Designing Test Collections That Provide Tight Confidence Intervals

RD‐003Designing Test Collections That

Provide Tight Confidence Intervals@tetsuyasakai

Waseda University

September 5@FIT 2014, Tsukuba University

Acknowledgement

This research is a part of Waseda University’s project “Taxonomising and Evaluating Web Search Engine User Behaviours,” supported by Microsoft Research.

THANK YOU!

Takeaways

• It is possible to determine the topic set size n based on statistical requirements. Our approach requires a tight CI for any pairwise system comparisons.

• CIs depend on variances, and variances depend on the choice of evaluation measures. Therefore test collections should be designed with evaluation measures in mind.

• Our analysis can save a lot of relevance assessment cost – provides a set of statistically equally reliable designs (n, pd) with substantially different costs.

Topic set size Pool depth

TALK OUTLINE

1. How Information Retrieval (IR) test collections are constructed2. Statistical reform3. How test collections SHOULD be constructed4. Experimental results5. Conclusions and future work

Test collections = standard data sets for evaluation

Test collection A Test collection BEvaluationmeasurevalues

Evaluationmeasurevalues

An Information Retrieval (IR) test collection

Topic Relevance assessments(relevant/nonrelevant documents)

Document collection



: :

Topic set “Qrels = query relevance sets”

FIT 2014 home page www.ipsj.or.jp/event/fit/fit2014/: highly relevant

www.ipsj.or.jp/event/fit/fit2014/exhibit.html: partially relevantwww.honda.co.jp/Fit/: nonrelevant

How IR people build test collections (1)

Okay, let’s build a test collection…

Organiser


…with maybe n=50topics (search requests)…

Well n>25 sounds good for statistical significance testing, but why 50? Why not 100? Why not 30?

TopicTopicTopicTopicTopic 1



50 topicsOkay folks, give me your runs (search results)!

run run run

Participants



50 topicsPool depth pd=100 looks

affordable…

run run run

Top pd=100 documentsfrom each run

Pool for

Topic 1Document collection too large to doexhaustive relevance assessments sojudge pooled documents only



50 topics


Pool for

Topic 1Relevance assessments

Highly relevant

Partially relevant

Nonrelevant

An Information Retrieval (IR) test collection


Document collection



: :

Topic set “Qrels = query relevance sets”

FIT 2014 home page www.ipsj.or.jp/event/fit/fit2014/: highly relevant

www.ipsj.or.jp/event/fit/fit2014/exhibit.html: partially relevantwww.honda.co.jp/Fit/: nonrelevant

n=50topics…why?

Pool depth pd=100(not exhaustive)

TALK OUTLINE


NHST = null hypothesis significance testing (1)

EXAMPLE: paired t‐test for comparing systems X and Y with n topics

Assumptions:

Null hypothesis:

Test statistic:

Population means are the same


EXAMPLE: paired t‐test for comparing systems X and Y with n topics

Null hypothesis:

Test statistic:

Under H0, t0 obeys a t distribution with n‐1 degrees of freedom.


EXAMPLE: paired t‐test for comparing systems X and Y with n topicsNull hypothesis:Under H0, t0 obeys a t distribution with n‐1 degrees of freedom.

Given a significance criterion α(=0.05), reject H0 if |t0| >= t(n‐1; α).

0

0.1

0.2

0.3

0.4

‐t(n‐1; α)

n=50

t(n‐1; α)

“H0 is probably not true because the chance of observing t0 under H0

is very small”


EXAMPLE: paired t‐test for comparing systems X and Y with n topicsNull hypothesis:Given a significance criterion α(=0.05), reject H0 if |t0| >= t(n‐1; α).

0

0.1

0.2

0.3

0.4

‐t(n‐1; α)

n=50

t(n‐1; α)

0

0.1

0.2

0.3

0.4

‐t(n‐1; α)

n=50

t(n‐1; α)

Conclusion:X ≠ Y!

t0 t0Conclusion:

H0 not rejected, so don’t know

NHST is not good enough [Cumming12]

• Dichotomous thinking ( “different or not different?” )A more important question is “what is the magnitude of the difference?” Another is “How accurate is my estimate?”• p‐values a little more informative than “significant at α=0.05” but…

0

0.1

0.2

0.3

0.4

‐t(n‐1; α)

n=50

t(n‐1; α)

t0

Probability of observing t0 or something more extreme under H0

The p‐value is not good enough either [Nagata03]

Reject H0 if |t0| >= t(n‐1; α) where

But a large |t0| could mean two things:(1) Sample effect size (ES) is large;(2) Topic set size n is large.

If you increase the sample size n, you can always achieve statistical significance!

Difference between X and Y measured in standard deviation

units

Statistical reform – effect sizes [Cumming12,Okubo12]

• ES: “how much difference is there?”• ES for paired t test measures difference in standard deviation unitsPopulation ES =

Sample ES as an estimate of the above =

In several research disciplines such as psychology and medicine, it is requiredto report ESs! But ESs are rarely discussed in IR, NLP, etc…

Statistical reform – confidence intervals

• CIs are much more informative than NHST(point estimate + uncertainty/accuracy)• Estimation thinking, not dichotomous thinking[Cumming12]

In several research disciplines such as psychology and medicine, it is requiredto report CIs! But CIs are rarely discussed in IR, NLP, etc…

[Sakai14forum]

TALK OUTLINE


CI basics (1)

obeys a t distribution with n‐1 degrees of freedom.

Hence, for a given α, α/2 α/2

CI basics (2)obeys a t distribution with n‐1 degrees of freedom.

Hence, for a given α,⇒

where

That is, the 95% CI of the difference between X and Y is given by

Sample size design based on a tight CI (1) [Nagata03]

• To set the topic set size n, require that the CI (2*MOE) be no larger than a constant δ.

• Since contains a random variable V,impose the above on the expectation of CI. That is,require:


• Require: • It is known that

cf.

• So what we want is the smallest n that satisfies:

No closedform for n

• So what we want is the smallest n that satisfies:• To find the n, start with the “easy” case where the population variance is known.


No closedform for n

Variance unknown Variance known

• So what we want is the smallest n that satisfies:• To find the n, start with the “easy” case where the population variance is known.

• Require: • Obtain the smallest n’ s.t.and increment untilthe original requirement is met!


No closedform for n

But we need an estimateof

Estimating (1)

Data #topics runs pd #docsTREC03new 50 78 125 528,155 news articlesTREC04new 49 78 100 dittoTREC11w 50 37 25 One billion web pagesTREC12w 50 28 20/30 dittoTREC11wD 50 25 25 dittoTREC12wD 50 20 20/30 ditto

Adhoc news IR

Adhoc web IR

Diversified web IR

Compute V for every system pair (78*77/2=3,003 pairs);

then take the 95% percentile [Webber08]

Pool variance estimates fromtwo data sets

Estimating (2)

Evaluating top1,000 documents

Evaluating top10 documents

See [Sakai14PROMISE] for definitions of

measures

Demo

Just enter and you will get your n!http://www.f.waseda.jp/tetsuya/FIT2014/samplesizeCI.xlsx

TALK OUTLINE


Results

Q requires the fewest topics

Required n depends heavily on the stability of the evaluation measure!

D‐nDCG requires the fewest topics

What if we reduce the pool depth pd?


n=50 topics


Pool for

Topic 1Relevance assessments

Highly relevant

Partially relevant

Nonrelevant

For adhoc/news l=1000 (pd=100) only

Pool depth vs pd reduced from 100 to 10

#relevance assessments per topic also reduced

Variance increases in general, except for nERR

Statisticallyequivalenttest collectiondesigns for TREC adhocnews (l=1,000)

For Q, the pd=10 designis only 18%as costly asthe pd=100 design!

TALK OUTLINE


Takeaways

• It is possible to determine the topic set size n based on statistical requirements. Our approach requires a tight CI for any pairwise system comparisons.

• CIs depend on variances, and variances depend on the choice of evaluation measures. Therefore test collections should be designed with evaluation measures in mind.

• Our analysis can save a lot of relevance assessment cost – provides a set of statistically equally reliable designs (n, pd) with substantially different costs.

Topic set size Pool depth

Future work

• Alternative approach: determining n from a minimum detectable ES instead of a maximum allowable CI: DONE [Sakai14CIKM]

• Using variance estimates based on ANOVA statistics: DONE• Estimating n for various tasks (not just IR) – the method is applicable to any paired‐data evaluation tasks

• Given a set of statistically equally reliable designs (n,pd), choose the best one based on reusability and assessment cost

Can we evaluate new systems fairly?

References

[Cumming12] Cumming, G.: Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta‐Analysis. Routledge, 2012.[Nagata03] Nagata, Y.: How to Design the Sample Size. Asakura Shoten, 2003.[Okubo12] Okubo, M. and Okada, K. Psychological Statistics to Tell Your Story: Effect Size, Condence Interval (in Japanese). Keiso Shobo, 2012.[Sakai14PROMISE] Sakai, T.: Metrics, Statistics, Tests. PROMISE Winter School 2013: Bridging between Information Retrieval and Databases (LNCS 8173), pp.116‐163, Springer, 2014. [Sakai14forum] Sakai, T.: Statistical Reform in Information Retrieval?, SIGIR Forum, 48(1), 2014. [Sakai14CIKM] Sakai, T.: Designing Test Collections for Comparing Many Systems, ACM CIKM 2014, to appear, 2014.[Webber08] Webber, W., Moffat, A. and Zobel, J.: Statistical power in Retrieval Experimentation. ACM CIKM 2008, pp.571–580, 2008.

Designing Test Collections That Provide Tight Confidence Intervals

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