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![Fitting the IRT model
• Maximising the expectation
• - discrimination parameter of algorithm
• - scaling parameter for the algorithm
• - difficulty parameter for the algorithm
• - score of the algorithm on the dataset/problem
• - prior probabilities
Eθ|Λ(t),Z [ln p (Λ|θ, Z)] = N
n
∑
j=1
(ln αj + ln γj) −
1
2
N
∑
i=1
n
∑
j=1
α2
j ((βj + γjzij − μ(t)
i )
2
+ σ(t)2
)
+ ln p (Λ) + const
αj
γj
βj
zij
Λ](https://image.slidesharecdn.com/adsnsktalknew-240106004018-0902b411/85/Explainable-insights-on-algorithm-performance-18-320.jpg)
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Explainable insights on algorithm performance
The document discusses the distinction between explanation and prediction in algorithm performance evaluation, advocating for the integration of social science methods in machine learning. It introduces Item Response Theory (IRT) as a framework for evaluating algorithms through a causal lens, allowing for a deeper understanding of algorithm strengths and weaknesses. The application of IRT in algorithm analysis can help visualize performance across various datasets and inform the selection of effective algorithm portfolios.
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Explainable insights on algorithm performance
- 1. Explainable insights on algorithm performance SevvandiKandanaarachchi Work with Kate Smith-Miles 1
- 2. To explain orto predict? – Galit Shmueli ● Paper by Shmueli in 2010 ● Talks about these two topics ● Argues that explanation and prediction are different ● Two modelling paths – for predicting and explaining ● Social sciences have done explanatory models for a long time
- 3. What is anexplanation? • To explain an event is to provide some information about its causal history. – Lewis, 1986 (Causal Explanation) • A statement or an account that makes something clear – Google • It is important to note that the solution to explainable AI is not just ‘more AI’ - Miller, 2019 • Miller (2019) argues for Social Science + Computer Science in XAI In the fields of philosophy, cognitive psychology/science, and social psychology, there is a vast and mature body of work that studies these exact topics. 3
- 4. Message: Bring inthe social scientists to the party! Integrate their methods! 4
- 5. What is thistalk about? ● Using a method in social sciences to do two ML type tasks ● Evaluate algorithms ● It gives us more meaningful metrics about algorithms ● Has some causal interpretations ● Visually inspect where algorithms perform well (and poorly) ● Ensembles ● Anomaly detection ensembles
- 6. What is algorithmevaluation? • Performance of many algorithms to many problems • How do you explain the algorithm performance? • Standard statistical analysis misses many things Algo 1 Algo 2 Algo 3 Algo 4 Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 6
- 7. We want toevaluate algorithms performance . . . . . . in a way that we understand algorithms and problems better! 7
- 8.
- 9. Item Response Theory (IRT) •Modelsusedinsocialsciences/psychometrics • Unobservablecharacteristicsandobserved outcomes • Verbalormathematicalability • Racialprejudiceor stressproneness • Politicalinclinations • Intrinsic“quality”thatcannotbemeasured directly 9 This Photo by Unknown Author is licensed under CC BY-SA
- 10. IRT in education •Finds the discrimination and difficulty of test questions • And the ability of the test participants • By fitting an IRT model • In education – questions that can discriminate between students with different ability is preferred to “very difficult” questions. 10
- 11. How it works 11 Questions StudentsQ 1 Q 2 Q 3 Q 4 Stu 1 0.95 0.87 0.67 0.84 Stu 2 0.57 0.49 0.78 0.77 Stu n 0.75 0.86 0.57 0.45 IRT Model Discrimination of questions Difficulty of questions Ability of students (latent trait) Matrix βj αj θi
- 12. What does IRTgive us? • Q1 - discrimination , difficulty • Q2 - discrimination , difficulty • Q3 - discrimination , difficulty • Q4 - discrimination , difficulty • Student 1 ability ︙ • Student n ability α1 β1 α2 β2 α3 β3 α4 β4 θ1 θn Q 1 Q 2 Q 3 Q 4 Stu 1 0.95 0.87 0.67 0.84 Stu 2 0.57 0.49 0.78 0.77 Stu n 0.75 0.86 0.57 0.45 12
- 13. The causal understanding 𝛼 𝑗 𝛽 𝑗 𝜃 𝑖 𝑥 𝑖 𝑗 Discriminationof Q j Difficulty of Q j Ability of student i Marks of student i for Question j Student Question Marks 13
- 14. Dichotomous IRT ● Multiplechoice ● True or false ● ● - outcome/score of examinee for item ● - examinee’s ability ● - guessing parameter for item ● - difficulty parameter ● - discrimination 𝜙 ( 𝑥 𝑖 𝑗 = 1 𝜃 𝑖 , 𝛼 𝑗 , 𝑑 𝑗 , 𝛾 𝑗 ) = 𝛾 𝑗 + 1 − 𝛾 𝑗 1 + exp( − 𝛼 𝑗 ( 𝜃 𝑖 − 𝑑 𝑗 )) 𝑥 𝑖 𝑗 𝑖𝑗𝜃 𝑖 ( 𝑖 ) 𝛾 𝑗 𝑗𝑑 𝑗 𝛼 𝑗 This Photo by Unknown Author is licensed under CC BY-NC 14
- 15. Continuous IRT • Gradesout of 100 • A 2D surface of probabilities f (zj |θ) = αjγj 2π exp ( − α2 j 2 (θ − βj − γjzj) 2 ) 15
- 16. Mapping algorithm evaluationto IRT IRT Model Students Test questions 16 Problems/datasets Algorithms
- 17. The new mapping 𝛼 𝑗 𝛽 𝑗 𝜃 𝑖 𝑥 𝑖 𝑗 Discriminationof Algo j Difficulty of Algo j Ability of Dataset i Marks of dataset i for algorithm j Dataset Algorithm Performance 17
- 18. Fitting the IRTmodel • Maximising the expectation • - discrimination parameter of algorithm • - scaling parameter for the algorithm • - difficulty parameter for the algorithm • - score of the algorithm on the dataset/problem • - prior probabilities Eθ|Λ(t),Z [ln p (Λ|θ, Z)] = N n ∑ j=1 (ln αj + ln γj) − 1 2 N ∑ i=1 n ∑ j=1 α2 j ((βj + γjzij − μ(t) i ) 2 + σ(t)2 ) + ln p (Λ) + const αj γj βj zij Λ
- 19. New meaning ofIRT parameters? ● Discrimination -> anomalousness, algorithm consistency ● Difficulty -> algorithm difficulty limit ● Student ability -> Dataset difficulty spectrum
- 20. What can wesay . . . • Consistent algorithms give similar performance for easy or hard datasets • Algorithms with higher difficulty limits can handle harder problems • Anomalous algorithms give bad performance for easy problems and good performance for difficult problems 20
- 21. Dataset difficulty ● ● Isa function of discrimination, difficulty and scores dataset i di ffi culty = − ∑j ̂ α2 j ( ̂ βj + ̂ γjzij) ∑j ̂ α2 j
- 22. Example – fittingIRT model • Anomaly detection algorithms • 8 anomaly detection algorithms • 3142 datasets • Our performance metric is AUROC (looking at the performance vs actual) 22
- 23. Anomaly detection algorithms 23 Algorithm ConsistencyDifficulty Limit Anomalous Ensemble 55.08 -66.55 FALSE LOF 4.50 5.10 FALSE KNN 1.72 2.30 FALSE FAST_ABOD 9.39 10.23 FALSE Isolation Forest 2.35 3.05 FALSE KDEOS_1 0.86 -0.31 TRUE KDEOS-2 1.16 -0.51 TRUE LDF 2.01 2.08 FALSE
- 24. Dataset difficulty spectrum IRTStudent Ability -> Dataset Difficulty 24
- 25. Focusing on algorithmperformance • We have algorithm performance (y axis) and problem difficulty (x axis) • We can fit a model and find how each algorithm performs • We use smoothing splines • Can visualize them • No parameters to specify 25
- 26.
- 27. Strengths and weaknessesof algorithms • If the curve is on top – it is strong in that region • If the curve is at bottom – weak in that region 27
- 28. AIRT IRT Question and student characteristics Algorithm and dataset characteristics Visualisestrengths and weaknesses Portfolio construction 28
- 29. AIRT performs well,when . . . • The set of algorithms is diverse. • Ties back to IRT basics • IRT in education – If all the questions are equally discriminative and difficult, IRT doesn’t add much • IRT useful when we have a diverse set of questions and we want to know • Whichquestionsaremorediscriminative • Whichquestionsaredifficult 29
- 30. AIRT • Understand moreaboutalgorithms •Anomalousness,consistency,difficultylimit • Visualisethestrengthsandweaknessesofalgorithms • Selectaportfolioofgood algorithms • Includesdiagnostics • Rpackage airt(onCRAN) • https://sevvandi.github.io/airt/ • 30
- 31. A different applicationof IRT 31
- 32. IRT to buildan ensemble ● Previous work was using performance - marks ● What about using original responses? ● Like survey questions ● Rosenberg's Self-Esteem Scale - I feel I am a person of worth (Strongly agree/Agree/Neutral/Disagree/Strongly disagree) ● No right or wrong answer ● Latent trait gives the person’s self esteem ● Latent trait uncovers the “hidden quality”
- 33. Unsupervised algorithms ● Insteadof performance values what if you have original responses? Q 1 Q 2 Q 3 Q 4 Stu 1 0.95 0.87 0.67 0.84 Stu 2 0.57 0.49 0.78 0.77 Stu n 0.75 0.86 0.57 0.45 latent value (i) = − ∑j ̂ α2 j ( ̂ βj + ̂ γjzij) ∑j ̂ α2 j
- 34. What is ananomaly detection ensemble? Dataset Unsupervised AD methods • The AD methods are heterogenous methods • Ensembles – use existing methods to come up with better anomaly detection/ scores AD ensemble Ensemble Score
- 35. Anomaly detection ensembles ●Latent trait = anomalousness of the observations = the ensemble score ● , a weighted score of original responses ● ensemble score of observa ti on (i) = − ∑j ̂ α2 j ( ̂ βj + ̂ γjzij) ∑j ̂ α2 j
- 36.
- 37. IRT for anomalydetection ensembles • R package – outlierensembles – on CRAN
- 38. IRT and algorithms ●Algorithm evaluation - AIRT ● Anomaly detection ensembles ● IRT used in ML more
- 39.
- 40. New AIRT parameters ● ● ● ●Where M, V and C denote mean, variance, and covariance terms γ(t+1) j = V (μ(t) i ) + σ(t)2 Cj (zij, μ(t) i ) β(t+1) j = M (μ(t) i ) − γ(t+1) j Mj (zij) α(t+1) j = ( γ(t+1)2 j Vj(zij) − V (μ(t) i ) − σ(t)2 ) −1/2
- 41. Explaining notation ● ● ● ● ● Mj (zij)= ∑i zij N M (μ(t) i ) = ∑i μ(t) i N V (zij) = ∑i z2 ij N − Mj (zij) 2 V (μ(t) i ) = ∑i μ(t)2 i N − M (μ(t) i ) 2 Cj (zij, μ(t) i ) = ∑i zijμ(t) i N − Mj (zij) M (μ(t) i )
- 42. More notation ● ● isthe th iteration ● ● p (θi |Λ(t) , zi) = 𝒩 (θi |μ(t) i , σ(t)2 ) Λ(t) = (λ1 (t) , …, λn (t) ) , λj (t) = (α(t) j , β(t) j , γ(t) j ) T t σ(t)2 = ∑ j α(t)2 j + σ−2 −1 μ(t) i = σ(t)2 ∑ j α(t)2 j (β(t) j + γ(t) j zij) + μ
- 43. Algorithm portfolio selection •Can use algorithm strengths to select a good portfolio of algorithms • We call this portfolio airt portfolio • airt – Algorithm IRT (old Scottish word – to guide) 43
- 44. AIRT framework Performance data IRT Model Algorithmand dataset metrics Fitting smoothing splines Algorithm strengths and weaknesses Airt portfolio Evaluate portfolios General block AIRT output 44
- 45. What happens tothe IRT parameters? • IRT - ability of student • As increases probability of a higher score increases • What is in terms of a dataset? • easiness of the dataset • Dataset difficulty score θi θi θi −θi 45
- 46. Discrimination parameter • Discriminationof item • increases slope of curve increases • What is in terms of an algorithm? • - lack of stability/robustness of algo • Consistency of algo αj αj αj αj 1 |αj | 46
- 47. Consistent algorithms • Education– such a question doesn’t give any information • Algorithms – these algorithms are really stable or consistent • Consistency = 1 |αj | 47
- 48. Anomalous algorithms • Algorithmsthat perform poorly on easy datasets and well on difficult datasets • Negative discrimination • In education – such items are discarded or revised • If an algorithm anomalous, it is interesting • Anomalousness = = sign(αj) This Photo by Unknown Author is licensed under CC BY-NC-ND 48