Evaluation in (Music) Information Retrieval through the Audio Music Similarity task

Evaluation in (Music) Information Retrieval
through the Audio Music Similarity task
Julián Urbano

Barcelona, Spain · January 16th 2014

Spam
• @julian_urbano
• Postdoctoral researcher
– Music Technology Group, Universitat Pompeu Fabra

• Recently: PhD, Computer Science
– (Evaluation in) (Music) Information Retrieval

2

Information Retrieval
• Automatic representation, storage and search of
unstructured information
– Traditionally textual information
– Lately multimedia too: images, video, music

• A user has an information need and uses an IR
system that retrieves the relevant or significant
information from a collection of documents
3

Information Retrieval Evaluation
• IR systems are based on models to estimate
relevance, implementing different techniques
• How good is my system? What system is better?
– Answered with IR Evaluation experiments
– “if you can’t measure it, you can’t improve it”
– But we need to be able to trust our measurements

• Research on IR Evaluation
– Improve our methods to evaluate systems
– Critical for the correct development of the field
4

Disclaimer
• If you see…
A system is evaluated with a test collection
containing queries, documents and judgments
telling how relevant a document is to a query

• …you can think of
An algorithm is evaluated with a dataset
containing queries, songs and annotations
telling how similar a song is to a query
5

Talk outline
•
•
•
•
•

Why we want to Evaluate…
…and what we do with Cranfield
Validity: users versus systems
Reliability: estimating from samples
Efficiency: reducing annotations

6

Introduction:
Why we want to Evaluate…

The two questions
• How good is my system?
– What does good mean?
– What is good enough?

• Is system A better than system B?
– What does better mean?
– How much better?

• Efficiency? Effectiveness? Ease?
8

Measure user experience
• We are interested in user-measures
– Time to complete task, idle time, success rate, failure
rate, frustration, ease to learn, ease to use …

• Their distributions describe user experience, fully
– For an arbitrary user, query and document collection,
what is the distribution of…

0

none
time to complete task

some
frustration

much
9

The big(ger) picture
• Different user-measures attempting to assess the
same thing: user satisfaction
– How likely is it that an arbitrary user, with an arbitrary
query (and with an arbitrary document collection) will
be satisfied by the system?

• This is the ultimate goal: the good, the better

10

The big(ger) question
• User satisfaction…as Bernoulli trial

no
yes
satisfaction

• Probability of satisfaction P(Sat = yes)?
• Probability that k in n users are satisfied?
• Probability of >80% users satisfied?
11

Introduction:
…what we do with Cranfield

Sources of variability
user-measure = f(documents, query, user, system)
• Our goal is the distribution of the user-measure
for our system, which is impossible to calculate
– (Possibly?) infinite population

• The best we can do is estimate it
– Sample documents, queries and users
– Measure user experience, implicitly or explicitly
– Representativeness, cost, ethics, privacy…
13

Fix samples
• Hard to replicate experiment and repeat results
• Just plain impossible to reproduce results
• Get a (hopefully) good sample and fix it
– Documents and queries

• But we can’t fix the users!

14

Simulate users…and fix them
• Cranfield paradigm: remove users, but include a
user-abstraction, fixed across experiments
– Static user component: judgments in the ground truth
– Dynamic user component: effectiveness measures

• Remove all sources of variability, except systems

15

Simulate users…and fix them
• Cranfield paradigm: remove users, but include a
user-abstraction, fixed across experiments
– Static user component: judgments in the ground truth
– Dynamic user component: effectiveness measures

• Remove all sources of variability, except systems
user-measure = f(system)
15

Test collections
• Controlled set of documents, queries and
judgments, shared across researchers
• (Most?) important resource for IR research
– Experiments are inexpensive (collections are not!)
– Research becomes systematic
– Reproducibility becomes possible and easy

16

Wait a minute
• Are we estimating distributions about users or
distributions about systems?
system-effectiveness = f(system, scale, measure)
• We come up with different distributions of
system-effectiveness, depending on how we
abstract users from the experiment
– Different scales to assess relevance
– Different measures to model user behavior
17

Assumption
• System-measures correspond to user-measures
Users
Time to complete task
Idle time
Success rate
Failure rate
Frustration
Ease to learn
Ease to use
Satisfaction
…

Systems
P
AP
RR
DCG
nDCG
ERR
GAP
Q
…

18

Assumption
• System-measures correspond to user-measures
Users
Time to complete task
Idle time
Success rate
Failure rate
Frustration
Ease to learn
Ease to use
Satisfaction
…

Systems
P
AP
RR
DCG
nDCG
ERR
GAP
Q
…

19

Experiments with Test Collections
• Our goal is the users
• but Cranfield tells us about systems

20

Experiments with Test Collections
• Our goal is the users
• but Cranfield tells us about systems
• This poses several problems
– That we have been dealing with for over 50 years
– But hey, they’re extremely interesting!
20

Validity, Reliability and Efficiency
• Validity: are we measuring what we want to?
– Internal: are observed effects due to hidden factors?
– External: are queries, documents and users representative?
– Construct: do system-measures match user-measures?
– Conclusion: how good is good and how better is better?

• Reliability: how repeatable are the results?
– How large do collections need to be?
– What statistical methods should be used?

• Efficiency: how inexpensive is it to get valid and
reliable results? (i.e. to build a test collection)
– Can we estimate results with fewer judgments?
21

In this talk
How to study and improve
the validity, reliability and efficiency
of the methods used to evaluate IR systems
• Audio Music Similarity task as example
– Song as query input to system, audio signal
– Retrieve songs musically similar to it, by content
– Resembles traditional Ad Hoc retrieval in Text IR
– Important task in Music IR
• Music recommendation
• Playlist generation
• Plagiarism detection
22

Validity:
Effectiveness and Satisfaction

Assumption of Cranfield
• Systems with better effectiveness are perceived
by users as more useful, more satisfactory
• Tricky: different effectiveness measures and
relevance scales produce different distributions
– Which one is better to predict satisfaction?

• Map system effectiveness onto user satisfaction,
experimentally
– If P@10 = 0.2, how likely is it that an arbitrary user will
find the results satisfactory?
– What is P(Sat | P@10 = 0.2)?
24

User-oriented System-measures
• Effectiveness measures are generally not
formulated to correlate with user-satisfaction
– If effectiveness is λ = 0, we expect P(Sat) = 0
– If effectiveness is λ = 1, we expect P(Sat) = 1
– In general, we expect P(Sat | λ) = λ

• But this is not what we have
– Effectiveness measures need to be reformulated
– Upper bounds, recall components, ideal rankings
– Many mathematical details omitted in this talk

25

User Components: Measures and Scales
• How is relevance measured in the judgments?
– Nominal, ordinal, interval, ratio

• How are results consumed?
– Set, list

• What determines document utility?
– Positional, cascade
– Linear, exponential

• What determines user persistence?
– Navigational, informational
26

Measures and Scales
Measure
P@5
AP@5
RR@5
CGl@5
CGe@5
DCGl@5
DCGe@5
EDCGl@5
EDCGe@5
Ql@5
Qe@5
RBPl@5
RBPe@5
ERRl@5
ERRe@5
GAP@5
ADR@5

Original
Broad
Fine

X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X

Artificial Graded
nℒ=3
nℒ=4
nℒ=5

X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X
X
X
X
X
X
X
X

ℓmin=20
X
X
X
P@5
P@5
X
DCGl@5
X
EDCGl@5
AP@5
AP@5
X
RBPl@5
X
ERRl@5
AP@5
X

Artificial Binary
ℓmin=40 ℓmin=60
X
X
X
X
X
X
P@5
P@5
P@5
P@5
X
X
DCGl@5 DCGl@5
X
X
EDCGl@5 EDCGl@5
AP@5
AP@5
AP@5
AP@5
X
X
RBPl@5 RBPl@5
X
X
ERRl@5 ERRl@5
AP@5
AP@5
X
X

ℓmin=80
X
X
X
P@5
P@5
X
DCGl@5
X
EDCGl@5
AP@5
AP@5
X
RBPl@5
X
ERRl@5
AP@5
X
27

Measures and Scales
Measure
P@5
AP@5
RR@5
CGl@5
CGe@5
DCGl@5
DCGe@5
EDCGl@5
EDCGe@5
Ql@5
Qe@5
RBPl@5
RBPe@5
ERRl@5
ERRe@5
GAP@5
ADR@5

Original
Broad
Fine

Artificial Graded
nℒ=3
nℒ=4
nℒ=5

MIREX
X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X

X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X
X
X
X
X
X
X
X

ℓmin=20
X
X
X
P@5
P@5
X
DCGl@5
X
EDCGl@5
AP@5
AP@5
X
RBPl@5
X
ERRl@5
AP@5
X

Artificial Binary
ℓmin=40 ℓmin=60
X
X
X
X
X
X
P@5
P@5
P@5
P@5
X
X
DCGl@5 DCGl@5
X
X
EDCGl@5 EDCGl@5
AP@5
AP@5
AP@5
AP@5
X
X
RBPl@5 RBPl@5
X
X
ERRl@5 ERRl@5
AP@5
AP@5
X
X

ℓmin=80
X
X
X
P@5
P@5
X
DCGl@5
X
EDCGl@5
AP@5
AP@5
X
RBPl@5
X
ERRl@5
AP@5
X
27

What can we infer?
• Preference: difference noticed by user
– Positive: user agrees with evaluation
– Negative: user disagrees with evaluation

• Non-preference: difference not noticed by user
– Good: both systems are satisfactory
– Bad: both systems are not satisfactory

29

Data
• Queries, documents and judgments from MIREX
• 4115 unique and artificial examples
– At least 200 examples per (measure-scale-λ)

• 432 unique queries, 5636 unique documents
• Answers collected via Crowdsourcing
– Quality control with trap questions

• 113 unique subjects
30

Single system: how good is it?
• For 2045 examples (49%) users could not decide
which system was better

What do we expect?

31

• For 2045 examples (49%) users could not decide
which system was better

31

• Large ℓmin thresholds underestimate satisfaction

32

• Users don’t pay attention to ranking?

33

• Exponential gain underestimates satisfaction

34

• Document utility independent of others

35

Two systems: which one is better?
• For 2090 examples (51%) users did prefer one
system over the other one

What do we expect?

36

• For 2090 examples (51%) users did prefer one
system over the other one

36

• Large differences needed for users to note them

37

• More relevance levels are better to discriminate

38

• Cascade and navigational user models are not
appropriate

39

• Users do prefer the (supposedly) worse system

40

Summary
• Effectiveness and satisfaction are clearly correlated

– There is a 20% bias: P(Sat | 0) > 0 and P(Sat | 1) < 1
– Room to improve: personalization, better user abstraction

• Magnitude of differences does matter
– Just looking at rankings is very naive
• Be careful with statistical significance

– Need Δλ≈0.4 for users to agree with effectiveness
• Historically, only 20% of times in MIREX

• Differences among measures and scales
– Linear gain slightly better than exponential gain
– Informational and positional user models better than
navigational and cascade
– The more relevance levels, the better
41

Measures and scales
Measure
P@5
AP@5
RR@5
CGl@5
CGe@5
DCGl@5
DCGe@5
EDCGl@5
EDCGe@5
Ql@5
Qe@5
RBPl@5
RBPe@5
ERRl@5
ERRe@5
GAP@5
ADR@5

Original
Broad
Fine

X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X

Artificial Graded
nℒ=3
nℒ=4
nℒ=5

X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X
X
X
X
X
X
X
X

ℓmin=20
X
X
X
P@5
P@5
X
DCGl@5
X
EDCGl@5
AP@5
AP@5
X
RBPl@5
X
ERRl@5
AP@5
X

Artificial Binary
ℓmin=40 ℓmin=60
X
X
X
X
X
X
P@5
P@5
P@5
P@5
X
X
DCGl@5 DCGl@5
X
X
EDCGl@5 EDCGl@5
AP@5
AP@5
AP@5
AP@5
X
X
RBPl@5 RBPl@5
X
X
ERRl@5 ERRl@5
AP@5
AP@5
X
X

ℓmin=80
X
X
X
P@5
P@5
X
DCGl@5
X
EDCGl@5
AP@5
AP@5
X
RBPl@5
X
ERRl@5
AP@5
X
42

Measures and scales
Measure
P@5
AP@5
RR@5
CGl@5
CGe@5
DCGl@5
DCGe@5
EDCGl@5
EDCGe@5
Ql@5
Qe@5
RBPl@5
RBPe@5
ERRl@5
ERRe@5
GAP@5
ADR@5

Original
Broad
Fine

X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X

Artificial Graded
nℒ=3
nℒ=4
nℒ=5

X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X
X
X
X
X
X
X
X

ℓmin=20
X
X
X
P@5
P@5
X
DCGl@5
X
EDCGl@5
AP@5
AP@5
X
RBPl@5
X
ERRl@5
AP@5
X

Artificial Binary
ℓmin=40 ℓmin=60
X
X
X
X
X
X
P@5
P@5
P@5
P@5
X
X
DCGl@5 DCGl@5
X
X
EDCGl@5 EDCGl@5
AP@5
AP@5
AP@5
AP@5
X
X
RBPl@5 RBPl@5
X
X
ERRl@5 ERRl@5
AP@5
AP@5
X
X

ℓmin=80
X
X
X
P@5
P@5
X
DCGl@5
X
EDCGl@5
AP@5
AP@5
X
RBPl@5
X
ERRl@5
AP@5
X
43

Validity:
Satisfaction over Samples

Evaluate in terms of user satisfaction
• So far, arbitrary users for a single query
– P Sat Ql @5 = 0.61 = 0.7

• Easily for n users and a single query
– P Sat15 = 10 Ql @5 = 0.61 = 0.21

• What about a sample of queries 𝒬?
– Map queries separately for the distribution of P(Sat)
– For easier mappings, P(Sat | λ) functions are
interpolated with simple polynomials
45

Expected probability of satisfaction
• Now we can compute point and interval estimates
of the expected probability of satisfaction
• Intuition fails when interpreting effectiveness

46

System success
• If P(Sat) ≥ threshold the system is successful
– Setting the threshold was rather arbitrary before
– Now it is meaningful, in terms of user satisfaction

• Intuitively, we want the majority of users to find
the system satisfactory
– P Succ = P P Sat > 0.5 = 1 − FP

Sat

(0.5)

• Improving queries for which we are bad is
worthier than further improving those for which
we are already good
47

Distribution of P(Sat)
• But we (will) only have a handful queries, estimates
will probably be bad
– Need to estimate the cumulative distribution function of
user satisfaction: FP(Sat)
– Not described by any typical distribution family

• More than ≈25 queries in the collection
– ecdf approximates better

• Less than ≈25 queries in the collection

– Normal for graded scales, ecdf for binary scales

• Beta is always the best with the Fine scale
– Which turns out to be the best scale, overall
48

Intuition fails, again
Intuitive conclusions based on effectiveness alone
contradict those based on user satisfaction
– E Δλ = −0.002

– E ΔP Sat
– E ΔP Succ

= 0.001
= 0.07

49

Historically, in MIREX
• Systems are not as satisfactory as we thought
• But they are more successful
– Good (or bad) for some kinds of queries

50

Measures and scales
Measure
P@5
AP@5
CGl@5
CGe@5
DCGl@5
DCGe@5
Ql@5
Qe@5
RBPl@5
RBPe@5
GAP@5

Original
Broad
Fine

X
X
X
X
X
X
X
X
X

X
X
X
X
X

Artificial Graded
nℒ=4
nℒ=5

X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X
X
X

Artificial Binary
ℓmin=20 ℓmin=40
X
X
X
X
P@5
P@5
P@5
P@5
X
X
DCGl@5 DCGl@5
AP@5
AP@5
AP@5
AP@5
X
X
RBPl@5 RBPl@5
AP@5
AP@5

51

Measures and scales
Measure
P@5
AP@5
CGl@5
CGe@5
DCGl@5
DCGe@5
Ql@5
Qe@5
RBPl@5
RBPe@5
GAP@5

Original
Broad
Fine

X
X
X
X
X
X
X
X
X

X
X
X
X
X

Artificial Graded
nℒ=4
nℒ=5

X
X
X
X
X
X
X
X
X

X
X
X
X
X
X
X
X
X

Artificial Binary
ℓmin=20 ℓmin=40
X
X
X
X
P@5
P@5
P@5
P@5
X
X
DCGl@5 DCGl@5
AP@5
AP@5
AP@5
AP@5
X
X
RBPl@5 RBPl@5
AP@5
AP@5

52

Reliability:
Optimal Statistical Significance Tests

Random error
• Test collections are just samples from larger,
possibly infinite, populations
• If we conclude system A is better than B, how
confident can we be?
– Δλ 𝒬 is just an estimate of the population mean μΔλ

• Usually employ some statistical significance test
for differences in location
• If it is statistically significant, we have confidence
that the true difference is at least that large
54

Statistical hypothesis testing
• Set two mutually exclusive hypotheses
– H0 : μΔλ = 0
– H1 : μΔλ ≠ 0

• Run test, obtain p-value= P μΔλ ≥ Δλ 𝒬 H0
– p ≤ α: statistically significant, high confidence
– p > α: statistically non-significant, low confidence

• Possible errors in the binary decision
– Type I: incorrectly reject H0
– Type II: incorrectly accept H0
55

Statistical significance tests
• (Non-)parametric tests
– t-test, Wilcoxon test, Sign test

• Based on resampling
– Bootstrap test, permutation/randomization test

• They make certain assumptions about
distributions and sampling methods
– Often violated in IR evaluation experiments
– Which test behaves better, in practice, knowing that
assumptions are violated?
56

Optimality criteria
• Power
– Achieve significance as often as possible (low Type II)
– Usually increases Type I error rates

• Safety
– Minimize Type I error rates
– Usually decreases power

• Exactness
– Maintain Type I error rate at α level
– Permutation test is theoretically exact
57

Experimental design
• Randomly split query set in two
• Evaluate all systems with both subsets
– Simulating two different test collections

• Compare p-values with both subsets
– How well do statistical tests agree with themselves?
– At different α levels

• All systems and queries from MIREX 2007-2011
– >15M p-values
58

Power and success
• Bootstrap test is the most powerful
• Wilcoxon, bootstrap and permutation are the
most successful, depending on α level

59

Conflicts
• Wilcoxon and t-test are the safest at low α levels
• Wilcoxon is the most exact at low α levels, but
bootstrap is for usual levels

60

Summary
• Bootstrap test is the most powerful, and still it
has smaller Type I error rates, so we are safe
• Power and success:
– CGl@5 > GAP@5 > DCGl@5 > RBPl@5
– Fine > Broad > binary

• Conflicts:
– Very similar across measures and scales
– Corrections for multiple comparisons (e.g. Tukey) do
not seem necessary
61

Reliability:
Test Collection Size

Acceptable sample size
• Reliability is higher with larger sample sizes
– But it is also more expensive
– What is an acceptable test collection size?

• Answer with Generalizability Theory
– G-Study: estimate variance components
– D-Study: estimate reliability of different sample sizes
and experimental designs

63

G-study: variance components
Fully crossed experimental design: s × q
λq,A = λ + λA + λq + εqA

σ2 =

σ 2 + σ2 + σ 2
s
q
sq

• Estimated with Analysis of Variance

64

Intuition
𝜆𝐴 𝜆𝐵

𝜆𝐶 𝜆𝐷𝜆𝐸 𝜆𝐹

• If σ2 is small or σ2 is large, we need more queries
s
q

65

Intuition
𝜆𝐴 𝜆𝐵


s
q
𝜆𝐴 𝜆𝐵 𝜆𝐶 𝜆 𝐷 𝜆𝐸 𝜆𝐹

Larger σ2
s

65

Intuition
𝜆𝐴 𝜆𝐵


s
q
𝜆𝐴 𝜆𝐵 𝜆𝐶 𝜆 𝐷 𝜆𝐸 𝜆𝐹

Larger

σ2
s

𝜆𝐴 𝜆𝐵


Smaller σ2 or
q
more queries

65

D-study: variance ratios
• Stability of absolute scores

Φ nq

σ2
s
=
σ2 + σ2
q
e
2
σs +
nq

• Stability of relative scores
Eρ2 nq =

σ2
s
σ2
σ2 + e
s
nq

• We can easily estimate how many queries are
needed to reach some level of stability (reliability)
66

Effect of query set size
•
•
•
•

Average absolute stability Φ = 0.97
≈65 queries needed for Φ2 = 0.95, ≈100 in worst cases
Fine scale slightly better than Broad and binary scales
RBPl@5 and nDCGl@5 are the most stable

67

Effect of query set size
•
•
•
•

Average relative stability Eρ2 = 0.98
≈35 queries needed for Eρ2 = 0.95, ≈60 in worst cases
Fine scale better than Broad and binary scales
CGl@5 and RBPl@5 are the most stable

68

Effect of cutoff k
• What if we use a deeper cutoff, k=10?
– From 100 queries and k=5 to 50 queries and k=10
– Should still have stable scores
– Judging effort should decrease
– Rank-based measures should become more stable

• Tested in MIREX 2012
– In 2013 too, but not analyzed here

69

Effect of cutoff k
• Judging effort reduced to 72% of the usual
• Generally stable
– From Φ = 0.81 to Φ = 0.83
– From Eρ2 = 0.93 to Eρ2 = 0.95

70

Effect of cutoff k
• Reliability given a fixed budged for judging?
– k=10 allows us to use fewer queries, about 70%
– Slightly reduced relative stability

71

Effect of assessor set size
• More assessors or simply more queries?
– Judging effort is multiplied

• Can be studied with MIREX 2006 data
– 3 different assessors per query
– Nested experimental design: s × h: q

72

Effect of assessor set size
•

2
2
Broad scale: σs ≈ σh:q
Fine scale: σ2 ≫ σ2
s
h:q

•
• Always better to spend resources on queries

73

Summary
• MIREX collections generally larger than necessary
• For fixed budget
– More queries better than more assessors
– More queries slightly better than deeper cutoff
• Worth studying alternative user model?

•
•
•
•

Employ G-Theory while building the collection
Fine better than Broad, better than binary
CGl@5 and DCGl@5 best for relative stability
RBPl@5 and nDCGl@5 best for absolute stability
74

Implications
• Fixing the number of queries across years is
unrealistic
– Especially because they are not intended for reuse

• Fixing the number of queries across task is simply
nonsense
• Need to analyze on a case-by-case basis, while
building the collections
– GT4IReval, R package online
– https://github.com/julian-urbano/GT4IREval
75

Efficiency:
Learning Relevance Distributions

Probabilistic evaluation
• The MIREX setting is still expensive
– Need to judge all top k documents from all systems
– Takes days, even weeks sometimes

• Model relevance probabilistically
– Relevance judgments are random variables over the space
of possible assignments of relevance
E Rd =

P 𝑅𝑑 =ℓ ·ℓ
ℓ∈ℒ

P 𝑅 𝑑 = ℓ · ℓ2 − E 𝑅 𝑑

Var 𝑅 𝑑 =

2

ℓ∈ℒ

• Effectiveness measures are also probabilistic
77

Probabilistic evaluation
• Accuracy increases as we make judgments
– E R d ← rd

• Reliability increases too (confidence)
– Var R d ← 0

• Iteratively estimate relevance and effectiveness
– If confidence is low, make judgments
– If confidence is high, stop

• Judge as few documents as possible
78

Learning distributions of relevance
• Uniform distribution is very uninformative
• Historical distribution in MIREX has high variance
• Estimate from a set of features: P R d = ℓ θd
– For each document separately
– Ordinal Logistic Regression

• Three sets of features
– Output-based, can always be used
– Judgment-based, to exploit known judgments
– Audio-based, to exploit musical similarity
79

Learned models
• Mout : can be used even without judgments
– Similarity between systems’ outputs
– Genre and artist metadata
• Genre is highly correlated to similarity

– Decent fit, R2 ≈ 0.35

• Mjud : can be used when there are judgments
– Similarity between systems’ outputs
– Known relevance of same system and same artist
• Artist is extremely correlated to similarity

– Excellent fit, R2 ≈ 0.91
80

Estimation errors
• Actual vs. predicted by Mout
– 0.36 with Broad and 0.34 with Fine

• Actual vs. predicted by Mjud

• Among assessors in MIREX 2006

• Negligible under the current MIREX setting
81

Efficiency:
Probabilistic Evaluation

Probabilistic effectiveness measures
• Effectiveness scores become random variables too
• Example: DCGl@k
– (Usual) deterministic formulation:
𝑘
𝑖=1 𝑟𝑖 / log 2 𝑖 + 1
𝐷𝐶𝐺 𝑙 @𝑘 = 𝑘
𝑖=1 𝑛ℒ − 1 / log 2 𝑖 + 1
– (New) probabilistic formulation:
𝑘
1
E 𝑅𝑖
E 𝐷𝐶𝐺 𝑙 @𝑘 =
𝜂 𝐷𝐶𝐺 𝑙
𝑖=1 log 2 𝑖 + 1
𝑘
1
Var 𝑅 𝑖
Var 𝐷𝐶𝐺 𝑙 @𝑘 = 2
𝑖=1 log 2 𝑖 + 1

2
83

• Effectiveness scores become random variables too
• Example: DCGl@k
– (Usual) deterministic formulation:
𝑘
𝑖=1 𝑟𝑖 / log 2 𝑖 + 1
𝐷𝐶𝐺 𝑙 @𝑘 = 𝑘
𝑖=1 𝑛ℒ − 1 / log 2 𝑖 + 1
– (New) probabilistic formulation:
𝑘
1
E 𝑅𝑖
E 𝐷𝐶𝐺 𝑙 @𝑘 =
𝑖=1 log 2 𝑖 + 1
𝑘
1
Var 𝑅 𝑖
Var 𝐷𝐶𝐺 𝑙 @𝑘 = 2
𝑖=1 log 2 𝑖 + 1


2
83

• From there we can compute Δ𝐷𝐶𝐺 𝑙 @𝑘AB
• And averages over a sample of queries 𝒬
• Different approaches to compute estimates
– Deal with dependence of random variables
– Different definitions of confidence

• For measures based on ideal ranking (nDCGl@k
and RBPl@k) we do not have a closed form
– Approximated with Delta method and Taylor series
84

Ranking without judgments
1. Estimate relevance with Mout
2. Estimate relative differences and rank systems
• Average confidence in the rankings is 94%
• Average accuracy of the ranking is 92%

85

Ranking without judgments
• Can we trust individual estimates?
– Ideally, we want X% accuracy when X% confidence
– Confidence slightly overestimated in [0.9, 0.99)
Confidence
[0.5, 0.6)
[0.6, 0.7)
[0.7, 0.8)
[0.8, 0.9)
[0.9, 0.95)
[0.95, 0.99)
[0.99, 1)
E[Accuracy]

DCGl@5
Broad
In bin
Accuracy
23 (6.5%)
0.826
14 (4%)
0.786
14 (4%)
0.571
22 (6.2%)
0.864
23 (6.5%)
0.87
24 (6.8%)
0.917
232 (65.9%)
0.996
0.938

Fine
In bin
22 (6.2%)
16 (4.5%)
11 (3.1%)
21 (6%)
19 (5.4%)
27 (7.7%)
236 (67%)

Accuracy
0.636
0.812
0.364
0.762
0.895
0.926
0.996
0.921

86

Relative estimates with judgments
2. Estimate relative differences and rank systems
3. While confidence is low (<95%)
1. Select a document and judge it
2. Update relevance estimates with Mjud when possible
3. Update estimates of differences and rank systems

• What documents should we judge?
– Those that are the most informative
– Measure-dependent
87

Relative estimates with judgments
• Judging effort dramatically reduced
– 1.3% with CGl@5, 9.7% with RBPl@5

• Average accuracy still 92%, but improved individually
– 74% of estimates with >99% confidence, 99.9% accurate
– Expected accuracy improves slightly from 0.927 to 0.931

88

Absolute estimates with judgments
2. Estimate absolute effectiveness scores
3. While confidence is low (expected error >±0.05)
1. Select a document and judge it
2. Update relevance estimates with Mjud when possible
3. Update estimates of absolute effectiveness scores

• What documents should we judge?
– Those that reduce variance the most
– Measure-dependent
89

• The stopping condition is overly confident
– Virtually no judgments are even needed (supposedly)

• But effectiveness is highly overestimated

– Especially with nDCGl@5 and RBPl@5
– Mjud, and especially Mout, tend to overestimate relevance

90

• Practical fix: correct variance
• Estimates are better, but at the cost of judging
– Need between 15% and 35% of judgments

91

Summary
• Estimate ranking of systems with no judgments
– 92% accuracy on average, trustworthy individually
– Statistically significant differences are always correct

• If we want more confidence, judge documents
– As few as 2% needed to reach 95% confidence
– 74% of estimates have >99% confidence and accuracy

• Estimate absolute scores, judging as necessary
– Around 25% needed to ensure error <0.05

92

Implications
• We do not need dozens of volunteers to make
thousands of judgments over several days
• Just one person spending a couple hours is fine

• The spare manpower can be put to better use
– Redundant judgments to have better estimates
– Make annotations for other tasks

• It naturally promotes collaborative creation of
test collections by iteratively adding the
judgments needed in each experiment (if any)
93

Validity
• User studies to understand user behavior
• What information to include in test collections
• Other forms of relevance judgment to better
capture document utility
• Explicitly define judging guidelines
• Similar mapping for Text IR
– Different user models within the same task
95

Reliability
• Corrections for Multiple Comparisons
• Methods to reliably estimate reliability while
building test collections

96

Efficiency
• Better models to estimate document relevance
• Correct variance when having just a few
relevance judgments available
• Estimate relevance beyond k=5
• Other stopping conditions and document weights

97

Conduct similar studies
for the wealth of tasks in
Music Information Retrieval

Evaluation in (Music) Information Retrieval through the Audio Music Similarity task

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