an optimization framework for query recommendation...recommendation are np-complete – reduction...
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An Optimization Framework for Query RecommendationAris Anagnostopoulos, Luca Becchetti,
Carlos Castillo, Aristides Gionis
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As you set
out for Ithaca,
hope your road
is a long one,
full of adventure,
full of discovery.
K. Kavafis
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6 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Problem
Given a set of possible user histories
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7 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Problem
Given a value for different states
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8 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Problem
Given a value for different states
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9 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Problem
“Nudge” the users in a certain direction
-
-
+
+
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10 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Problem
“Nudge” the users in a certain direction
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11 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Problem definition
Given a set of possible user sessions
Given a certain value for different states
“Nudge” the users in a certain direction
Objectives
– 1. collect a large reward along the way -or-
– 2. end the session at a rewarding action
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12 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Constraints
Source: not-of-this-earth.com
• We are not almighty
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13 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Constraints
• We are not almighty
– We can only suggest, not order
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14 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Constraints
• We are not almighty
– We can only suggest, not order
• We are not all-knowing
Source: Wikimedia commons.
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15 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Constraints
• We are not almighty
– We can only suggest, not order
• We are not all-knowing
– We do not know how the users will react
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Framework
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17 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Setting
• Paper: general framework
– e.g. for optimizing links on web sites
• Talk: query recommendation
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20 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Query recommendations
• Reformulation probabilities
– P(q,q') original
central park
central park map
central park new york
central park hotel
central park zoo
0.3
0.2
0.2
0.3
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21 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Query recommendations
• Reformulation probabilities
– P(q,q') original
– P'(q,q') perturbed = P(q,q') + ρ(Q,q,q')
central park
central park map
central park new york
central park hotel
central park zoo
0.3
0.2
0.2
0.3
-0.1
-0.1
+0.1
+0.1
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22 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Query recommendations
• Reformulation probabilities
– P(q,q') original
– P'(q,q') perturbed = P(q,q') + ρ(Q,q,q')
central park
central park map
central park new york
central park hotel
central park zoo
0.2
0.1
0.3
0.4
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23 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Example values w(·)
• Search engine results page
– Quality of search results
• General page
– Dwell time
– User ratings
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24 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Objective functions U(·)
Kavafian
“a road full of adventure”
U(<q1,q2,...,qt>) = Σw(qi)
Machiavellian
“ends justify means”
U(<q1,q2,...,qt>) = w(qt)
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25 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
The Kavafian objective
Useful when users want to explore, or be entertained
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26 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
The Kavafian objective
Useful when users want to explore, or be entertained
-
+ “funny video”
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27 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Optimization problem
• Given:
– Original transition probabilities P
– Starting node q
– Node values w
– Perturbation function ρ
• Add up to k links (per node), maximize expected utility of paths starting at q
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28 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Single-step recommendation
q t
• Recommend now, leave user alone later
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29 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Single-step recommendation
t
• Recommend now, leave user alone later
q
+
-
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30 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Multi-step recommendation
q t
• Recommend at each step in the future
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31 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Multi-step recommendation
t
• Recommend at each step in the future
q
- +
+
-
-
+ -
+
-
+
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32 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Multi-step case
• Multi- and Single-step recommendation are NP-complete
– Reduction from MAXIMUM-COVER
• Heuristic for multi-step problem:
– at each node, assume rest of the graph is unperturbed when computing utility of adding an edge
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33 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Single-step case
• Greedy heuristic for “Machiavellian” objective: find (qi, qj) maximizing
ρij(E[U(path(qj))] – wi)
• Repeat k times
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34 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Observation
• Greedy heuristic achieves utility at least (1-x) of the optimum, with x << 1 in cases of practical interest
– It is possible to construct pathological instances s.t. that greedy performs poorly
– x depends on termination probability at qi and probabilities of following recommendations
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Application
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36 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Large-scale experiment
We observe perturbed probabilities P'(q,q'), unless we disable search assist to see P(q,q')
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37 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Empirical observations
• Notation:
– τq, τ'q session-end probabilities
• Recommendations decrease termination probability:
• Average τq≈0.90
• Average τ'q≈0.84
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Termination probability
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39 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Empirical observations
• Recommendations decrease termination probability, τq≈0.90 τ'q≈0.84
• Decrease is almost entirely due to more clicks on recommendations
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'
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41 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Empirical observations
• Recommendations decrease termination probability from ≈0.90 to ≈0.84
• Decrease is almost entirely due to more clicks on recommendations
• ρ is difficult to estimate
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P(q,q'): without recommendations
P'(q
,q'):
with
rec
omm
enda
tions
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There is an increase
P(q,q'): without recommendations
P'(q
,q'):
with
rec
omm
enda
tions
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Many un-seen suggestionsare clicked when shown
P(q,q'): without recommendations
P'(q
,q'):
with
rec
omm
enda
tions
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The rest are in generaldifficult to predict
P(q,q'): without recommendations
P'(q
,q'):
with
rec
omm
enda
tions
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46 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
So what do we do?
• We approximate ρ by a linear function on
– P(q,q')
– Textual similarity of q and q'
– Terminal probability of q
• We have a low accuracy on this prediction
– r ≈ 0.5
• We use as weights the CTR on results
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Evaluation
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48 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Baselines:
– Prefer queries with large w
– Prefer queries with large ρ
– Prefer queries with large ρw
Greedy heuristic performs better for both utility functions
Evaluation results
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“Kavafian” objective “Machiavellian” objective
Expected utility
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50 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
Greedy heuristic performs well
What about relevance?
420 queries assessed by 3 judges There were no significant changes in
relevance between systems
Evaluation results
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51 A. Anagnostopoulos, L. Becchetti, C. Castillo, A. Gionis WSDM'10
• General framework for “nudging” users in a certain direction
• Open algorithmic and practical questions
• In the paper: related work
Conclusions