Zone scoring Machine-learned scoring Ranking SVMs
PV211: Introduction to Information Retrieval
https://www.fi.muni.cz/~sojka/PV211
IIR 15-2: Learning to rank
Handout version
Petr Sojka, Hinrich Schütze et al.
Faculty of Informatics, Masaryk University, Brno
Center for Information and Language Processing, University of Munich
2024-04-24
(compiled on 2024-04-24 10:20:55)
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Zone scoring Machine-learned scoring Ranking SVMs
Overview
1 Zone scoring
2 Machine-learned scoring
3 Ranking SVMs
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Zone scoring Machine-learned scoring Ranking SVMs
Take-away today
Basic idea of learning to rank (LTR): We use machine learning
to learn the relevance score (retrieval status value) of a
document with respect to a query.
Zone scoring: a particularly simple instance of LTR
Machine-learned scoring as a general approach to ranking
Ranking SVMs
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Zone scoring Machine-learned scoring Ranking SVMs
Main idea
The aim of term weights (e.g., tf-idf) is to measure term
salience.
The sum of term weights is a measure of the relevance of a
document to a query and the basis for ranking.
Now we view this ranking problem as a machine learning
problem – we will learn the weighting or, more generally, the
ranking.
Term weights can be learned using training examples that have
been judged.
This methodology falls under a general class of approaches
known as machine learned relevance or learning to rank.
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Zone scoring Machine-learned scoring Ranking SVMs
Learning weights
Main methodology
Given a set of training examples, each of which is a tuple of:
a query q, a document d, a relevance judgment for d on q
Simplest case: R(d, q) is either relevant (1) or non-relevant
(0)
More sophisticated cases: graded relevance judgments
Learn weights from these examples, so that the learned scores
approximate the relevance judgments in the training examples
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Zone scoring Machine-learned scoring Ranking SVMs
Binary independence model (BIM)
Is what BIM does a form of learning to rank?
Recap BIM:
Estimate classifier of probability of relevance on training set
Apply to all documents
Rank documents according to probability of relevance
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Zone scoring Machine-learned scoring Ranking SVMs
Learning to rank vs. Text classification
Both are machine learning approaches
Text classification, BIM and relevance feedback (if solved by
text classification) are query-specific.
We need a query-specific training set to learn the ranker.
We need to learn a new ranker for each query.
Learning to rank usually refers to query-independent ranking.
We learn a single classifier.
We can then rank documents for a query that we don’t have
any relevance judgments for.
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Zone scoring Machine-learned scoring Ranking SVMs
Learning to rank: Exercise
One approach to learning to rank is to represent each
query-document pair as a data point, represented as a vector.
We have two classes.
Class 1: the query is relevant to the document.
Class 2: the query is not relevant to the document.
This is a standard classification problem, except that the data
points are query-document pairs (as opposed to documents).
Documents are ranked according to probability of relevance of
corresponding document-query pairs.
What features/dimensions would you use to represent a
query-document pair?
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Zone scoring Machine-learned scoring Ranking SVMs
Simple form of learning to rank: Zone scoring
Given: a collection where documents have three zones (a.k.a.
fields): author, title, body
Weighted zone scoring requires a separate weight for each
zone, e.g. g1, g2, g3
Not all zones are equally important:
e.g. author < title < body
→ g1 = 0.2, g2 = 0.3, g3 = 0.5 (so that they add up to 1)
Score for a zone = 1 if the query term occurs in that zone, 0
otherwise (Boolean)
Example
Query term appears in title and body only
Document score: (0.3 · 1) + (0.5 · 1) = 0.8.
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Zone scoring Machine-learned scoring Ranking SVMs
General form of weighted zone scoring
Given query q and document d, weighted zone scoring assigns to
the pair (q, d) a score in the interval [0,1] by computing a linear
combination of document zone scores, where each zone contributes
a value.
Consider a set of documents, which have l zones
Let g1, . . . , gl ∈ [0, 1], such that l
i=1 gi = 1
For 1 ≤ i ≤ l, let si be the Boolean score denoting a match
(or non-match) between q and the ith zone
si = 1 if a query term occurs in zone i, 0 otherwise
Weighted zone score a.k.a ranked Boolean retrieval
Rank documents according to l
i=1 gi si
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Zone scoring Machine-learned scoring Ranking SVMs
Learning weights in weighted zone scoring
Weighted zone scoring may be viewed as learning a linear
function of the Boolean match scores contributed by the
various zones.
No free lunch: labor-intensive assembly of user-generated
relevance judgments from which to learn the weights
Especially in a dynamic collection (such as the Web)
Major search engine put considerable resources into creating
large training sets for learning to rank.
Good news: once you have a large enough training set, the
problem of learning the weights gi reduces to a simple
optimization problem.
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Zone scoring Machine-learned scoring Ranking SVMs
Learning weights in weighted zone scoring: Simple case
Let documents have two zones: title, body
The weighted zone scoring formula we saw before:
l
i=1
gi si
Given q, d, sT (d, q) = 1 if a query term occurs in title, 0
otherwise; sB(d, q) = 1 if a query term occurs in body, 0
otherwise
We compute a score between 0 and 1 for each (d, q) pair
using sT (d, q) and sB(d, q) by using a constant g ∈ [0, 1]:
score(d, q) = g · sT (d, q) + (1 − g) · sB(d, q)
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Zone scoring Machine-learned scoring Ranking SVMs
Learning weights: determine g from training examples
Example
Φj dj qj sT sB r(dj , qj)
Φ1 37 linux 1 1 Relevant
Φ2 37 penguin 0 1 Nonrelevant
Φ3 238 system 0 1 Relevant
Φ4 238 penguin 0 0 Nonrelevant
Φ5 1741 kernel 1 1 Relevant
Φ6 2094 driver 0 1 Relevant
Φ7 3194 driver 1 0 Nonrelevant
Training examples: triples of the form Φj = (dj , qj , r(dj , qj ))
A given training document dj and a given training query qj
are assessed by a human who decides r(dj , qj) (either relevant
or nonrelevant)
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Zone scoring Machine-learned scoring Ranking SVMs
Learning weights: determine g from training examples
Example
Example DocID Query sT sB Judgment
Φ1 37 linux 1 1 Relevant
Φ2 37 penguin 0 1 Nonrelevant
Φ3 238 system 0 1 Relevant
Φ4 238 penguin 0 0 Nonrelevant
Φ5 1741 kernel 1 1 Relevant
Φ6 2094 driver 0 1 Relevant
Φ7 3194 driver 1 0 Nonrelevant
For each training example Φj we have Boolean values
sT (dj , qj ) and sB(dj, qj ) that we use to compute a score:
score(dj , qj ) = g · sT (dj , qj) + (1 − g) · sB(dj, qj )
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Zone scoring Machine-learned scoring Ranking SVMs
Learning weights
We compare this score score(dj , qj ) with the human relevance
judgment for the same document-query pair (dj , qj).
We define the error of the scoring function with weight g as
ǫ(g, Φj ) = (r(dj, qj ) − score(dj , qj ))2
Then, the total error of a set of training examples is given by
j
ǫ(g, Φj )
The problem of learning the constant g from the given
training examples then reduces to picking the value of g that
minimizes the total error.
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Zone scoring Machine-learned scoring Ranking SVMs
Minimizing the total error ǫ: Example (1)
Training examples
Example DocID Query sT sB Judgment
Φ1 37 linux 1 1 1 (relevant)
Φ2 37 penguin 0 1 0 (nonrelevant)
Φ3 238 system 0 1 1 (relevant)
Φ4 238 penguin 0 0 0 (nonrelevant)
Φ5 1741 kernel 1 1 1 (relevant)
Φ6 2094 driver 0 1 1 (relevant)
Φ7 3194 driver 1 0 0 (nonrelevant)
Compute score:
score(dj , qj ) = g · sT (dj , qj) + (1 − g) · sB(dj, qj )
Compute total error: j ǫ(g, Φj ), where
ǫ(g, Φj ) = (r(dj , qj ) − score(dj , qj))2
Pick the value of g that minimizes the total error
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Zone scoring Machine-learned scoring Ranking SVMs
Minimizing the total error ǫ: Example (2)
Compute score score(dj , qj)
score(d1, q1) = g · 1 + (1 − g) · 1 = g + 1 − g = 1
score(d2, q2) = g · 0 + (1 − g) · 1 = 0 + 1 − g = 1 − g
score(d3, q3) = g · 0 + (1 − g) · 1 = 0 + 1 − g = 1 − g
score(d4, q4) = g · 0 + (1 − g) · 0 = 0 + 0 = 0
score(d5, q5) = g · 1 + (1 − g) · 1 = g + 1 − g = 1
score(d6, q6) = g · 0 + (1 − g) · 1 = 0 + 1 − g = 1 − g
score(d7, q7) = g · 1 + (1 − g) · 0 = g + 0 = g
Compute total error j ǫ(g, Φj )
(1−1)2 +(0−1+g)2 +(1−1+g)2 +(0−0)2 +(1−1)2 +(1−1+
g)2+(0−g)2 = 0+(−1+g)2+g2+0+0+g2+g2 = 1−2g+4g2
Pick the value of g that minimizes the total error
Setting derivative to 0, gives you a minimum of g = 1
4.
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Zone scoring Machine-learned scoring Ranking SVMs
Weight g that minimizes error in the general case
g =
n10r + n01n
n10r + n10n + n01r + n01n
n... are the counts of rows of the training set table with the
corresponding properties:
n10r sT = 1 sB = 0 document relevant
n10n sT = 1 sB = 0 document nonrelevant
n01r sT = 0 sB = 1 document relevant
n01n sT = 0 sB = 1 document nonrelevant
Derivation: see book
Note that we ignore documents that have 0 match scores for
both zones or 1 match scores for both zones – the value of g
does not change their final score.
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Zone scoring Machine-learned scoring Ranking SVMs
Exercise: Compute g that minimizes the error
DocID Query sT sB Judgment
Φ1 37 linux 0 0 Relevant
Φ2 37 penguin 1 1 Nonrelevant
Φ3 238 system 1 0 Relevant
Φ4 238 penguin 1 1 Nonrelevant
Φ5 238 redmond 0 1 Nonrelevant
Φ6 1741 kernel 0 0 Relevant
Φ7 2094 driver 1 0 Relevant
Φ8 3194 driver 0 1 Nonrelevant
Φ9 3194 redmond 0 0 Nonrelevant
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Zone scoring Machine-learned scoring Ranking SVMs
More general setup of machine learned scoring
So far, we have considered a case where we combined match
scores (Boolean indicators of relevance).
Now consider more general factors that go beyond Boolean
functions of query term presence in document zones.
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Zone scoring Machine-learned scoring Ranking SVMs
Two examples of typical features
The vector space cosine similarity between query and
document (denoted α)
The minimum window width within which the query terms lie
(denoted ω)
Query term proximity is often indicative of topical relevance.
Thus, we have one feature that captures overall
query-document similarity and one features that captures
proximity of query terms in the document.
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Zone scoring Machine-learned scoring Ranking SVMs
Learning to rank setup for these two features
Example
Example DocID Query α ω Judgment
Φ1 37 linux 0.032 3 relevant
Φ2 37 penguin 0.02 4 nonrelevant
Φ3 238 operating system 0.043 2 relevant
Φ4 238 runtime 0.004 2 nonrelevant
Φ5 1741 kernel layer 0.022 3 relevant
Φ6 2094 device driver 0.03 2 relevant
Φ7 3191 device driver 0.027 5 nonrelevant
α is the cosine score. ω is the window width.
This is exactly the same setup as for zone scoring except we now
have more complex features that capture whether a document is
relevant to a query.
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Zone scoring Machine-learned scoring Ranking SVMs
Graphic representation of the training set
This should look familiar.
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Zone scoring Machine-learned scoring Ranking SVMs
In this case: LTR approach learns a linear classifier in 2D
A linear classifier in 2D is
a line described by the
equation w1d1 + w2d2 = θ
Example for a 2D linear
classifier
Points (d1 d2) with
w1d1 + w2d2 ≥ θ are in
the class c.
Points (d1 d2) with
w1d1 + w2d2 < θ are in
the complement class c.
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Zone scoring Machine-learned scoring Ranking SVMs
Learning to rank setup for two features
Again, two classes: relevant = 1 and nonrelevant = 0
We now seek a scoring function that combines the values of
the features to generate a value that is (close to) 0 or 1.
We wish this function to be in agreement with our set of
training examples as much as possible.
A linear classifier is defined by an equation of the form:
Score(d, q) = Score(α, ω) = aα + bω + c,
where we learn the coefficients a, b, c from training data.
Regression vs. classification
We have only covered binary classification so far.
We can also cast the problem as a regression problem.
This is what we did for zone scoring just now.
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Zone scoring Machine-learned scoring Ranking SVMs
Different geometric interpretation of what’s happening
The function Score(α, ω)
represents a plane
“hanging above” the
figure.
Ideally this plane assumes
values close to 1 above
the points marked R, and
values close to 0 above
the points marked N.
0
2 3 4 5
0.05
0.025
cosinescore!
Term proximity "
R!
R!
R!
R!
R! R!
R!
R!R!
R!
R!
N!
N!
N!
N!
N!
N!
N!
N!
N!
N!
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Zone scoring Machine-learned scoring Ranking SVMs
Linear classification in this case
We pick a threshold θ.
If Score(α, ω) > θ, we
declare the document
relevant, otherwise we
declare it nonrelevant.
As before, all points that
satisfy Score(α, ω) = θ
form a line (dashed here)
→ linear classifier that
separates relevant from
nonrelevant instances.
0
2 3 4 5
0.05
0.025
cosinescore!
Term proximity "
R!
R!
R!
R!
R! R!
R!
R!R!
R!
R!
N!
N!
N!
N!
N!
N!
N!
N!
N!
N!
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Zone scoring Machine-learned scoring Ranking SVMs
Summary
The problem of making a binary relevant/nonrelevant
judgment is cast as a classification or regression problem,
based on a training set of query-document pairs and
associated relevance judgments.
In the example: The classifier corresponds to a line
Score(α, ω) = θ in the α-ω plane.
In principle, any method learning a linear classifier (including
least squares regression) can be used to find this line.
Big advantage of learning to rank: we can avoid hand-tuning
scoring functions and simply learn them from training data.
Bottleneck of learning to rank: maintaining a representative
set of training examples whose relevance assessments must be
made by humans.
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Zone scoring Machine-learned scoring Ranking SVMs
Learning to rank for more than two features
The approach can be readily generalized to a large number of
features.
In addition to cosine similarity and query term window, there
are lots of other indicators of relevance: PageRank-style
measures, document age, zone contributions, document
length, etc.
If these measures can be calculated for a training document
collection with relevance judgments, any number of such
measures can be used to machine-learn a classifier.
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Zone scoring Machine-learned scoring Ranking SVMs
LTR features used by Microsoft Research (1)
Zones: body, anchor, title, url, whole document
Features derived from standard IR models: query term
number, query term ratio, length, idf, sum of term frequency,
min of term frequency, max of term frequency, mean of term
frequency, variance of term frequency, sum of length
normalized term frequency, min of length normalized term
frequency, max of length normalized term frequency, mean of
length normalized term frequency, variance of length
normalized term frequency, sum of tf-idf, min of tf-idf, max of
tf-idf, mean of tf-idf, variance of tf-idf, boolean model, BM25
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Zone scoring Machine-learned scoring Ranking SVMs
LTR features used by Microsoft Research (2)
Language model features: LMIR.ABS, LMIR.DIR, LMIR.JM
Web-specific features: number of slashes in url, length of url,
inlink number, outlink number, PageRank, SiteRank
Spam features: QualityScore
Usage-based features: query-url click count, url click count,
url dwell time
See link in resources for more information
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Zone scoring Machine-learned scoring Ranking SVMs
Shortcoming of our LTR approach so far
Approaching IR ranking like we have done so far is not
necessarily the right way to think about the problem.
Statisticians normally first divide problems into classification
problems (where a categorical variable is predicted) versus
regression problems (where a real number is predicted).
In between is the specialized field of ordinal regression where a
ranking is predicted.
Machine learning for ad hoc retrieval is most properly thought
of as an ordinal regression problem, where the goal is to rank
a set of documents for a query, given training data of the
same sort.
Next up: ranking SVMs, a machine learning method that
learns an ordering directly.
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Zone scoring Machine-learned scoring Ranking SVMs
Exercise
Example
Example DocID Query Cosine ω Judgment
Φ1 37 linux 0.03 3 relevant
Φ2 37 penguin 0.04 5 nonrelevant
Φ3 238 operating system 0.04 2 relevant
Φ4 238 runtime 0.02 3 nonrelevant
Give parameters a, b, c of a line aα + bω + c that separates
relevant from nonrelevant.
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Zone scoring Machine-learned scoring Ranking SVMs
Basic setup for ranking SVMs
As before we begin with a set of judged query-document pairs.
But we do not represent them as query-document-judgment
triples.
Instead, we ask judges, for each training query q, to order the
documents that were returned by the search engine with
respect to relevance to the query.
We again construct a vector of features ψj = ψ(dj , q) for each
document-query pair – exactly as we did before.
For two documents di and dj , we then form the vector of
feature differences:
Φ(di , dj , q) = ψ(di , q) − ψ(dj , q)
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Zone scoring Machine-learned scoring Ranking SVMs
Training a ranking SVM
Vector of feature differences: Φ(di , dj, q) = ψ(di , q) − ψ(dj , q)
By hypothesis, one of di and dj has been judged more
relevant.
Notation: We write di ≺ dj for “di precedes dj in the results
ordering”.
If di is judged more relevant than dj, then we will assign the
vector Φ(di , dj , q) the class yijq = +1; otherwise −1.
This gives us a training set of pairs of vectors and
“precedence indicators”. Each of the vectors is computed as
the difference of two document-query vectors.
We can then train an SVM on this training set with the goal
of obtaining a classifier that returns
wTΦ(di , dj , q) > 0 iff di ≺ dj
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Zone scoring Machine-learned scoring Ranking SVMs
Advantages of Ranking SVMs vs. Classification/regression
Documents can be evaluated relative to other candidate
documents for the same query, rather than having to be
mapped to a global scale of goodness.
This often is an easier problem to solve since just a ranking is
required rather than an absolute measure of relevance.
Especially germane in web search, where the ranking at the
very top of the results list is exceedingly important.
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Zone scoring Machine-learned scoring Ranking SVMs
Why simple ranking SVMs don’t work that well
Ranking SVMs treat all ranking violations alike.
But some violations are minor problems, e.g., getting the order
of two relevant documents wrong.
Other violations are big problems, e.g., ranking a nonrelevant
document ahead of a relevant document.
Some queries have many relevant documents, others few.
Depending on the training regime, too much emphasis may be
put on queries with many relevant documents.
In most IR settings, getting the order of the top documents
right is key.
In the simple setting we have described, top and bottom ranks
will not be treated differently.
→ Learning-to-rank frameworks actually used in IR are more
complicated than what we have presented here.
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Zone scoring Machine-learned scoring Ranking SVMs
Example for superior performance of LTR
SVM algorithm that directly optimizes MAP (as opposed to
ranking).
Proposed by: Yue, Finley, Radlinski, Joachims, ACM SIGIR 2002.
Performance compared to state-of-the-art models: cosine, tf-idf,
BM25, language models (Dirichlet and Jelinek-Mercer)
Learning-to-rank clearly better than non-machine-learning
approaches
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Zone scoring Machine-learned scoring Ranking SVMs
Optimizing scaling/representation of features
Both of the methods that we’ve seen treat the features as
given and do not attempt to modify the basic representation
of the document-query pairs.
Much of traditional IR weighting involves nonlinear scaling of
basic measurements (such as log-weighting of term frequency,
or idf).
At the present time, machine learning is very good at
producing optimal weights for features in a linear
combination, but it is not good at coming up with good
nonlinear scalings of basic measurements.
This area remains the domain of human feature engineering.
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Zone scoring Machine-learned scoring Ranking SVMs
Assessment of learning to rank
The idea of learning to rank is old.
Early work by Norbert Fuhr and William S. Cooper
But it is only very recently that sufficient machine learning
knowledge, training document collections, and computational
power have come together to make this method practical and
exciting.
While skilled humans can do a very good job at defining
ranking functions by hand, hand tuning is difficult, and it has
to be done again for each new document collection and class
of users.
The more features are used in ranking, the more difficult it is
to manually integrate them into one ranking function.
Web search engines use a large number of features → web
search engines need some form of learning to rank.
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Zone scoring Machine-learned scoring Ranking SVMs
Exercise
Write down the training set from the last exercise as a training set
for a ranking SVM.
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Zone scoring Machine-learned scoring Ranking SVMs
Take-away today
Basic idea of learning to rank (LTR): We use machine learning
to learn the relevance score (retrieval status value) of a
document with respect to a query.
Zone scoring: a particularly simple instance of LTR
Machine-learned scoring as a general approach to ranking
Ranking SVMs
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Zone scoring Machine-learned scoring Ranking SVMs
Resources
Chapter 15-2 of IIR
Resources at https://www.fi.muni.cz/~sojka/PV211/
and http://cislmu.org, materials in MU IS and FI MU
library
References to ranking SVM results
Microsoft learning to rank datasets
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