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

1. Evaluation in (Music) Information Retrieval through the Audio Music Similarity task Julián Urbano Barcelona, Spain · January 16th 2014

2. Spam • @julian_urbano • Postdoctoral researcher – Music Technology Group, Universitat Pompeu Fabra • Recently: PhD, Computer Science – (Evaluation in) (Music) Information Retrieval 2

3. 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

4. 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

5. 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

6. 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

7. Introduction: Why we want to Evaluate…

8. 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

9. 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

10. 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

11. 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

12. Introduction: …what we do with Cranfield

13. 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

14. 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

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(documents, query, user, system) 15

16. 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(documents, query, user, system) user-measure = f(system) 15

17. 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

18. 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

19. 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

24. Experiments with Test Collections • Our goal is the users user-measure = f(system) • but Cranfield tells us about systems system-effectiveness = f(system, scale, measure) 20

25. Experiments with Test Collections • Our goal is the users user-measure = f(system) • but Cranfield tells us about systems system-effectiveness = f(system, scale, measure) 20

26. Experiments with Test Collections • Our goal is the users user-measure = f(system) • but Cranfield tells us about systems system-effectiveness = f(system, scale, measure) • This poses several problems – That we have been dealing with for over 50 years – But hey, they’re extremely interesting! 20

27. 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

28. 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

29. Validity: Effectiveness and Satisfaction

30. 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

31. 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

32. 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

33. 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

44. 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

45. Experimental design 28

46. 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

47. 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

48. Single system: how good is it? • For 2045 examples (49%) users could not decide which system was better What do we expect? 31

49. Single system: how good is it? • For 2045 examples (49%) users could not decide which system was better 31

50. Single system: how good is it? • Large ℓmin thresholds underestimate satisfaction 32

51. Single system: how good is it? • Users don’t pay attention to ranking? 33

52. Single system: how good is it? • Exponential gain underestimates satisfaction 34

53. Single system: how good is it? • Document utility independent of others 35

54. Two systems: which one is better? • For 2090 examples (51%) users did prefer one system over the other one What do we expect? 36

55. Two systems: which one is better? • For 2090 examples (51%) users did prefer one system over the other one 36

56. Two systems: which one is better? • Large differences needed for users to note them 37

57. Two systems: which one is better? • More relevance levels are better to discriminate 38

58. Two systems: which one is better? • Cascade and navigational user models are not appropriate 39

59. Two systems: which one is better? • Users do prefer the (supposedly) worse system 40

60. 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

61. 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

62. 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

63. Validity: Satisfaction over Samples

64. 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

65. Expected probability of satisfaction • Now we can compute point and interval estimates of the expected probability of satisfaction • Intuition fails when interpreting effectiveness 46

66. 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

67. 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

68. 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

71. 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

72. 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

73. 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

74. Reliability: Optimal Statistical Significance Tests

75. 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

76. 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

77. 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

78. 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

79. 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

80. Power and success • Bootstrap test is the most powerful • Wilcoxon, bootstrap and permutation are the most successful, depending on α level 59

81. 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

82. 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

83. Reliability: Test Collection Size

84. 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

85. 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

95. Intuition 𝜆𝐴 𝜆𝐵 𝜆𝐶 𝜆𝐷𝜆𝐸 𝜆𝐹 • If σ2 is small or σ2 is large, we need more queries s q 65

96. Intuition 𝜆𝐴 𝜆𝐵 𝜆𝐶 𝜆𝐷𝜆𝐸 𝜆𝐹 • If σ2 is small or σ2 is large, we need more queries s q 𝜆𝐴 𝜆𝐵 𝜆𝐶 𝜆 𝐷 𝜆𝐸 𝜆𝐹 Larger σ2 s 65

97. Intuition 𝜆𝐴 𝜆𝐵 𝜆𝐶 𝜆𝐷𝜆𝐸 𝜆𝐹 • If σ2 is small or σ2 is large, we need more queries s q 𝜆𝐴 𝜆𝐵 𝜆𝐶 𝜆 𝐷 𝜆𝐸 𝜆𝐹 Larger σ2 s 𝜆𝐴 𝜆𝐵 𝜆𝐶 𝜆𝐷𝜆𝐸 𝜆𝐹 Smaller σ2 or q more queries 65

98. 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

99. 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

100. 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

101. 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

102. 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

103. 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

104. 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

105. 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

106. 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

107. 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

108. 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

109. Efficiency: Learning Relevance Distributions

110. 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

111. 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

112. 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

113. 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

114. Estimation errors • Actual vs. predicted by Mout – 0.36 with Broad and 0.34 with Fine • Actual vs. predicted by Mjud – 0.14 with Broad and 0.09 with Fine • Among assessors in MIREX 2006 – 0.39 with Broad and 0.31 with Fine • Negligible under the current MIREX setting 81

115. Efficiency: Probabilistic Evaluation

116. 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 𝜂 𝐷𝐶𝐺 𝑙 𝑖=1 log 2 𝑖 + 1 2 83

117. 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 𝜂 𝐷𝐶𝐺 𝑙 𝑖=1 log 2 𝑖 + 1 𝜂 𝐷𝐶𝐺 𝑙 2 83

118. Probabilistic effectiveness measures • 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

119. 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

120. 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

121. Relative estimates with judgments 1. Estimate relevance with Mout 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

122. 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

123. Absolute estimates with judgments 1. Estimate relevance with Mout 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

124. Absolute estimates with judgments • 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

125. Absolute estimates with judgments • Practical fix: correct variance • Estimates are better, but at the cost of judging – Need between 15% and 35% of judgments 91

126. 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

127. 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

128. Future Work

129. 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

130. Reliability • Corrections for Multiple Comparisons • Methods to reliably estimate reliability while building test collections 96

131. 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

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

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

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

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