learning to rank for information retrieval -...

Learning to Rank for Information Retrieval

Tie-Yan Liu

Lead Researcher

Microsoft Research Asia

4/20/2008 1Tie-Yan Liu @ Tutorial at WWW 2008

The Speaker

• Tie-Yan Liu– Lead Researcher, Microsoft Research Asia.

– Ph.D., Tsinghua University, China.

– Research Interests: Learning to Rank, Large-scale Graph Learning.

– ~70 Papers: SIGIR(9), WWW(3), ICML (3), KDD(2), etc.

– Winner of Most Cited Paper Award, JVCIR, 2004 - 2006.

– Senior PC Member of SIGIR 2008.

– Co-chair, SIGIR Workshop on Learning to Rank, 2008.

– Co-chair, SIGIR Workshop on Learning to Rank, 2007.

– Speaker, Tutorial on Learning to Rank, SIGIR 2008 (to be given in July), AIRS 2008, etc.

4/20/2008 Tie-Yan Liu @ Tutorial at WWW 2008 2

This Tutorial

• Learning to rank for information retrieval– But not other generic ranking problems.

• Supervised learning– But not unsupervised or semi-supervised learning.– Mostly discriminative learning but not generative learning.

• Learning in vector space– But not on graphs or other structured data.

• Mainly based on papers published at SIGIR, WWW, ICML, KDD, and NIPS in the past five years.– Papers at other conferences and journals might not be covered

comprehensively in this tutorial.


Background Knowledge Required

• Information Retrieval– We will just briefly introduce, but not comprehensively review

the literature of IR.

• Machine Learning– We will assume you are familiar with regression, classification

and their learning algorithms, such as SVM, Boosting, NN, etc. – No comprehensive introduction to these algorithms and their

principles will be given.

• Probability Theory.• Linear Algebra.• Optimization.


Outline

• Ranking in Information Retrieval

• Learning to Rank

– Overview

– Pointwise approach

– Pairwise approach

– Listwise approach

• Summary


Ranking in Information Retrieval


We are Overwhelmed by Flood of Information


Information Explosion


2008?

Search Engine as A Tool


Inside Search Engine

Ranking model

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IR Evaluation

• Objective

– Evaluate the effectiveness of a ranking model

• A standard test set, containing

– A large number of queries, their associated documents, and the label (relevance judgments) of these documents.

• A measure

– Evaluating the effectiveness of a ranking model for a particular query.

– Averaging the measure over the entire test set to represent the expected effectiveness of the model.


Widely-used Judgments

• Binary judgment

– Relevant vs. Irrelevant

• Multi-level ratings

– Perfect > Excellent > Good > Fair > Bad

• Pairwise preferences

– Document A is more relevant than document B with respect to query q


Evaluation Measures

• MAP (Mean Average Precision)

• NDCG (Normalized Discounted Cumulative Gain)

• MRR (Mean Reciprocal Rank)

– For query , rank position of the first relevant document:

– MRR: average of over all queries

• WTA (Winners Take All)

– If top ranked document is relevant: 1; otherwise 0

– average over all queries

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MAP

• Precision at position n

• Average precision

• MAP: averaged over all queries in the test set

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Bad 0=20-1


CG: Cumulative GIf each rank position is treated equal

URL Gain Cumulative Gain

#1 http://abc.go.com/ 31 31

#2 http://www.abcteach.com/ 3 34 = 31 +3

#3 http://abcnews.go.com/sections/scitech/ 15 49 = 31 + 3 + 15

#4 http://www.abc.net.au/ 15 64 = 31 + 3 + 15 + 15

#5 http://abcnews.go.com/ 15 79 = 31 + 3 + 15 + 15 + 15

#6 … … …

Query={abc}


DCG: Discounted CG

URL Gain Discounted Cumulative Gain

#1 http://abc.go.com/ 31 31 = 31x1

#2 http://www.abcteach.com/ 3 32.9 = 31 + 3x0.63

#3 http://abcnews.go.com/sections/scitech/ 15 40.4 = 32.9 + 15x0.50

#4 http://www.abc.net.au/ 15 46.9 = 40.4 + 15x0.43

#5 http://abcnews.go.com/ 15 52.7 = 46.9 + 15x0.39

#6 … … …

• Discounting factor: Log(2) / (Log(1+rank))


Ideal Ordering: Max DCG

URL Gain Max DCG

#1 http://abc.go.com/ 31 31 = 31x1

#2 http://abcnews.go.com/sections/scitech/ 15 40.5 = 31 + 15x0.63

#3 http://www.abc.net.au/ 15 48.0 = 40.5 + 15x0.50

#4 http://abcnews.go.com/ 15 54.5 = 48.0 + 15x0.43

#5 http://www.abc.org/ 15 60.4 = 54.5 + 15x0.39

#6 … … …


• Sort the documents according to their labels

NDCG: Normalized DCG

URL Gain DCG Max DCG NDCG

#1 http://abc.go.com/ 31 31 31 1 = 31/31

#2 http://www.abcteach.com/ 3 32.9 40.5 0.81=32.9/40.5

#3 http://abcnews.go.com/sections/scitech/ 15 40.4 48.0 0.84=40.4/48.0

#4 http://www.abc.net.au/ 15 46.9 54.5 0.86=46.9/54.5

#5 http://abcnews.go.com/ 15 52.7 60.4 0.87=52.7/60.4

#6 … … … … …


• Normalized by the Max DCG

More about Evaluation Measures

• Query-level– Averaged over all testing queries.

– The measure is bounded, and every query contributes equally to the averaged measure.

• Position– Position discount is used here and there.

• Non-smooth– Computed based on ranks of documents.

– With small changes to parameters of the ranking model, the scores will change smoothly, but the ranks will not change until one document’s score passes another.


Conventional Ranking ModelsCategory Example Models

Similarity-based models

Boolean model

Vector space model

Latent Semantic Indexing

……

Probabilistic models

BM25 model

Language model for IR

…

Hyperlink-basedmodels

HITS

PageRank

……


Discussions on Conventional Ranking Models

• For a particular model

– Parameter tuning is usually difficult, especially when there are many parameters to tune.

• For comparison between two models

– Given a test set, it is difficult to compare two models, one is over-tuned (over-fitting) while the other is not.

• For a collection of models

– There are hundreds of models proposed in the literature.

– It is non-trivial to combine them effectively.


Machine Learning Can Help

• Machine learning is an effective tool

– To automatically tune parameters

– To combine multiple evidences

– To avoid over-fitting (regularization framework, structure risk minimization, etc.)


Learning to Rank for IR

OverviewPointwise Approach

Pairwise ApproachListwise Approach


Framework of Learning to Rank for IR

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Learning System

Ranking System

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Learning to Rank Algorithms


Ranking SVM (ICANN 1999)

RankBoost (JMLR 2003)

Discriminative model for IR (SIGIR 2004)

LDM (SIGIR 2005)

RankNet (ICML 2005)IRSVM (SIGIR 2006)

LambdaRank (NIPS 2006) Frank (SIGIR 2007)

GBRank (SIGIR 2007)QBRank (NIPS 2007)

MPRank (ICML 2007)

McRank (NIPS 2007) AdaRank (SIGIR 2007)

SVM-MAP (SIGIR 2007)

SoftRank (LR4IR 2007)

GPRank (LR4IR 2007)

CCA (SIGIR 2007)

MHR (SIGIR 2007)

RankCosine (IP&M 2007)

ListNet (ICML 2007)

ListMLE (ICML 2008)

Query refinement (WWW 2008)

Supervised Rank Aggregation (WWW 2007)Relational ranking (WWW 2008)

SVM Structure (JMLR 2005)

Nested Ranker (SIGIR 2006)

Categorization: Relation to Conventional Machine Learning

• With certain assumptions, learning to rank can be reduced to conventional learning problems

– Regression• Assume labels to be scores

– Classification• Assume labels to have no orders

– Pairwise classification • Assume document pairs to be independent of each other


Categorization: Relation to Conventional Machine Learning

• Ranking in IR has unique properties– Query determines the logical structure of the ranking

problem. • Loss function should be defined on ranked lists w.r.t. a query, since

IR measures are computed at query level.

– Relative order is important• No need to predict category, or value of f(x).

– Position sensitive• Top-ranked objects are more important.

– Rank based evaluation • Learning objective is non-smooth and non-differentiable.


Categorization: Basic Unit of Learning

• Pointwise

– Input: single documents

– Output: scores or class labels

• Pairwise

– Input: document pairs

– Output: partial order preference

• Listwise

– Input: document collections

– Output: ranked document List


Categorization of Learning to Rank Algorithms

PointwiseApproach

Pairwise Approach Listwise Approach

Reduced to classification or regression

Discriminative model for IR (SIGIR 2004)McRank (NIPS 2007)…

Ranking SVM (ICANN 1999)RankBoost (JMLR 2003)LDM (SIGIR 2005)RankNet (ICML 2005)Frank (SIGIR 2007)GBRank (SIGIR 2007)QBRank (NIPS 2007)MPRank (ICML 2007)…

Make use of unique properties of Ranking for IR

IRSVM (SIGIR 2006)…

LambdaRank (NIPS 2006)AdaRank (SIGIR 2007)SVM-MAP (SIGIR 2007)SoftRank (LR4IR 2007)GPRank (LR4IR 2007)CCA (SIGIR 2007)RankCosine (IP&M 2007)ListNet (ICML 2007)ListMLE (ICML 2008)…



Overview

Pointwise ApproachPairwise ApproachListwise Approach


Overview of Pointwise Approach

• Reduce ranking to regression or classification on single documents.

• Examples:

– Discriminative model for IR.

– McRank: learning to rank using multi-class classification and gradient boosting.


Discriminative Model for IR(R. Nallapati, SIGIR 2004)

• Features extracted for each document

• Treat relevant documents as positive examples, while irrelevant documents as negative examples.


Discriminative Model for IR

• Learning algorithms– Max Entropy

– Support Vector Machines

• Experimental results– Comparable with LM


McRank(P. Li, et al. NIPS 2007)

• Loss in terms of DCG is upper bounded by multi-class classification error

• Multi-class classification:

• Multiple ordinal classification:

• Regression:


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Different Reductions

• From classification to ranking

– Learn a classifier for each category

– Classifier outputs converted to probabilities using logistic function

– Convert classification to ranking:

• Experimental results

– Multiple ordinal classification > Multi-class classification > Regression


Discussions

• Assumption

– Relevance is absolute and query-independent.

– E.g. documents associated with different queries are put into the same category, if their labels are all “perfect”.

• However, in practice, relevance is query-dependent

– An irrelevant document for a popular query might have higher term frequency than a relevant document for a rare query.

– If simply put documents associated with different queries together, the training process may be hurt.




Pairwise ApproachListwise Approach


Overview of Pairwise Approach

• No longer assume absolute relevance.

• Reduce ranking to classification on document pairs w.r.t. the same query.

• Examples

– RankNet, FRank, RankBoost, Ranking SVM, etc.

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• Target probability:

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• Modeled probability:

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• Cross entropy as the loss function–

RankNet(C. Burges, et al. ICML 2005)


RankNet (2)

• Use Neural Network as model, and gradient descent as algorithm, to optimize the cross-entropy loss.

• Evaluate on single documents: output a relevance score for each document w.r.t. a new query.


FRank(M. Tsai, T. Liu, et al. SIGIR 2007)

• Similar setting to that of RankNet

• New loss function: fidelity


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FRank (2)

RankNet (Cross entropy loss)

• Non-zero minimum loss

• Unbounded

• Convex

FRank (Fidelity loss)

• Zero minimum loss

• Bounded within [0,1]

• Non-convex


Experimental results show:FRank can outperform RankNet in many cases

RankBoost(Y. Freund, et al. JMLR 2003)

• Given: initial distribution D1 over

• For t=1,…, T:

– Train weak learning using distribution Dt

– Get weak ranking ht: X R

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Use AdaBoost to perform pairwise classification

Weak Learners

• Feature values

• Thresholding

• Note: many theoretical properties of AdaBoost can be inherited by RankBoost.


Ranking SVM(R. Herbrich, et al. ICANN 1999)

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Use SVM to perform binary classification on these instances,

to learn model parameter w

Use w for testing

Testing


Other Work in this Category

• Linear discriminant model for information retrieval (LDM), (J. Gao, H. Qi, et al. SIGIR 2005)

• A Regression Framework for Learning Ranking Functions using Relative Relevance Judgments (GBRank), (Z. Zheng, H. Zha, et al. SIGIR 2007)

• A General Boosting Method and its Application to Learning Ranking Functions for Web Search (QBRank), (Z. Zheng, H. Zha, et al. NIPS 2007)

• Magnitude-preserving Ranking Algorithms (MPRank), (C. Cortes, M. Mohri, et al. ICML 2007)


Discussions

• Progress made as compared to pointwise approach

– No longer assume absolute relevance

• However,

– Unique properties of ranking in IR have not been fully modeled.


Problems with Pairwise Approach (1)

• Number of instance pairs varies according to query

– Two queries in total

– Same error in terms of pairwise classification780/790 = 98.73%.

– Different errors in termsof query level evaluation99% vs. 50%.


Problems with Pairwise Approach (2)

• Negative effects of making errors on top positions– Same error in terms of pairwise classification– Different errors in terms of position-discounted evaluation.

p: perfect, g: good, b: bad

Ideal: p g g b b b b

ranking 1: g p g b b b b one wrong pair Worseranking 2: p g b g b b b one wrong pair Better


As a Result, …

• Users only see ranked list of documents, but not document pairs

• It is not clear how pairwise loss correlates with IR evaluation measures, which are defined on query level.


Pairwise loss vs. (1-NDCG@5)TREC Dataset

Incremental Solution to Problems (1)

IRSVM: Change Loss of Ranking SVM(Y. Cao, J. Xu, T. Liu, et al. SIGIR 2006)

Query-level normalizer


Experimental Results


Web Data

Theoretical Analysis(Y. Lan, T. Liu, et al. ICML 2008)

• Stability theory on query-level generalization bound


Loss function

Learning instance

Ground truth

Loss on a single query Risks on a set

Theoretical Analysis (2)

• Stability– Represents the degree of

change in the loss when randomly removing a query and its associated documents from the training set.

• Generalization Ability– If an algorithm has query-

level stability, with high probability, expected query-level risk can be bounded by empirical risk as follows.


Query qj removed from training set

Bound depending on query number and stability coefficientStability coefficient

Generalization Bounds for Ranking SVM and IRSVM

• For Ranking SVM

• For IRSVM


When number of document pairs per query varies largely, the generalization bound of IRSVM will be much tighter than that of Ranking SVM

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Distribution of Pair Numbers


Web Data

Variance is large

IR SVM will have a better generalization ability than Ranking SVM

Incremental Solution to Problems (2)

IRSVM: Change Loss of Ranking SVM(Y. Cao, J. Xu, T. Liu, et al. SIGIR 2006)

Implicit Position Discount: Larger weight for more critical type of pairs

Learned from a labeled set




Web Data

More Fundamental Solution

Listwise Approach to Ranking

• Directly operate on ranked lists

– Directly optimize IR evaluation measures• AdaRank, SVM-MAP, SoftRank, LambdaRank, RankGP, …

– Define listwise loss functions• RankCosine, ListNet, ListMLE, …


Contextual Ads

• SIGIR 2008 workshop on learning to rank for IR

– http://research.microsoft.com/users/LR4IR-2008/

– Paper submission due: May 16, 2008.

– Organizer: Tie-Yan Liu, Hang Li, Chengxiang Zhai

• We organized a successful workshop on the same topic at SIGIR 2007 (the largest workshop, with 100+ registrations)


http://research.microsoft.com/users/LR4IR-2008/



Contextual Ads (2)

• SIGIR 2008 tutorial on learning to rank for IR

– Speaker: Tie-Yan Liu


• Differences from this WWW tutorial

– Include more new algorithms (SIGIR 2008, ICML 2008, etc.)

– Discussions on the whole pipeline of learning to rank (feature extraction, ground truth mining, loss function, ranking function, post processing, etc.)

Contextual Ads (3)

• LETOR: Benchmark Dataset for Learning to Rank– http://research.microsoft.com/users/LETOR/– 500+ downloads till now.– Released by Tie-Yan Liu, Jun Xu, et al.


http://research.microsoft.com/users/LETOR/

- Next –Listwise Approach to Learning to Rank




Pairwise Approach

Listwise Approach


Overview of Listwise Approach

• Instead of reducing ranking to regression or classification, perform learning directly on document list.

– Treats ranked lists as learning instances.

• Two major types

– Directly optimize IR evaluation measures

– Define listwise loss functions


Directly Optimize IR Evaluation Measures

• It is a natural idea to directly optimize what is used to evaluate the ranking results.

• However, it is non-trivial.

– Evaluation measures such as NDCG are usually non-smooth and non-differentiable since they depend on the ranks.

– It is challenging to optimize such objective functions, since most of the optimization techniques were developed to work with smooth and differentiable cases.


Tackle the Challenges

• Use optimization technologies designed for smooth and differentiable problems– Embed the evaluation measure in the logic of existing

optimization technique (AdaRank)

– Optimize a smooth and differentiable upper bound of the evaluation measure (SVM-MAP)

– Soften (approximate) the evaluation measure so as to make it smooth and differentiable (SoftRank)

• Use optimization technologies designed for non-smooth and non-differentiable problems– Genetic programming (RankGP)

– Directly define gradient (LambdaRank)


AdaRank(J. Xu, et al. SIGIR 2007)

• The optimization process of AdaBoost


Use the loss function to update the distributions of learning instances and to determine the parameter α

AdaRank(J. Xu, et al. SIGIR 2007)

• Use Boosting to perform the optimization.

• Embed IR evaluation measure in the distribution update of Boosting.– Focus on those hard

queries.

– Weak learner that canrank important queriesmore correctly will havelarger weight α


Theoretical Analysis

• Training error will be continuously reduced during learning phase when <1


Assumes the linearity of the IR evaluation measure.

Practical Solution

• In practice, we cannot guarantee <1, therefore, AdaRank might not converge.

• Solution: when a weak ranker is selected, we test whether <1, if not, the second best weak ranker is selected.




TD 2003 Data

SVM-MAP(Y. Yue, et al. SIGIR 2007)

• Use SVM framework for optimization

• Incorporate IR evaluation measures in the listwise constraints: – The score w.r.t true labeling should be higher than that w.r.t. incorrect labeling.

• Sum of slacks ∑ξ upper bounds ∑ (1-E(y,y’)).


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Challenges in SVM-MAP

• 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.,

• Exponential number of rankings, thus an exponential number of constraints!


Structural SVM Training

• STEP 1: Perform optimization on only current working set of constraints.

• STEP 2: Use the model learned in STEP 1 to find the most violated constraint from the exponential set of constraints.

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

STEP 1-3 is guaranteed to loop for at most a polynomial number of iterations. [Tsochantaridis et al. 2005]


Finding the Most Violated Constraint

• Most violated y:

• If the relevance at each position is fixed, E(y,y’) will be the same. But if the documents are sorted by their scores in descending order, F(q,d,y’) will be maximized.

• Strategy– Sort the relevant and irrelevant documents and form a perfect

ranking.– Start with the perfect ranking and swap two adjacent relevant

and irrelevant documents, so as to find the optimal interleaving of the two sorted lists.

– For real cases, the complexity is O(nlogn).


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Comparison with other SVM methods

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SoftRank(M. Taylor, et al. LR4IR 2007)

• Key Idea:

– Avoid sorting by treating scores as random variables

• Steps

– Construct score distribution

– Map score distribution to rank distribution

– Compute expected NDCG (SoftNDCG) which is smooth and differentiable.

– Optimize SoftNDCG by gradient descent.


Construct Score Distribution

• Considering the score for each document sj as random variable, by using Gaussian.


From Scores to Rank Distribution

• Probability of doci being ranked before docj

• Expected rank

• Rank Distribution


Define the probability of a document being ranked at a particular position

Soft NDCG

• From hard to soft

• Since depends on , the optimization can be done if we know .




Here Gn means NDCG @ position n

RankGP(J. Yeh, et al. LR4IR 2007)

• RankGP = Preprocessing + Learning + Prediction

• Preprocessing– Query-based normalization on features

• Learning– Single-population GP

– Widely used to optimize non-smoothing non-differentiable objectives.

• Prediction–


Ranking Function Learning

• Define ranking function as a tree

• Use GP to learn the optimal tree• Evolution mechanism

– Crossover, mutation, reproduction, tournament selection.

• Fitness function– IR evaluation measure (MAP).




TD 2003 Data

LambdaRank(C. Burges, et al. NIPS 2006)

• Basic idea– IR evaluation measures are non-smooth and non-

differentiable.

– It is usually much easier to specify rules determining how to change rank order of documents than to construct a smooth loss function.

• Example– Two relevant documents

D1 and D2;

– WTA as the evaluation measure.


To achieve WTA=1

Lambda Function, Instead of Loss Function

• Instead of explicitly defining the loss function, directly define the gradient:

• A lambda which was shown to effectively optimize NDCG.


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4/20/2008 Tie-Yan Liu @ Tutorial at WWW 2008 92Web Data

Other Work in this Category

• A combined component approach for finding collection-adapted ranking functions based on genetic programming (CCA), (H. Almeida, M. Goncalves, et al. SIGIR 2007).

• A Markov random field model for term dependencies, (D. Metzler, W. Croft. SIGIR 2005).


Discussions

• Progress has been made as compared to pointwise and pairwise approaches

• Unsolved problems– Is the upper bound in SVM-MAP tight enough?– Is SoftNDCG really correlated with NDCG?– Is there any theoretical justification on the correlation

between the implicit loss function used in LambdaRankand NDCG?

– Multiple measures are not necessarily consistent with each other: which to optimize?


Define Listwise Loss Function

• Indirectly optimizing IR evaluation measures– Consider properties of ranking for IR.

• Examples– RankCosine: use cosine similarity between score vectors as

loss function– ListNet: use KL divergence between permutation

probability distributions as loss function– ListMLE: use negative log likelihood of the ground truth

permutation as loss function

• Theoretical analysis on listwise loss functions


RankCosine(T. Qin, T. Liu, et al. IP&M 2007)

• Loss function define as

• Properties

– Loss is computed by using all documents of a query.

– Insensitive to number of documents / document pairs per query

– Emphasize correct ranking by setting high scores for top in ground truth.

– Bounded:


Optimization

• Additive model as ranking function

• Loss over queries

• Gradient descent for optimization


More Investigation on Loss Functions

• A Simple Example:– function f: f(A)=3, f(B)=0, f(C)=1 ACB

– function h: h(A)=4, h(B)=6, h(C)=3 BAC

– ground truth g: g(A)=6, g(B)=4, g(C)=3 ABC

• Question: which function is closer to ground truth?– Based on pointwise similarity: sim(f,g) < sim(g,h).– Based on pairwise similarity: sim(f,g) = sim(g,h)

– Based on cosine similarity between score vectors?f: <3,0,1> g:<6,4,3> h:<4,6,3>

• However, according to position discount, f should be closer to g!


sim(g,h)=0.93sim(f,g)=0.85

Closer!

Permutation Probability Distribution

• Question:

– How to represent a ranked list?

• Solution

– Ranked list ↔ Permutation probability distribution

– More informative representation for ranked list: permutation and ranked list has 1-1 correspondence.


Luce Model: Defining Permutation Probability

• Probability of permutation 𝜋 is defined as

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Properties of Luce Model

• Nice properties

– Continuous, differentiable, and convex w.r.t. score s.

– Suppose g(A) = 6, g(B)=4, g(C)=3, P(ABC) is largest and P(CBA) is smallest; for the ranking based on f: ABC, swap any two, probability will decrease, e.g., P(ABC) > P(ACB)

– Translation invariant, when

– Scale invariant, when

)exp()( ss

sas )(


Distance between Ranked Lists

dis(f,g) = 0.46

dis(g,h) = 2.56

φ = exp

1034/20/2008

Using KL-divergenceto measure difference between distributions

Tie-Yan Liu @ Tutorial at WWW 2008

ListNet Algorithm(Z. Cao, T. Qin, T. Liu, et al. ICML 2007)

• Loss function = KL-divergence between two permutation probability distributions (φ = exp)

• Model = Neural Network

• Algorithm = Gradient Descent

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tu jy

jyn

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tu jy

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u

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),...,( 1 )(

)(

1 )(

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1 )exp(

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Pairwise (RankNet)


Training Performance on TD2003 Dataset

Listwise (ListNet)

More correlated!

Limitations of ListNet

• Still too complex in practice: O(n⋅n!)

• Performance of ListNet depends on the mapping function from ground truth label to scores

– Ground truths are permutations (ranked list) or group of permutations; but not naturally scores.


Solution

• Never assume ground truth to be scores.

• Given the scores outputted by the ranking model, compute the likelihood of a ground truth permutation, and maximize it to learn the model parameter.

• The complexity is reduced from O(n⋅n!) to O(n).


Likelihood Loss

• Permutation Likelihood

• Likelihood Loss


ListMLE Algorithm(F. Xia, T. Liu, et al. ICML 2008)

• Loss function = likelihood loss

• Model = Neural Network

• Algorithm = Stochastic Gradient Descent




TD2004 Dataset

Listwise Ranking Framework

• Input space: X

– Elements in X are sets of objects to be ranked

• Output space: Y

– Elements in Y are permutations of objects

• Joint probability distribution: PXY

• Hypothesis space: H

–

• Expected loss

–


True Loss in Listwise Ranking

• To analysis the theoretical properties of listwise loss functions, the “true” loss of ranking is to be defined.

– The true loss describes the difference between a given ranked list (permutation) and the ground truth ranked list (permutation).

• Ideally, the “true” loss should be cost-sensitive, but for simplicity, we investigate the “0-1” loss.

–


Surrogate Loss in Listwise Approach

• Widely-used ranking function

–

• Corresponding empirical loss

–

• Challenges

– Due to the sorting function and the 0-1 loss, the empirical loss is non-differentiable.

– To tackle the problem, a surrogate loss is used.

–


Surrogate Loss Minimization Framework

• RankCosine, ListNet and ListMLE can all be well fitted into this framework of surrogate loss minimization.

– RankCosine

– ListNet

– ListMLE


Evaluation of Surrogate Loss

• Continuity, differentiability and convexity

• Computational efficiency

• Statistical consistency

• Soundness

These properties have been well studied in classification, but not sufficiently in ranking.


Continuity, Differentiability, Convexity, Efficiency

Loss Continuity Differentiability Convexity Efficiency

Cosine Loss(RankCosine)

√ √ X O(n)

Cross-entropy loss(ListNet)

√ √ √ O(n·n!)

Likelihood loss(ListMLE)

√ √ √ O(n)


Statistical Consistency

• When minimizing the surrogate loss is equivalent to minimizing the expected 0-1 loss, we say the surrogate loss function is consistent.

• A theory for verifying consistency in ranking.


The ranking of an object is inherently determined by its own.

Starting with a ground-truth permutation, the loss will increase after exchanging the positions of two objects in it, and the speed of increase in loss is sensitive to the positions of objects.

Statistical Consistency (2)

• It has been proven (F. Xia, T. Liu, et al. ICML 2008)

– Cosine Loss is statistically consistent.

– Cross entropy loss is statistically consistent.

– Likelihood loss is statistically consistent.


Soundness

• Cosine loss is not very sound

– Suppose we have two documents D2 ⊳ D1.


g1

g2 g1=g2

α

Correct rankingIncorrect Ranking

Soundness (2)

• Cross entropy loss is not very sound



g2 g1=g2

g1


Soundness (3)

• Likelihood loss is sound



g2 g1=g2

g1


Discussion

• Progress has been made as compared to pointwiseand pairwise approaches

• Likelihood loss seems to be one of the best listwiseloss functions, according to the above discussions.

• In real ranking problems, the true loss should be cost-sensitive.

– Need further investigations.


Summary

• Ranking is a new application, and also a new machine learning problem.

• Learning to rank: from pointwise, pairwise to listwiseapproach.



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inw

ise

pai

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2000 2001 2002 2003 2004 2005 2006 2007

MCRankDiscriminative IR model

RankNetRankingSVM

RankBoostFRank

IRSVM

AdaRank

SVM-MAP

SoftRankRankCosine

RankGP

MHR

ListNet* Papers published by our group

Supervised Rank Aggregation

LambdaRank

ListMLE

LDMGBRank

MPRank

QBRank

CCA

Relational Ranking

Rank Refinement

Future Work

• From loss function to ranking function.– Beyond the ranking function on single documents.

– Beyond single ranking model for all kinds of queries.

• From learning process to preprocessing and post-processing.– Automatic ground truth mining

– Feature extraction and selection might be even more important than selecting learning algorithms in practice.

– Dedup and diversification are helpful.

• From discriminative learning to generative learning

• From algorithms to learning theory.– “True loss” for ranking.

– Generalization ability of listwise approach.


You May Want to Read…

• Ground Truth Mining– Active Exploration for Learning Rankings from Clickthrough Data (F.

Radlinski, T. Joachims, KDD 2007)

– Query Chains: Learning to Rank from Implicit Feedback (F. Radlinski, T. Joachims, KDD 2005)

• Feature Selection– Feature Selection for Ranking (X. Geng, T. Liu, et al. SIGIR 2007)

• Ranking Function– Multi-hyperplane ranker (T. Qin, T. Liu, et al. SIGIR 2007)

– Multiple Nested Ranker (I. Matveeva, C.J.C. Burges, et al. SIGIR 2006)

– Supervised Rank Aggregation (Y. Liu, T. Liu, et al. WWW 2007)

– Learning to Rank Relational Objects (T. Qin, T. Liu, et al. WWW 2008)

– Ranking Refinement and Its Application to Information Retrieval (R. Jin, H. Valizadegan, et al. WWW 2008)


• R. Herbrich, T. Graepel, et al. Support Vector Learning for Ordinal Regression, ICANN1999.

• T. Joachims, Optimizing Search Engines Using Clickthrough Data, KDD 2002.

• Y. Freund, R. Iyer, et al. An Efficient Boosting Algorithm for Combining Preferences, JMLR 2003.

• R. Nallapati, Discriminative model for information retrieval, SIGIR 2004.

• J. Gao, H. Qi, et al. Linear discriminant model for information retrieval, SIGIR 2005.

• D. Metzler, W. Croft. A Markov random field model for term dependencies, SIGIR 2005.

• C.J.C. Burges, T. Shaked, et al. Learning to Rank using Gradient Descent, ICML 2005.

• I. Tsochantaridis, T. Joachims, et al. Large Margin Methods for Structured and Interdependent Output Variables, JMLR, 2005.

• F. Radlinski, T. Joachims, Query Chains: Learning to Rank from Implicit Feedback, KDD 2005.

• I. Matveeva, C.J.C. Burges, et al. High accuracy retrieval with multiple nested ranker, SIGIR 2006.

• C.J.C. Burges, R. Ragno, et al. Learning to Rank with Nonsmooth Cost Functions , NIPS 2006

• Y. Cao, J. Xu, et al. Adapting Ranking SVM to Information Retrieval, SIGIR 2006.

• Z. Cao, T. Qin, et al. Learning to Rank: From Pairwise to Listwise Approach, ICML 2007.


References

• T. Qin, T.-Y. Liu, et al, Multiple hyperplane Ranker, SIGIR 2007.

• T.-Y. Liu, J. Xu, et al. LETOR: Benchmark dataset for research on learning to rank for information retrieval, LR4IR 2007.

• M.-F. Tsai, T.-Y. Liu, et al. FRank: A Ranking Method with Fidelity Loss, SIGIR 2007.

• Z. Zheng, H. Zha, et al. A General Boosting Method and its Application to Learning Ranking Functions for Web Search, NIPS 2007.

• Z. Zheng, H. Zha, et al, A Regression Framework for Learning Ranking Functions Using Relative Relevance Judgment, SIGIR 2007.

• M. Taylor, J. Guiver, et al. SoftRank: Optimising Non-Smooth Rank Metrics, LR4IR 2007.

• J.-Y. Yeh, J.-Y. Lin, et al. Learning to Rank for Information Retrieval using Generic Programming, LR4IR 2007.

• T. Qin, T.-Y. Liu, et al, Query-level Loss Function for Information Retrieval, Information Processing and Management, 2007.

• X. Geng, T.-Y. Liu, et al, Feature Selection for Ranking, SIGIR 2007.


References (2)

References (3)

• Y. Yue, T. Finley, et al. A Support Vector Method for Optimizing Average Precision, SIGIR 2007.

• Y.-T. Liu, T.-Y. Liu, et al, Supervised Rank Aggregation, WWW 2007.

• J. Xu and H. Li, A Boosting Algorithm for Information Retrieval, SIGIR 2007.

• F. Radlinski, T. Joachims. Active Exploration for Learning Rankings from Clickthrough Data, KDD 2007.

• P. Li, C. Burges, et al. McRank: Learning to Rank Using Classification and Gradient Boosting, NIPS 2007.

• C. Cortes, M. Mohri, et al. Magnitude-preserving Ranking Algorithms, ICML 2007.

• H. Almeida, M. Goncalves, et al. A combined component approach for finding collection-adapted ranking functions based on genetic programming, SIGIR 2007.

• T. Qin, T.-Y. Liu, et al, Learning to Rank Relational Objects and Its Application to Web Search, WWW 2008.

• R. Jin, H. Valizadegan, et al. Ranking Refinement and Its Application to Information Retrieval, WWW 2008.

• F. Xia. T.-Y. Liu, et al. Listwise Approach to Learning to Rank – Theory and Algorithm, ICML 2008.

• Y. Lan, T.-Y. Liu, et al. On Generalization Ability of Learning to Rank Algorithms, ICML 2008.


Acknowledgement

• Hang Li (Microsoft Research Asia)

• Wei-Ying Ma (Microsoft Research Asia)

• Jun Xu (Microsoft Research Asia)

• Tao Qin (Tsinghua University)

• Soumen Chakrabarti (IIT)


[email protected]://research.microsoft.com/users/tyliu/

mailto:[email protected]

http://research.microsoft.com/users/tyliu/