (1 ) | |

m m

m m m mmm i i m i i

i P i N

oP p A N p A

15

L2 Regularization

• Improves retrieval quality– On the personal paper recommendation task

1.0

1.1

1.2

1.3

1.4

1.5

1.6

0.0000001 0.00001 0.001 0.1λ2 (λ1=0)

Neg

ativ

e L

og-li

kelih

ood

l=2l=3l=4

0.20

0.25

0.30

0.35

0.40

0.45

1E-07 0.00001 0.001 0.1λ2 (λ1=0)

MA

P

l=2l=3l=4

16

L1 Regularization

• Does not improve retrieval quality

1.10

1.20

1.30

1.40

1E-05 0.0001 0.001 0.01 0.1λ1 (λ2=0.00001)

Ne

ga

tive

Lo

g-l

ike

liho

od

l=2l=3l=4

0.0

0.1

0.2

0.3

0.4

0.5

1E-05 0.0001 0.001 0.01 0.1λ1 (λ2=0.00001)

MA

Pl=2l=3l=4

17

L1 Regularization

• But can help select features

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1E-05 0.0001 0.001 0.01 0.1λ1 (λ2=0.00001)

MR

R

l=2l=3l=4

1

10

100

1000

1E-05 0.0001 0.001 0.01 0.1λ1 (λ2=0.00001)

No

. Act

ive

Fe

atu

res

l=2l=3l=4

1818

Ext.1: Query Independent Paths

• PageRank – assign an importance score (query independent) to each web page– later combined with relevance score (query dependent)

• Generalize to multiple entity and relation type setting– We include to each query a special entity e0 of special type T0 – T0 has relation to all other entity types– e0 has links to each entity– Therefore, we have a set of query independent relation paths

(distributions of which can be calculate offline)

• Example

Paper

Paper

AuthorT0

AuthorPaper

Paper

Wrote

WrittenBy

CiteBy

Citewell cited papers

productive authors

all papers

all authors

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Ext.2: Entity Biases

• There are entity specific characteristics which cannot be captured by a general model

– E.g. Some document with lower rank to a query may be interesting to the users because of features not captured in the data (log mining)

– E.g. Different users may have completely different information needs and goals under the same query (personalized)

– The identity of entity matters

20

Ext.2: Popular Entity Biases

• For a task with query type T0, and target type Tq, – Introduce a bias θe for each entity e in IE(Tq)– Introduce a bias θe’,e for each entity pair (e’,e) where e in IE(Tq) and e’

in IE(T0)

• Then

– Or in matrix form

• Efficiency consideration– Only add to the model top J parameters (measured by |O(θ)/θe|)

at each LBFGS iteration

2121

Experiment Setup• Data sources for bio-informatics

– PubMed on-line archive of over 18 million biological abstracts– PubMed Central (PMC) full-text copies of over 1 million of these papers– Saccharomyces Genome Database (SGD) a database for yeast– Flymine a database for fruit flies

• Tasks– Gene recommendation: author, yeargene– Venue recommendation: genes, title wordsjournal– Reference recommendation: title words,yearpaper– Expert-finding: title words, genesauthor

• Data split– 2000 training, 2000 tuning, 2000 test

• Time variant graph – each edge is tagged with a time stamp (year)– only consider edges that are earlier than the query, during random walk

22

Example Features

• A PRA+qip+pop model trained for the reference recommendation task on the yeast data

6) resembles a commonly used ad-hoc retrieval system

1) papers co-cited with the on-topic papers

7,8) papers cited during the past two years

9) well cited papers

12,13) general papers published during the past two years

10,11) (important) early papers about specific query terms (genes)

14) old papers

2323

Experiment Result

• Compare the MAP of PCRW to– RWR model– query independent paths (qip) – popular entity biases (pop)

Except these† , all improvements are statistically significant at p<0.05 using paired t-test

2424

Outline

• Problem definition and related work

• Retrieval Models with PCRW (ECML PKDD 2010)– Path Ranking Algorithm (PRA) – Ext.1: query-independent experts– Ext.2: popular entity experts

• Comparing efficient random walk strategies (KDD 2010)– Sampling– Truncation

25

Four Strategies for Efficiency• Fingerprint Strategy (Fogaras et al. 2004)

– Simulate a large number of random walkders

• Fixed Truncation– Truncate by fixed value

• Beam Truncation– Keep top W probable entities

• Weighted Particle Filtering– A combination of exact inference and sampling

26

Weighted Particle Filtering

• Start from exact inference, then switch to sampling when the branching is heavy

27

Results on the Yeast DataExpert Finding Gene Recommendation Reference

Recommendation

T0 = 0.17s, L= 3 T0 = 1.6s, L = 4 T0 = 2.7s, L= 3

RWR

Particle Filtering

Fixed Truncation

Beam Truncation

Exact

Exact(Edge-Parameter)

Exact(No Learning)

28

Results on the Fly DataExpert Finding Gene Recommendation Reference

Recommendation

T0 = 0.15s, L= 3 T0 = 1.8s, L= 4 T0 = 0.9s, L= 3

RWR

Particle Filtering

Fixed Truncation

Beam Truncation

Exact

Exact(Edge-Parameter)

Exact(No Learning)

2929

Observations• Sampling strategies are better than truncation strategies

• Particle filtering produces better MAP than fingerprinting– By reducing the variances of estimations– 10~100 fold speedup compared to exact RW

• Retrieval quality is improved in many cases– By producing better weight of the model– See (Lao & Cohen, KDD 2010) for details

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The End

• Thanks