assia2015sakai

Evaluation 1: System-Oriented
Tetsuya Sakai
@tetsuyasakai
Waseda University
August 24, 2015@ASSIA 2015, Taipei.

About Tetsuya Sakai
• Professor – Department of Computer Science at Waseda University
• Associate Dean – IT Strategies Division of Waseda University
• Visiting professor – National Institute of Informatics
• Researcher in information retrieval, natural language processing,
interaction
• Editor-in-chief (Asia/Australasia) – Information Retrieval Journal (Springer)
• SIGIR 2013 PC co-chair
• SIGIR 2017 general co-chair
• NTCIR general co-chair
• Toshiba → Cambridge U → Toshiba → NewsWatch
→ Microsoft Research Asia → Waseda

LECTURE OUTLINE
1. Why evaluate?
2. Set retrieval evaluation measures
3. Ranked retrieval evaluation measures
4. More evaluation measures
5. Statistical significance, power, effect sizes
6. Summary
7. References

• IR researchers’ goal: build systems
that satisfy the user’s information
needs.
• We cannot ask users all the time, so
we need measures as surrogates of
user satisfaction/performance.
• “If you cannot measure it, you
cannot improve it.”
http://zapatopi.net/kelvin/quotes/
system
system
system
Measure
Usersatisfaction
Improvements
Does it correlate with user
satisfaction?
Why measure?

Improvements that don’t add up [Armstrong09]
Armstrong et al. analysed 106 papers from SIGIR ’98-’08,
CIKM ’04-’08 that used TREC data, and reported:
• Researchers often use low baselines
• Researchers claim statistically significant improvements,
but the results are often not competitive with the best
TREC systems
• IR effectiveness has not really improved over a decade!
What we want What we’ve got?

The best IR system in the world
I’ve invented
an IR system

I’ve invented
an IR system
A
I’ve built Test
Collection A
to evaluate it

I’ve invented
an IR system
A
I’ve built Test
Collection A
to evaluate it
A
I’ve evaluated my
system with A and
it’s the best

I’ve invented
an IR system
A
I’ve built Test
Collection A
to evaluate it
A
I’ve evaluated my
system with A and
it’s the best
I’ve invented
an IR system
B
I’ve built Test
collection B
to evaluate it
B
I’ve evaluated my
system with B and
it’s the best

A typical test collection
Topic
Relevance assessments
(relevant/nonrelevant documents)
Document collection
Topic
Topic
: :
Topic set
:
“Qrels”The Sakai Lab
home page
sakailab.com: relevant
www.f.waseda.jp/tetsuya/: relevant
http://tanabe-agency.co.jp/talent/sakai_masato/:
nonrelevant

Recall, Precision and E-measure
[vanRijsbergen79]
• E-measure = (|A∪B|-|A∩B|)/(|A|+|B|)
= 1 – 1/(0.5*(1/Prec) + 0.5*(1/Rec))
where Prec=|A∩B|/|B|, Rec=|A∩B|/|A|.
A generalised form
= 1 – 1/(α*(1/Prec) + (1-α)*(1/Rec))
= 1 – (β + 1)*Prec*Rec/(β *Prec+Rec)
where α = 1/(β + 1).
A: Relevant docs B: Retrieved docs
A ∩ B
2 2
2

F-measure
• F-measure = 1 – E-measure
= 1/(α*(1/Prec) + (1-α)*(1/Rec))
= (β + 1)*Prec*Rec/(β *Prec+Rec)
where α = 1/(β + 1).
• F with β=b is often expressed as Fβ Fb.
• F1 = 2*Prec*Rec/(Prec+Rec)
i.e. harmonic mean of Prec and Rec
2 2
2
User attaches
β times as much
importance to Rec
as Prec
(dE/dRec=dE/dPrec
when
Prec/Rec=β)
[vanRijsbergen79]

Harmonic vs. arithmetic mean
0
0.3
0.6
0.90
0.2
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0.8
1
00.10.20.30.40.50.60.70.80.91
0.8-1
0.6-0.8
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00.10.20.30.40.50.60.70.80.91
0.8-1
0.6-0.8
0.4-0.6
0.2-0.4
0-0.2
Prec=0, Rec=1
Prec=0.5, Rec=0.5
F1=0
F1=0.5
Prec=0.1, Rec=0.9
F1=0.18
(Prec+Rec)/2=0.5
(Prec+Rec)/2=0.5
(Prec+Rec)/2=0.5
Balance
important
Balance
NOT
important

Interpolated precision
relevant
nonrel
nonrel
relevant
relevant
nonrel
relevant
nonrel
1
2
3
4
5
6
7
8
Rec(r) Prec(r)
0.2 1
0.2 0.5
0.2 0.33
0.4 0.5
0.6 0.6
0.6 0.5
0.8 0.57
0.8 0.5
R=5
0 1
0.1 1
0.2 1
0.3 0.6
0.4 0.6
0.5 0.6
0.6 0.6
0.7 0.57
0.8 0.57
0.9 0
1 0
i IPiInterpolated Precision
IPi = max Prec(r)
r s.t. Rec(r)>=i
“The major issue addressed by interpolation is that it rarely happens that
any particular recall point is achieved.” [Buckley05, p.56]

Recall-precision graphs
0 1
0.1 1
0.2 1
0.3 0.6
0.4 0.6
0.5 0.6
0.6 0.6
0.7 0.57
0.8 0.57
0.9 0
1 0
i IPi
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
To draw a Rec-Prec curve for a set (T)
of topics, plot ΣT IPi / |T| for each i
Interpolated Precision
IPi = max Prec(r)
r s.t. Rec(r)>=i
Recall level i
Interpolatedprecisionati

Average Precision [Buckley05]
• Introduced at TREC-2 (1993), implemented in
trec_eval by Buckley
R: total number of relevant docs
r: document rank
I(r): flag indicating a relevant doc
C(r): number of relevant docs
within ranks [1,r]
Highly rel
Partially rel
Highly rel
Partially rel
Partially rel
Partially rel
=
Most widely-used
binary-relevance
IR metric since 1990s,
but cannot distinguish
between Systems A and B..
System A System B

A user model for AP [Robertson08]
• Different users stop scanning the
ranked list at different ranks. They
only stop at a relevant document.
• The user distribution is uniform
across all (R) relevant documents.
• At each stopping point, compute
utility (Prec).
• Hence AP is the expected utility for
the user population.

Normalised Discounted Cumulative Gain
[Jarvelin02]
• Introduced at ACM SIGIR 2000/TOIS 2012, a variant of
the sliding ratio [Pollack68]
• Popular “Microsoft version” [Burges05] :
Original definition [Jarvelin02] not recommended: a system that returns a relevant
document at rank 1 and one that returns a relevant document at rank b are treated as
equally effective, where b is the logarithm base (patience parameter). b’s cancel out in the
Burges definition.
md: document cutoff (e.g. 10)
g(r): gain value at rank r
e.g. 1 if doc is partially relevant
3 if doc is highly relevant
g*(r) gain value at rank r of an
ideal ranked list

Q-measure [Sakai05AIRS,Sakai07IPM]
• A graded relevance version of AP (see also Graded AP
[Robertson10]).
• Same user model as AP, but the utility is computed
using the blended ratio BR(r) instead of Prec(r).
•
where
β: patience parameter
(β=0 ⇒ BR=Prec,
hence Q=AP)
Combines Precision and normalised cumulative gain (nCG) [Jarvelin02]

Value of the first relevant document at rank r according to
BR(r) (binary relevance, R=5) [Sakai14PROMISE]
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
β=0.1
β=1
β=10
r<=R ⇒
BR(r)=(1+β)/(r+βr)=1/r=P(r)
r>R ⇒
BR(r)=(1+β)/(r+βR)
rank
Large β ⇒ more
tolerance to relevant
docs at low ranks

Normalised Cumulative Utility [Sakai08EVIA]
• Generalises AP and Q
• NCU =
Σ Pr(r)*NU(r)
r
Normalised
Utility
Prec(r) or BR(r)
Stopping
probability
Rank-biased Graded-uniform

Expected Reciprocal Rank [Chapelle09]
• "ERR can be seen as a special case of Normalized Cumulative Utility
(NCU)“ [Chapelle09, p.625]
• No recall component
where
Probability that the user
is finally satisfied at r
Utility
at r

ERR’s diminishing return property
“Thus, if for example document two merely restates information
already gleaned from document one and hence is of no actual benefit
to this user, he may wish to assign it a negative document utility, no
matter how ‘relevant’ its content might have been to the original
information need.” [Cooper73, p.90]
“This is a diminishing return property which seems highly desirable for
most IR tasks: if we have already shown a lot of relevant documents,
there should be less added value in showing more relevant
documents.” [Chapelle11,p.582]
Rank-biased NCU [Sakai08EVIA] also has this property

Ranked retrieval measures: summary 1
(not exhaustive)
AP Q-measure ERR nDCG
Handling graded
relevance
Diminishing return
(navigational intent)
Discriminative power
[Sakai06SIGIR,07SIGIR]
Widely used
Used widely at NTCIR
NCU = [Sakai08EVIA]
f( stopping_probability_over_r, utility_at_r )
How many
statistically
significant
system pairs can
be obtained
(See Section 5)
There are a few graded-relevance versions, but AP
almost always means binary-relevance AP

Time-Biased Gain (TBG) [Smucker12]
Gain at rank r Discounting based on time to reach r
Value of information decays with time
Time to reach r:
reads (r-1) snippets, and possibly click
some docs and read them
Snippet reading
time: a constant
Doc reading time:
linear with doc length

U-measure [Sakai13SIGIR]
• U can be used not only for traditional IR, but also for various other
tasks such as session IR, aggregated search, summarisation, question
answering etc.
• While other measures are based on ranks, U abandons the notion of
rank. Focusses on the amount of text that the user has read within a
search session.
Instead of ranks, uses the positions of relevant pieces of information on a trailtext

Trailtext for U
Just concatenate all the texts that the
user has (probably) read.
For web search, one simple user model
would be to assume that users read all
snippets, plus parts of relevant
documents

If the nonrel at rank 2
(snippet) is replaced
with a rel
(snippet + full text),
the value of the rel at
rank 4 is always reduced
Satisfies
diminishing return
fixed-length snippets
Position-based discounting for U

Ranked retrieval measures: summary 2 (not exhaustive)
AP Q-measure ERR nDCG TBG U-measure
Handling graded relevance
Diminishing return (navigational
intent)
Considers document lengths and
search engine snippets
Handles nonlinear traversal
[Sakai14PROMISE]
Widely used Users do NOT always
scan from top to
bottom!
TREC Contextual Suggestion

Diversified search – a new IR task
Since 2003 or so
• Given an ambiguous/underspecified query, produce a
single Search Engine Result Page that satisfies
different user intents!
• Challenge: balancing relevance and diversity
SERP(SearchEngineResultPage)
Highly relevant
near the top
Give more
space to
popular intents?
Give more space
to informational
intents?
Cover many
intents
Diversity test collections
have relevance assessments
for each intent,
rather than for each topic

Diversified search measures summary
α-nDCG
[Clarke08]
ERR-IA
[Chapelle11]
D#-nDCG
[Sakai11SIGIR]
DIN#-nDCG, P+Q#
[Sakai12WWW]
U-IA
[Sakai13SIGIR]
Handling per-intent graded relevance
Handling intent probabilities
Handling both informational and
navigational intents
Per-intent diminishing return
Concordance test [Sakai12WWW,13IRJ]
Considers document lengths and search
engine snippets
Widely used
Agree with simple measures?
M-measure@NTCIR MobileClick

So you used a test collection that has n=20 topics to
compute nDCG scores for two systems X and Y.
Which system is more effective?
Scores for X, Y:
Per-topic difference:
Sample mean of the differences:
Sample variance:
0.0750
0.0251

Population
distribution of X
Population
distribution of Y
Random sampling from normal distributions
Under the above assumptions,
obeys where
Population
mean
Population
variance
Population mean of the
difference

Under the above assumptions,
obeys where
Population mean
of the difference
Which system is more effective?
Or, which of these hypotheses is true?
If you look at the populations, X and Y are
equally effective
actually different
obeys

equally effective
actually different
Which of these hypotheses is true? All we have is
the sample data:
If H0 is true, this t statistic obeys a t distribution with
φ=(n-1) degrees of freedom.
Sum of
squares
Number of independent variables in a sum of
squares = accuracy of the sum

If H0 is true, this t statistic obeys a t distribution with
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φ=4 φ=99 Observed value of t0 computed from sample
P-value: area under curve =
probability of observing t0 or
something more extreme
IF H0 is true.

If H0 is true, the t statistic obeys a t distribution with
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φ=4 φ=99 t0
P-value: area under curve =
probability of observing t0 or
something more extreme
IF H0 is true.(1-α)
Significance level α: areas under curve =
a pre-determined probability (e.g. 5%) of observing something very rare

0
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α/2 α/2
(1-α)
p-value
If p-value <= α, then something highly unlikely (e.g. 5% chance)
under H0 has happened ⇒ H0 is probably wrong, with
(1-α)% (e.g. 95%) confidence!
We reject H0, and say that
the difference is statistically
significant at the significance level
of α. The population means
are probably different!

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2.0
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3.5
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4.5
5.0
φ=4 φ=99 t0
α/2 α/2
(1-α) p-value
If p-value > α, then what we have observed is something
we expect under H0. We accept H0, and say that
the difference is NOT statistically
significant at the significance level
of α. This just means that we cannot
tell from data whether H0 is true.

Example: paired t-test using Excel
Significance level α = 0.05 (95% confidence)
Sample size n = 20
Degrees of freedom φ = 20-1 = 19
Sample mean
Sample variance
t statistic
p-value = T.DIST.2T( 2.116, 19 ) = 0.048 < α
X is statistically significantly better than Y at α=0.05.
Mean nDCG
over 20 topics
X 0.3450
Y 0.2700

Limitations of significance testing (1)
• Normality assumptions: computer-based alternatives (bootstrap
[Savoy97, Sakai06SIGIR], randomisation test [Smucker07]) that do not
rely on the assumptions are available. But the results are similar to
those obtained by the t-test.
• Dichotomous decision:
p-value = 0.049 < α ⇒ statistically significant! Publish a paper!
p-value = 0.051 > α ⇒ not statistically significant! Put it in the drawer!
Saying “p-value=0.049” is much more informative than
saying “significant at α=0.05”. Report the p-value! [Sakai14forum]

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φ=4 φ=99 t0
p-value
We get a statistically significant result
whenever p-value is small ⇔ t-value is large.
t-value is large when
(a) sample size n is large; or
(b) sample effect size
is large.
Difference measured in standard
deviation units
If n is large, you can get a statistically significant
result with ANYTHING!

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φ=4 φ=99 t0
p-value
t-value is large when
(a) sample size n is large; or
(b) sample effect size is large.
Don’t just report the p-value. Report
the sample effect size! [Sakai14forum]
0.4734 in the previous example.
This reflect how substantial the
difference may be.

What about the sample size n?
In significance testing, there are four important parameters. If three of
them are set, the fourth one is uniquely determined.
α: probability of Type I error
β: probability of Type II error
effect size:
magnitude of the difference
sample size n: number of topics
H0 is true H1 is true
H0 accepted 1-α β
H0 rejected α 1-β
Detecting a
nonexistent
difference
Missing a true
difference
While IR test collections typically have n=50 topics, it is possible to
determine the right n by setting α, β, and the minimum effect size
that you want to detect [Sakai15IRJ].
Statistical power: ability to detect a
true difference

Comparing more than two systems
• Conducting a t-test for every system pair is not good (though there
are exceptions [Sakai15IRJ]) - the familywise error rate problem.
• Use a proper multiple comparison procedure.
• Recommended: randomised Tukey HSD test
[Carterette12,Sakai14PROMISE].
• [Sakai14forum] says do an ANOVA (analysis of variance) test first,
followed by a Tukey HSD test. But this also causes a problem similar
to the familywise error rate. If you are interested in the difference
between every system pair, conduct Tukey without conducting
ANOVA.

Summary
• Ranked retrieval measures as surrogates of user
satisfaction/performance, with different sets of assumptions. They
maybe compared using discriminative power [Sakai06SIGIR,07SIGIR],
concordance test [Sakai12WWW,13IRJ] etc. We want measures that
reliably measure what we want to measure!
• Principles and limitations of statistical significance testing, esp. paired
t-test. Report the p-values and effect sizes [Sakai14IRJ]. Type I errors,
Type II errors (1-power), effect sizes and sample sizes. A multiple
comparison procedure should be used for more than two systems.
Let’s write good IR papers!

Tools (by Tetsuya Sakai)
• NTCIREVAL (computes various evaluation measures)
http://research.nii.ac.jp/ntcir/tools/ntcireval-en.html
• BOOTS (bootstrap hypothesis test as an alternative to the t-test)
http://research.nii.ac.jp/ntcir/tools/boots-en.html
• Discpower (randomisation test as an alternative to the t-test,
and randomised Tukey HSD test for comparing more than two systems)
http://research.nii.ac.jp/ntcir/tools/discpower-en.html
• Topic set size design Excel tools (how many topics do we need?):
http://www.f.waseda.jp/tetsuya/tools.html

LECTURE OUTLINE
1. Why evaluate?
2. Set retrieval evaluation measures
3. Ranked retrieval evaluation measures
4. More evaluation measures
5. Statistical significance, power, effect sizes
6. Reporting your results
7. Summary
8. References

References (1)
[Armstrong09] Armstrong, T.G., Moffat, A., Webber, W. and Zobel, J.: Improvements that Don’t Add Up: Ad-hoc Retrieval Results Since
1998, ACM CIKM 2009, pp.601-610, 2009.
[Buckley05] Buckley, C. and Voorhees, E.M.: Retrieval System Evaluation, In TREC: Experiment and Evaluation in Information Retrieval
(Voorhees, E.M. and Harman, D.K., eds.), Chapter 3, The MIT Press, 2005.
[Burges05] Burges, C., Shaked, T., Renshaw, E., Lazier, A., Deeds, M., Hamilton, N., Hullender, G.: Learning to Rank Using Gradient
Descent, ICML 2005, pp.89-96, 2005.
[Chapelle09] Chapelle, O., Metzler, D., Zhang, Y., Grispan, P.: Expected Reciprocal Rank for Graded Relevance, ACM CIKM 2009,
pp.621-630, 2009.
[Chapelle11] Chapelle, O., Ji, S., Liao, C., Velipasaoglu, E., Lai, L., Wu, S.L.: Intent-based Diversification of Web Search Results: Metrics
and Algorithms, Information Retrieval, 14(6), pp.572-592, 2011.
[Clarke08] Clarke, C.L.A., Kolla, M., Cormack, G.V., Vechtomova, O., Ashkan, A., Buttcher, S. and MacKinnon, I.: Novelty and Diversity in
Information Retrieval Evaluation, ACM SIGIR 2008, pp.659-666, 2008.
[Cooper73] Cooper, W.S.: On Selecting a Measure of Retrieval Effectiveness, JASIS 24(2), pp.87–100, 1973.

References (2)
[Jarvelin02] Jarvelin, K. and Kekalainen, J.: Cumulated Gain-based Evaluation of IR Techniques, ACM TOIS, 20(4), p.422-446, 2002.
[Pollack68] Pollack, S.M.: Measures for the Comparison of Information Retrieval Systems, American Documentation, 19(4), pp.387-
397, 1968.
[Robertson08] Robertson, S.E.: A New Interpretation of Average Precision, ACM SIGIR 2008, pp.689-690, 2008.
[Robertson10] Robertson, S.E., Kanoulas, E., Yilmaz, E.: Extending Average Precision to Graded Relevance Judgments, ACM SIGIR 2010,
pp.603-610, 2010.
[Savoy97] Savoy, J.: Statistical Inference in Retrieval Effectiveness Evaluation, Information Processing and Management, 33(4), pp.495-
512, 1997.

References (3)
[Sakai05AIRS] Sakai, T.: Ranking the NTCIR Systems based on Multigrade Relevance, AIRS 2004 (LNCS 3411), pp.251-262, 2005.
[Sakai06SIGIR] Sakai, T.: Evaluating Evaluation Metrics based on the Bootstrap, ACM SIGIR 2006, pp.525-532, 2006.
[Sakai07SIGIR] Sakai, T.: Alternatives to Bpref, ACM SIGIR 2007, pp.71-78, 2007.
[Sakai07IPM] Sakai, T.: On the Reliability of Information Retrieval Metrics based on Graded Relevance, Information Processing and
Management, 43(2), pp.531-548, 2007.
[Sakai08EVIA] Sakai, T. and Robertson, S.: Modelling A User Population for Designing Information Retrieval Metrics, EVIA 2008, pp.30-
41, 2008.
[Sakai11SIGIR] Sakai, T. and Song, R.: Evaluating Diversified Search Results Using Per-Intent Graded Relevance, ACM SIGIR 2011,
pp.1043-1052, 2011.
[Sakai12WWW] Sakai, T.: Evaluation with Informational and Navigational Intents, WWW 2012, pp.499-508, 2012.
[Sakai13SIGIR-U] Sakai, T., Dou, Z.: Summaries, Ranked Retrieval and Sessions: A Unified Framework for Information Access Evaluation,
ACM SIGIR 2013, pp.473-482, 2013.
[Sakai13IRJ] Sakai, T. and Song, R.: Diversified Search Evaluation: Lessons from the NTCIR-9 INTENT Task, Information Retrieval, 16(4),
pp.504-529, Springer, 2013.
[Sakai14PROMISE] Sakai, T.: Metrics, Statistics, Tests, PROMISE Winter School 2013: Bridging between Information Retrieval and
Databases (LNCS 8173), Springer, pp.116-163, 2014.
[Sakai14forum] Sakai, T.: Statistical Reform in Information Retrieval?, SIGIR Forum, 48(1), pp.3-12, 2014.
[Sakai15IRJ] Sakai, T.: Topic Set Size Design, Information Retrieval Journal, submitted.

References (4)
[Smucker07] Smucker, M.D., Allan, J. and Carterette, B.: A Comparison of Statistical Significance Tests for Information Retrieval
Evaluation, ACM CIKM 2007, pp.623-632, 2007.
[Smucker12] Smucker, M.D. and Clarke, C.L.A.: Time-based Calibration of Effectiveness Measures, ACM SIGIR 2012, pp. 95–104 , 2012.
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