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- 1. SIGIR 2018 · July 11th · Ann ArborPicture by qiyang
- 2. MOTIVATION
- 3. Experiments in IR 3 Core research “how well?” input IR systems Evaluation research “what if?” output test collection AP P@10 conditions input no. topics stat. signif. tests output AP P@10 p-values Kendall τ conditions
- 4. Experiments in IR 4 Core research “how well?” input IR systems Evaluation research “what if?” output test collection AP P@10 conditions input no. topics stat. signif. tests output AP P@10 p-values Kendall τ conditions
- 5. Experiments in IR 5 Core research “how well?” input IR systems Evaluation research “what if?” output test collection AP P@10 conditions input no. topics stat. signif. tests output AP P@10 p-values Kendall τ conditions
- 6. Current Limitations 1.Finite data 2.Unknown Truth 3.Lack of Control 6 How we Make Do
- 7. Current Limitations 1.Finite data 2.Unknown Truth 3.Lack of Control Artificially create other collections by resampling from the existing data 7 How we Make Do Limited to dozens of systems and topics from past evaluations like TREC s t ? ?
- 8. Current Limitations 1.Finite data 2.Unknown Truth 3.Lack of Control Split in two topic sets and consider results with one subset as the truth 8 How we Make Do Don’t know true properties of systems, such as mean or variance over topics s t 𝑿 𝑿 ? 𝑿 𝑿 ?
- 9. Current Limitations 1.Finite data 2.Unknown Truth 3.Lack of Control Artificial modifications of effectiveness scores that lead to invalid data 9 How we Make Do Can’t control properties of systems, such as true mean. Systems are how they are ? -1 10 -1 10
- 10. PROPOSAL 10
- 11. Stochastic Simulation 11 Core research “how well?” IR systems Evaluation research “what if?” test collection AP P@10 no. topics stat. signif. tests AP P@10 p-values Kendall τ Model AP P@10
- 12. • Build a generative model of the joint distribution of system scores • Simulate scores on new, random topics • Lack of data • Unknown truth • Lack of control Stochastic Simulation 12 Core research “how well?” IR systems Evaluation research “what if?” test collection AP P@10 no. topics stat. signif. tests AP P@10 p-values Kendall τ Model
- 13. • Build a generative model of the joint distribution of system scores • Simulate scores on new, random topics • Lack of data • Unknown truth • Lack of control • Fit the model to existing data to make it realistic • Needs to be flexible to model real data Stochastic Simulation 13 Core research “how well?” IR systems Evaluation research “what if?” test collection AP P@10 no. topics stat. signif. tests AP P@10 p-values Kendall τ Model
- 14. Model • …of the joint distribution of system scores • We use copula models, which separate: 1.Marginal distributions, of individual systems 2.Dependence structure, among systems • Easy to customize: plug and play simulate 14
- 15. • Fit the model: Model 15 𝑌1, … , 𝑌𝑛 𝑋1,…,𝑋n *generalizes to several systems
- 16. • Fit the model: 1. Fit the margins Model 15 𝑌1, … , 𝑌𝑛 𝑋1,…,𝑋n *generalizes to several systems
- 17. • Fit the model: 1. Fit the margins 2. Turn to pseudo- observations Model 15 𝑌1, … , 𝑌𝑛 𝑉𝑖 = 𝐹𝑌 𝑌𝑖 𝑋1,…,𝑋n 𝑈𝑖=𝐹𝑋𝑋𝑖 *generalizes to several systems
- 18. • Fit the model: 1. Fit the margins 2. Turn to pseudo- observations 3. Fit the copula Model 15 𝑌1, … , 𝑌𝑛 𝑉𝑖 = 𝐹𝑌 𝑌𝑖 𝑋1,…,𝑋n 𝑈𝑖=𝐹𝑋𝑋𝑖 *generalizes to several systems
- 19. • Fit the model: 1. Fit the margins 2. Turn to pseudo- observations 3. Fit the copula • Or instantiate at will Model 16 *generalizes to several systems
- 20. • Fit the model: 1. Fit the margins 2. Turn to pseudo- observations 3. Fit the copula • Or instantiate at will • Simulate from the model: 1. Generate pseudo- observations Model 16 𝑉 𝑈 *generalizes to several systems
- 21. • Fit the model: 1. Fit the margins 2. Turn to pseudo- observations 3. Fit the copula • Or instantiate at will • Simulate from the model: 1. Generate pseudo- observations 2. Turn into effectiveness scores Model 16 𝑌 = 𝐹𝑌 −1 𝑉 𝑉 𝑋=𝐹𝑋 −1 𝑈 𝑈 *generalizes to several systems
- 22. Modeling Dependences • Gaussian copulas – Only correlation – Only symmetric • R-Vine copulas – Allows tail dependence – Allows asymmetricity – Built from pair-copulas (bivariate) – Eg: F(S1,S2), F(S4,S2|S1), F(S4,S3|S1,S2), … – ~40 alternatives based on 12 different families 17
- 23. Modeling Margins • All effectiveness measures have discrete distributions, but for some we can fairly assume they’re continuous –AP, nDCG • For some others, this assumption is clearly wrong, so we must preserve the support –P@10: 1, 0.9, 0.8, … –RR: 1, 1/2, 1/3, … 18
- 24. Modeling Margins Continuous • (Truncated) Normal • Beta • (Truncated) Normal Kernel Smoothing • Beta Kernel Smoothing Discrete • Beta-Binomial • Discrete Kernel Smoothing • Discrete Kernel Smoothing w/ controlled smoothness 19
- 25. Transform to Predefined Mean Problem: given 𝐹, transform to 𝐹 such that 𝝁 = 𝝁∗ and preserving the support Solution: transform with a specific Beta find 𝛼, 𝛽 > 1 such that 𝜇 = 𝜇∗ where 𝐹 𝑥 = 𝐹𝐵𝑒𝑡𝑎 𝐹 𝑥 ; 𝛼, 𝛽 20
- 26. RESULTS 21
- 27. Data • TREC Web Ad hoc runs 2010-2014 – 50 topics and 30-88 systems each – 12924 total system-topic pairs • Continuous measures: AP, nDCG@20, ERR@20 • Discrete measures: P@10, P@20, RR • Points of Interest 1. Margins 2. Copulas 3. Simulated scores 22
- 28. • 1572 system-measure pairs • 5425 models successfully fitted • Log-Likelihood: • Kernel Smoothing (esp. discrete) • Normal & Beta 25% of cases • AIC and BIC: • Normal & Beta 67% of cases • Beta-Binomial 50% of P@k • Transform all to the mean in the given data and select again: • Kernel Smoothing nearly always 1. Margins 23
- 29. • 39627 system pairs • Fit pair-copulas and select according to Log-Likelihood • Wide diversity • Gaussian copulas rarely selected; correlation is not enough • Complex models are preferred 2. Dependence 24
- 30. • Simulate 1000 new topics and record deviations from the model • 𝜇 − 𝑋 and 𝜎2 − 𝑠2 • Repeat 1000 times • Full knowledge of truth encoded in the model 3. Simulation: Scores 25
- 31. • Web 2010, nDCG@20 • Simulate 500 new topics • Dependence captured in the model 3. Simulation: Dependencies 26
- 32. SAMPLE APPLICATIONS
- 33. [Voorhees, 2009] 1. Type I Errors? 28 S1 S2
- 34. [Voorhees, 2009] 1. Type I Errors? 28 S1 S2
- 35. [Voorhees, 2009] 1. Type I Errors? 28 𝑫 𝟐 + p-value𝑫 𝟏 + p-value conflict? S1 S2
- 36. [Voorhees, 2009] • Limited data • Unknown truth (is H0 true?) • No control over H0 • Cannot measure Type I error rates directly • Conflict rates at α=5%: • AP: 2.8% • P@10: 10.9% 1. Type I Errors? 28 𝑫 𝟐 + p-value𝑫 𝟏 + p-value conflict? S1 S2
- 37. [With simulation] Same margins 1. Type I Errors 29
- 38. [With simulation] Same margins 1. Type I Errors 29
- 39. [With simulation] Same margins 1. Type I Errors 29
- 40. [With simulation] Same margins 1. Type I Errors 29
- 41. [With simulation] Same margins • Type I errors at α=5% and 1%: • AP: 4.9% and 0.9% • P@10: 4.9% and 1% 1. Type I Errors 29 p-value Type I error?
- 42. [With simulation] Same margins • Type I errors at α=5% and 1%: • AP: 4.9% and 0.9% • P@10: 4.9% and 1% Transformed margins 1. Type I Errors 30
- 43. [With simulation] Same margins • Type I errors at α=5% and 1%: • AP: 4.9% and 0.9% • P@10: 4.9% and 1% Transformed margins 1. Type I Errors 30
- 44. [With simulation] Same margins • Type I errors at α=5% and 1%: • AP: 4.9% and 0.9% • P@10: 4.9% and 1% Transformed margins 1. Type I Errors 30
- 45. [With simulation] Same margins • Type I errors at α=5% and 1%: • AP: 4.9% and 0.9% • P@10: 4.9% and 1% Transformed margins • Type I errors at α=5% and 1%: • AP: 4.9% and 0.9% • P@10: 5% and 1% 1. Type I Errors 30 p-value Type I error?
- 46. 2. Sneak Peak: Statistical Power and σ 31 [Webber et al, 2008] • Show empirical evidence of the problem of sequential testing • Limited data • Unknown truth (true σ)
- 47. TAKE HOME
- 48. Today • Part of Evaluation Research has data-related limitations –Lack of data, no knowledge of truth, no control –How valid are our results? • We propose a methodology for stochastic simulation to eliminate these limitations –Flexible, realistic, highly customizable –Allows us to study new problems, directly 33
- 49. Tomorrow • Even more flexibility • Simulate new systems for given topics • Add third factors –Fixed: already possible –Random: we’ll see • Simulate full runs (doc scores & relevance) 34
- 50. simIReff • All results fully reproducible • Developed a full R-package for simulation https://github.com/julian-urbano/simIReff effs <- effDiscFitAndSelect(data, support("p20")) cop <- effcopFit(data, effs) y <- reffcop(1000, cop) 35

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