information retrieval as structured prediction university of massachusetts amherst machine learning...

Information Retrieval as Structured PredictionUniversity of Massachusetts Amherst

Machine Learning SeminarApril 29th, 2009

Yisong YueCornell University

Joint work with:Thorsten Joachims, Filip Radlinski, and Thomas Finley

Supervised Learning

• Find function from input space X to output space Y

such that the prediction error is low.

Microsoft announced today that they acquired Apple for the amount equal to the gross national product of Switzerland. Microsoft officials stated that they first wanted to buy Switzerland, but eventually were turned off by the mountains and the snowy winters…

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y7.3

Examples of Complex Output Spaces

• Natural Language Parsing– Given a sequence of words x, predict the parse tree y.– Dependencies from structural constraints, since y has to be a

tree.

The dog chased the catx

S

VPNP

Det NV

NP

Det N

y

• Part-of-Speech Tagging– Given a sequence of words x, predict sequence of tags y.

– Dependencies from tag-tag transitions in Markov model.

Similarly for other sequence labeling problems, e.g., RNA

Intron/Exon Tagging.

The rain wet the catx

Det NVDet Ny



• Information Retrieval– Given a query x, predict a ranking y.

– Dependencies between results (e.g. avoid redundant hits)

– Loss function over rankings (e.g. Average Precision)

SVMx 1. Kernel-Machines

2. SVM-Light3. Learning with Kernels4. SV Meppen Fan Club5. Service Master & Co.6. School of Volunteer Management7. SV Mattersburg Online…

y

Goals of this Talk

• Learning to Rank– Optimizing Average Precision– Diversified Retrieval

• Structured Prediction– Complex Retrieval Goals– Structural SVMs (Supervised Learning)

Learning to Rank

• At intersection of ML and IR• First generate input features

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),(,

dpagerank

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q

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Learning to Rank

• Design a retrieval function f(x) = wTx – (weighted average of features)

• For each query q – Score all sq,d = wTxq,d

– Sort by sq,d to produce ranking

• Which weight vector w is best?

Conventional SVMs

• Input: x (high dimensional point)

• Target: y (either +1 or -1)

• Prediction: sign(wTx)

• Training:

subject to:

• The sum of slacks smooth upper bound for 0/1 loss

N

ii

w N

Cw

1

2

, 2

1minarg

iiT xwi 1)(y : i

i

i

• 2 pairwise disagreements

Optimizing Pairwise Agreements

Pairwise Preferences SVM

ji

jiw N

Cw

,,

2

, 2

1minarg

ji

yyjixwxw

ji

jijijT

iT

, ,0

:, ,1

,

,

Such that:

Large Margin Ordinal Regression [Herbrich et al., 1999]

Can be reduced to time [Joachims, 2005] )log( nnO

Pairs can be reweighted to more closely model IR goals [Cao et al., 2006]

Mean Average Precision

• Consider rank position of each relevant doc– K1, K2, … KR

• Compute Precision@K for each K1, K2, … KR

• Average precision = average of P@K

• Ex: has AvgPrec of

• MAP is Average Precision across multiple queries/rankings

76.05

3

3

2

1

1

3

1

Optimization Challenges

• Rank-based measures are multivariate– Cannot decompose (additively) into document pairs– Need to exploit other structure

• Defined over rankings– Rankings do not vary smoothly– Discontinuous w.r.t model parameters– Need some kind of relaxation/approximation

[Yue & Burges, 2007]

Structured Prediction

• Let x be a structured input (candidate documents)• Let y be a structured output (ranking)

• Use a joint feature map to encode

the compatibility of predicting y for given x.– Captures all the structure of the prediction problem

• Consider linear models: after learning w, we can make predictions via

FR ),( xy

),(maxargˆ xyyy

Tw

Linear Discriminant for Ranking

• Let x = (x1,…xn) denote candidate documents (features)

• Let yjk = {+1, -1} encode pairwise rank orders

• Feature map is linear combination of documents.

• Prediction made by sorting on document scores wTxi

),(maxargˆ xyyy

Tw

relj relk

kjjk xxy: :!

)(),( xy

Structural SVM

• Let x denote a structured input (candidate documents)• Let y denote a structured output (ranking)

• Standard objective function:

• Constraints are defined for each incorrect labeling y’ over the set of documents x.

i

iN

Cw 2

2

1

iiiTiiTi ww )'(),'(),( :' )()()()( yxyxyyy

[Tsochantaridis et al., 2005]

Minimizing Hinge Loss

Suppose for incorrect y’:

Then:

i

iN

Cw 2

2

1



)'(75.0 yi

Structural SVM for MAP

• Minimize

subject to

where ( y jk = {-1, +1} )

and

• Sum of slacks is smooth upper bound on MAP loss.

relj relk

ik

ij

ii xxyjk

: :!

)()()()( )(),( xy

i

iN

Cw 2

2

1


)'(1)'( yy Avgprec

i

[Yue et al., SIGIR 2007]

Too Many Constraints!

• For Average Precision, the true labeling is a ranking where the relevant documents are all ranked in the front, e.g.,

• An incorrect labeling would be any other ranking, e.g.,

• This ranking has Average Precision of about 0.8 with (y’) ¼ 0.2

• Intractable number of rankings, thus an intractable number of constraints!

Cutting Plane Method

Original SVM Problem• Exponential constraints

• Most are dominated by a small set of “important” constraints

Structural SVM Approach• Repeatedly finds the next most

violated constraint…

• …until set of constraints is a good approximation.


Finding Most Violated Constraint

• A constraint is violated when

• Finding most violated constraint reduces to

• Highly related to inference/prediction:

0)'(),(),'( iTw yxyxy

)'(),'(maxargˆ'

yxyyy

Tw

),(maxarg xyy

Tw


Observations• MAP is invariant on the order of documents within a relevance

class– Swapping two relevant or non-relevant documents does not change MAP.

• Joint SVM score is optimized by sorting by document score, wTxj

• Reduces to finding an interleaving

between two sorted lists of documents

relj relk

kT

jT

jk xwxwy: :!'

)(')'(maxarg yy



►

• Start with perfect ranking• Consider swapping adjacent

relevant/non-relevant documents

relj relk

kT

jT

jk xwxwy: :!'

)(')'(maxarg yy



►


relevant/non-relevant documents• Find the best feasible ranking of

the non-relevant document

relj relk

kT

jT

jk xwxwy: :!'

)(')'(maxarg yy



►


relevant/non-relevant documents• Find the best feasible ranking of the

non-relevant document• Repeat for next non-relevant

document

relj relk

kT

jT

jk xwxwy: :!'

)(')'(maxarg yy



►




document• Never want to swap past previous

non-relevant document

relj relk

kT

jT

jk xwxwy: :!'

)(')'(maxarg yy



►




document• Never want to swap past previous

non-relevant document• Repeat until all non-relevant

documents have been considered

relj relk

kT

jT

jk xwxwy: :!'

)(')'(maxarg yy


Comparison with other SVM methods

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3

TREC 9 Indri TREC 10 Indri TREC 9Submissions

TREC 10Submissions

TREC 9Submissions(without best)


Dataset

Mea

n A

vera

ge

Pre

cisi

on

SVM-MAP

SVM-ROC

SVM-ACC

SVM-ACC2

SVM-ACC3

SVM-ACC4

Structural SVM for MAP

• Treats rankings as structured objects

• Optimizes hinge-loss relaxation of MAP– Provably minimizes the empirical risk

– Performance improvement over conventional SVMs

• Relies on subroutine to find most violated constraint

– Computationally compatible with linear discriminant

)'(),'(maxargˆ'

yxyyy

Tw

Structural SVM Recipe

• Joint feature map

• Inference method

• Loss function

• Loss-augmented (most violated constraint)

),(maxarg xyy

Tw

),( xy

)(y

)'(),(maxarg'

yxyy

Tw

Need for Diversity (in IR)

• Ambiguous Queries– Users with different information needs issuing the

same textual query– “Jaguar” or “Apple”– At least one relevant result for each information need

• Learning Queries– User interested in “a specific detail or entire breadth

of knowledge available” • [Swaminathan et al., 2008]

– Results with high information diversity

Example

•Choose K documents with maximal information coverage.•For K = 3, optimal set is {D1, D2, D10}

Diversity via Set Cover

• Documents cover information– Assume information is partitioned into discrete units.

• Documents overlap in the information covered.

• Selecting K documents with maximal coverage is a set cover problem– NP-complete in general

– Greedy has (1-1/e) approximation [Khuller et al., 1997]

Diversity via Subtopics

• Current datasets use manually determined subtopic labels– E.g., “Use of robots in the world today”

• Nanorobots• Space mission robots• Underwater robots

– Manual partitioning of the total information– Relatively reliable– Use as training data

Weighted Word Coverage

• Use words to represent units of information

• More distinct words = more information

• Weight word importance

• Does not depend on human labeling

• Goal: select K documents which collectively cover as many distinct (weighted) words as possible– Greedy selection yields (1-1/e) bound.– Need to find good weighting function (learning problem).

Example

D1 D2 D3 Best

Iter 1 12 11 10 D1

Iter 2

Marginal Benefit

V1 V2 V3 V4 V5

D1 X X X

D2 X X X

D3 X X X X

Word Benefit

V1 1

V2 2

V3 3

V4 4

V5 5

Document Word Counts

Example

D1 D2 D3 Best

Iter 1 12 11 10 D1

Iter 2 -- 2 3 D3

Marginal Benefit

V1 V2 V3 V4 V5

D1 X X X

D2 X X X

D3 X X X X

Word Benefit

V1 1

V2 2

V3 3

V4 4

V5 5

Document Word Counts

Related Work Comparison

• Essential Pages [Swaminathan et al., 2008]

– Uses fixed function of word benefit– Depends on word frequency in candidate set

• Our goals– Automatically learn a word benefit function

• Learn to predict set covers • Use training data• Minimize subtopic loss

– No prior ML approach • (to our knowledge)

Linear Discriminant

• x = (x1,x2,…,xn) - candidate documents

• y – subset of x • V(y) – union of words from documents in y.

• Discriminant Function:

• (v,x) – frequency features (e.g., ¸10%, ¸20%, etc).

• Benefit of covering word v is then wT(v,x)

)(

),(),(y

xxyVv

TT vww

),(maxargˆ xyyy

Tw

[Yue & Joachims, ICML 2008]

Linear Discriminant

• Does NOT reward redundancy – Benefit of each word only counted once

• Greedy has (1-1/e)-approximation bound

• Linear (joint feature space) – Allows for SVM optimization

• (Used more sophisticated discriminant in experiments.)

)(

),(),(y

xxyVv

TT vww


Weighted Subtopic Loss

• Example:– x1 covers t1

– x2 covers t1,t2,t3

– x3 covers t1,t3

• Motivation– Higher penalty for not covering popular subtopics

# Docs Loss

t1 3 1/2

t2 1 1/6

t3 2 1/3



• Encode each subtopic as an additional “word” to be covered.

• Use greedy algorithm: (1-1/e)-approximation

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1

y

y

y

x

x

xy

T T

Vv L

Vv

Lv

v

),'('maxargˆ'

xyyy

Tw

TREC Experiments

• TREC 6-8 Interactive Track Queries• Documents labeled into subtopics.

• 17 queries used, – considered only relevant docs– decouples relevance problem from diversity problem

• 45 docs/query, 20 subtopics/query, 300 words/doc

• Trained using LOO cross validation

• TREC 6-8 Interactive Track• Retrieving 5 documents

Can expect further benefit from having more training data.

Learning Set Cover Representations

• Given:– Manual partitioning of a space

• subtopics

– Weighting for how items cover manual partitions • subtopic labels + subtopic loss

– Automatic partitioning of the space• Words

• Goal:– Weighting for how items cover automatic partitions– The (greedy) optimal covering solutions agree

Summary

• Information Retrieval as Structured Prediction– Can be used to reason about complex retrieval goals

– E.g., mean average precision, diversity

– Software & papers available at www.yisongyue.com

• Beyond Supervised Learning– Training data expensive to gather

– Current work on interactive learning (with users)

• Thanks to Andrew McCallum, David Mimno & Marc Cartwright

• Work supported by NSF IIS-0713483, Microsoft Graduate Fellowship, and Yahoo! KTC Grant.

http://www.yisongyue.com/

Extra Slides

Structural SVM Training• STEP 1: Solve the SVM objective function using only the current

working set of constraints.

• STEP 2: Using the model learned in STEP 1, find the most violated constraint from the global set of constraints.

• STEP 3: If the constraint returned in STEP 2 is violated by more than epsilon, add it to the working set.

• Repeat STEP 1-3 until no additional constraints are added. Return the most recent model that was trained in STEP 1.

STEP 1-3 is guaranteed to loop for at most O(1/epsilon^2) iterations. [Tsochantaridis et al., 2005]

*This is known as a “cutting plane” method.

Structural SVM Training

• Suppose we only solve the SVM objective over a small subset of constraints (working set).

• Some constraints from global set might be violated.• When finding a violated constraint, only y’ is free,

everything else is fixed – y’s and x’s fixed from training– w and slack variables fixed from solving SVM objective

• Degree of violation of a constraint is measured by:

iiiiiTw )',(),(),'( )()()()( yyxyxy

iiiTiiTi ww )',(),'(),( :' )()()()()( yyxyxyyy

SVM-map

Experiments

• Used TREC 9 & 10 Web Track corpus.

• Features of document/query pairs computed from outputs of existing retrieval functions.

(Indri Retrieval Functions & TREC Submissions)

• Goal is to learn a recombination of outputs which improves mean average precision.

Comparison with Best Base methods

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3


TREC 10Submissions



Dataset

Mea

n A

vera

ge

Pre

cisi

on

SVM-MAP

Base 1

Base 2

Base 3

Comparison with other SVM methods

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3


TREC 10Submissions



Dataset

Mea

n A

vera

ge

Pre

cisi

on

SVM-MAP

SVM-ROC

SVM-ACC

SVM-ACC2

SVM-ACC3

SVM-ACC4

SVM-div

Result #18

Top of First Page

Bottom of First Page

Results From 11/27/2007

Query: “Jaguar”

More Sophisticated Discriminant

• Documents “cover” words to different degrees– A document with 5 copies of “Microsoft” might cover it

better than another document with only 2 copies.

• Use multiple word sets, V1(y), V2(y), … , VL(y)

• Each Vi(y) contains only words satisfying certain importance criteria.


More Sophisticated Discriminant

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)( 1

),(

),(

),(1

y

y

x

x

xy

LVv L

Vv

v

v

•Separate i for each importance level i. •Joint feature map is vector composition of all i

),(maxargˆ xyyy

Tw

•Greedy has (1-1/e)-approximation bound. •Still uses linear feature space.


Essential Pages

),(1log),(),(

),,(),(),,(

2 xxx

xxx

vrvrv

xvTFvxvC ii

[Swaminathan et al., 2008]

Benefit of covering word v with document xi

Importance of covering word v

Intuition: - Frequent words cannot encode information diversity.- Infrequent words do not provide significant information

x = (x1,x2,…,xn) - set of candidate documents for a queryy – a subset of x of size K (our prediction).

v

vC ),,(maxargˆ xyyy

Approximate Constraint Generation

• Theoretical guarantees no longer hold.– Might not find an epsilon-close approximation to the feasible

region boundary.

• Performs well in practice.

TREC Experiments

• 12/4/1 train/valid/test split– Approx 500 documents in training set

• Permuted until all 17 queries were tested once

• Set K=5 (some queries have very few documents)

• SVM-div – uses term frequency thresholds to define importance levels

• SVM-div2 – in addition uses TFIDF thresholds

TREC Interactive Track Results

Method Loss

Random 0.469

Okapi 0.472

Unweighted Model 0.471

Essential Pages 0.434

SVM-div 0.349

SVM-div2 0.382

Methods W / T / L

SVM-div vs Ess. Pages

14 / 0 / 3 **

SVM-div2 vs Ess. Pages

13 / 0 / 4

SVM-div vs SVM-div2

9 / 6 / 2

Approximate constraint generation seems to work perform well.

Synthetic Dataset

• Trec dataset very small• Synthetic dataset so we can vary retrieval size K

• 100 queries• 100 docs/query, 25 subtopics/query, 300 words/doc

• 15/10/75 train/valid/test split

Consistently outperforms Essential Pages

information retrieval as structured prediction university of massachusetts amherst machine learning...

Documents

loss slide

average precision svm

query x

incorrect y

snowy winters x y

space y

input space x

w t x q