The document discusses pairwise and listwise approaches to learning to rank. In the pairwise approach, training instances are document pairs and the objective is to classify pairs as correctly or incorrectly ranked. In the listwise approach, training instances are entire document lists and the objective is to minimize listwise loss functions like permutation probability and top one probability. The listwise approach directly optimizes ranking performance while the pairwise approach has drawbacks like treating all document pairs equally.

1. ì
Learning
To
Rank:
From
Pairwise
Approach
to
Listwise
Approach
Zhe
Cao,
Tao
Qin,
Tie-­‐Yan
Liu,
Ming-­‐Feng
Tsai,
and
Hang
Li
Hasan
Hüseyin
Topcu
Learning
To
Rank

2. Outline
ì Related
Work
ì Learning
System
ì Learning
to
Rank
ì Pairwise
vs.
Listwise
Approach
ì Experiments
ì Conclusion

3. Related
Work
ì Pairwise
Approach
:
Learning
task
is
formalized
as
classificaNon
of
object
pairs
into
two
categories
(
correctly
ranked
and
incorrectly
ranked)
ì The
methods
of
classificaNon:
ì Ranking
SVM
(Herbrich
et
al.,
1999)
and
Joachims(2002)
applied
RankingSVM
to
InformaNon
Retrieval
ì RankBoost
(
Freund
et
al.
1998)
ì RankNet
(Burges
et
al.
2005):

4. Learning
System

5. Learning
System
Training
Data,
Data
Preprocessing,
…
How
objects
are
idenNfied?
How
instances
are
modeled?
SVM,
ANN,
BoosNng
Evaluate
with
test
data
Adapted
from
Paaern
Classificaton(Duda,
Hart,
Stork)

6. Ranking

7. Learning
to
Rank

8. Learning
to
Rank
ì A
number
of
queries
are
provided
ì Each
query
is
associated
with
perfect
ranking
list
of
documents
(Ground-­‐Truth)
ì A
Ranking
funcNon
is
created
using
the
training
data
such
that
the
model
can
precisely
predict
the
ranking
list.
ì Try
to
opNmize
a
Loss
funcNon
for
learning.
Note
that
the
loss
funcNon
for
ranking
is
slightly
different
in
the
sense
that
it
makes
use
of
sorNng.

9. Training
Process

10. Data
Labeling
ì Explicit
Human
Judgment
(Perfect,
Excellent,
Good,
Fair,
Bad)
ì Implicit
Relevance
Judgment
:
Derived
from
click
data
(Search
log
data)
ì Ordered
Pairs
between
documents
(A
>
B)
ì List
of
judgments(scores)

11. Features

12. Pairwise
Approach
ì Training
data
instances
are
document
pairs
in
learning

13. Pairwise
Approach
ì Collects
document
pairs
from
the
ranking
list
and
for
each
document
pairs
it
assigns
a
label.
ì
Data
labels
+1
if
score
of
A
>
B
and
-­‐1
if
A
<
B
ì Formalizes
the
problem
of
learning
to
rank
as
binary
classificaNon
ì RankingSVM,
RankBoost
and
RankNet

14. Pairwise
Approach
Drawbacks
ì ObjecNve
of
learning
is
formalized
as
minimizing
errors
in
classificaNon
of
document
pairs
rather
than
minimizing
errors
in
ranking
of
documents.
ì Training
process
is
computaNonally
costly,
as
the
documents
of
pairs
is
very
large.

15. Pairwise
Approach
Drawbacks
ì Equally
treats
document
pairs
across
different
grades
(labels)
(Ex.1)
ì The
number
of
generated
document
pairs
varies
largely
from
query
to
query,
which
will
result
in
training
a
model
biased
toward
queries
with
more
document
pairs.
(Ex.2)

16. Listwise
Approach
ì Training
data
instances
are
document
list
ì The
objecNve
of
learning
is
formalized
as
minimizaNon
of
the
total
loses
with
respect
to
the
training
data.
ì Listwise
Loss
FuncNon
uses
probability
models:
Permuta(on
Probability
and
Top
One
Probability
ments d(i0
)
are given, we construct feature vectors x(i0
)
from
them and use the trained ranking function to assign scores
to the documents d(i0
)
. Finally we rank the documents d(i0
)
in descending order of the scores. We call the learning
problem described above as the listwise approach to learn-
ing to rank.
By contrast, in the pairwise approach, a new training data
set T 0
is created from T , in which each feature vector pair
x(i)
j and x(i)
k forms a new instance where j , k, and +1 is
assigned to the pair if y(i)
j is larger than y(i)
k otherwise 1.
It turns out that the training data T 0
is a data set of bi-
nary classification. A classification model like SVM can
be created. As explained in Section 1, although the pair-
of scores s is defined
Ps(⇡
where s⇡( j) is the scor
⇡.
Let us consider an ex
ing scores s = (s1, s
tions ⇡ = h1, 2, 3i an
lows:
Ps(⇡) =
(
(s1) + (
ments d(i0
)
are given, we construct feature vectors x(i0
)
from
them and use the trained ranking function to assign scores
to the documents d(i0
)
. Finally we rank the documents d(i0
)
in descending order of the scores. We call the learning
problem described above as the listwise approach to learn-
ing to rank.
By contrast, in the pairwise approach, a new training data
set T 0
is created from T , in which each feature vector pair
x(i)
j and x(i)
k forms a new instance where j , k, and +1 is
assigned to the pair if y(i)
j is larger than y(i)
k otherwise 1.
It turns out that the training data T 0
is a data set of bi-
nary classification. A classification model like SVM can
be created. As explained in Section 1, although the pair-
of scores s is defined
Ps(⇡
where s⇡( j) is the scor
⇡.
Let us consider an ex
ing scores s = (s1, s
tions ⇡ = h1, 2, 3i an
lows:
Ps(⇡) =
(
(s1) + (
ments d(i0
)
are given, we construct feature vectors x(i0
)
from
them and use the trained ranking function to assign scores
to the documents d(i0
)
. Finally we rank the documents d(i0
)
in descending order of the scores. We call the learning
problem described above as the listwise approach to learn-
ing to rank.
By contrast, in the pairwise approach, a new training data
set T 0
is created from T , in which each feature vector pair
x(i)
j and x(i)
k forms a new instance where j , k, and +1 is
assigned to the pair if y(i)
j is larger than y(i)
k otherwise 1.
It turns out that the training data T 0
is a data set of bi-
nary classification. A classification model like SVM can
be created. As explained in Section 1, although the pair-
of scores s is defined
Ps(⇡
where s⇡( j) is the scor
⇡.
Let us consider an ex
ing scores s = (s1, s
tions ⇡ = h1, 2, 3i an
lows:
Ps(⇡) =
(
(s1) + (

17. Permutation
Probability
ì Objects
:
{A,B,C}
and
PermutaNons:
ABC,
ACB,
BAC,
BCA,
CAB,
CBA
ì Suppose
Ranking
funcNon
that
assigns
scores
to
objects
sA,
sB
and
sC
ì Permuta5on
Probabilty:
Likelihood
of
a
permutaNon
ì P(ABC)
>
P(CBA)
if
sA
>
sB
>
sC

18. Top
One
Probability
ì Objects
:
{A,B,C}
and
PermutaNons:
ABC,
ACB,
BAC,
BCA,
CAB,
CBA
ì Suppose
Ranking
funcNon
that
assigns
scores
to
objects
sA,
sB
and
sC
ì Top
one
probability
of
an
object
represents
the
probability
of
its
being
ranked
on
the
top,
given
the
scores
of
all
the
objects
ì P(A)
=
P(ABC)
+
P(ACB)
ì NoNce
that
in
order
to
calculate
n
top
one
probabiliNes,
we
sNll
need
to
calculate
n!
permutaNon
probabiliNes.
ì P(A)
=
P(ABC)
+
P(ACB)
ì P(B)
=
P(BAC)
+
P(BCA)
ì P(C)
=
P(CBA)
+
P(CAB)

19. Listwise
Loss
Function
ì With
the
use
of
top
one
probability,
given
two
lists
of
scores
we
can
use
any
metric
to
represent
the
distance
between
two
score
lists.
ì For
example
when
we
use
Cross
Entropy
as
metric,
the
listwise
loss
funcNon
becomes
ì Ground
Truth:
ABCD
vs.
Ranking
Output:
ACBD
or
ABDC

20. ListNet
ì Learning
Method:
ListNet
ì OpNmize
Listwise
Loss
funcNon
based
on
top
one
probability
with
Neural
Network
and
Gradient
Descent
as
opNmizaNon
algorithm.
ì Linear
Network
Model
is
used
for
simplicity:
y
=
wTx
+
b

21. ListNet

22. Ranking
Accuracy
ì ListNet
vs.
RankNet,
RankingSVM,
RankBoost
ì 3
Datasets:
TREC
2003,
OHSUMED
and
CSearch
ì TREC
2003:
Relevance
Judgments
(Relevant
and
Irrelevant),
20
features
extracted
ì OHSUMED:
Relevance
Judgments
(Definitely
Relevant,
PosiNvely
Relevant
and
Irrelevant),
30
features
ì CSearch:
Relevance
Judgments
from
4(‘Perfect
Match’)
to
0
(‘Bad
Match’),
600
features
ì EvaluaNon
Measures:
Normalized
Discounted
CumulaNve
Gain
(NDCG)
and
Mean
Average
Precision(MAP)

23. Experiments
ì NDCG@n
on
TREC

24. Experiments
ì NDCG@n
on
OHSUMED

25. Experiments
ì NDCG@n
on
CSearch

26. Conclusion
ì Discussed
ì Learning
to
Rank
ì Pairwise
approach
and
its
drawbacks
ì Listwise
Approach
outperforms
the
exisNng
Pairwise
Approaches
ì EvaluaNon
of
the
Paper
ì Linear
Neural
Network
model
is
used.
What
about
Non-­‐Linear
model?
ì Listwise
Loss
FuncNon
is
the
key
issue.(Probability
models)

27. References
ì Zhe
Cao,
Tao
Qin,
Tie-­‐Yan
Liu,
Ming-­‐Feng
Tsai,
and
Hang
Li.
2007.
Learning
to
rank:
from
pairwise
approach
to
listwise
approach.
In
Proceedings
of
the
24th
interna(onal
conference
on
Machine
learning
(ICML
'07),
Zoubin
Ghahramani
(Ed.).
ACM,
New
York,
NY,
USA,
129-­‐136.
DOI=10.1145/1273496.1273513
hap://
doi.acm.org/10.1145/1273496.1273513
ì Hang
Li:
A
Short
Introduc5on
to
Learning
to
Rank.
IEICE
TransacNons
94-­‐D(10):
1854-­‐1862
(2011)
ì Learning
to
Rank.
Hang
Li.
Microsow
Research
Asia.
ACL-­‐IJCNLP
2009
Tutorial.
Aug.
2,
2009.
Singapore