The presentation discusses the sample bias problem in credit scoring and introduces shallow self-learning methods to improve reject inference. It highlights the impact of sample bias on model performance and evaluates various reject inference strategies. An illustrative example is used to demonstrate the method's effectiveness compared to traditional approaches.

1. слайд 1/18Nikita Kozodoi 2/3021.08.2019 Kreditech слайд 1/18Nikita Kozodoi17.09.2019 Würzburg
Shallow Self-Learning for
Reject Inference in Credit Scoring
Humboldt University of Berlin
nikita.kozodoi@hu-berlin.de

2. слайд 1/18Nikita Kozodoi 1
Presentation Outline
1. Sample Bias Problem
2. Shallow Self-Learning for Reject Inference
3. Evaluation Problem
4. Kickout Metric for Model Selection
5. Performance Evaluation
Würzburg17.09.2019

3. слайд 1/18Nikita Kozodoi 2
Motivation: Acceptance Cycle
1. Sample Bias
BAD
ACCEPTS
Scoring
Model
TRAINING
DATA
REJECTS
17.09.2019
- acceptance cycle creates sample bias
- labels are not missing at random
GOOD

4. 0.725
0.750
0.775
0.800
0 100 200 300
Iteration
PerformanceontheHoldoutSample
Training Data
Accepts
Population
(a) AUC Values
0.00
0.05
0.10
0.15
0 100 200 300
Iteration
PerformanceGap
(b) AUC Gap
0.725
0.750
0.775
0.800
0 100 200 300
Iteration
PerformanceontheHoldoutSample
Training Data
Accepts
Population
(a) AUC Values
0.00
0.05
0.10
0.15
0 100 200 300
Iteration
PerformanceGap
(b) AUC Gap
слайд 1/18Nikita Kozodoi 31. Sample Bias
AUCGap
Accepts
Unbiased
Training Data
Acceptance Cycle Acceptance Cycle
Sample Bias: Impact on Performance
Data: multivariate Gaussians with class-specific means and covariance
0 300 0 300
.725
0.750
0.775
AUCValues
.800
0
.05
.10
.15
lossduetobias
17.09.2019

5. слайд 1/18Nikita Kozodoi 4
Sample Bias: Gain from Reject Inference
Data: multivariate Gaussians with class-specific means and covariance
0.725
0.750
0.775
0.800
0 100 200 300
Iteration
PerformanceontheHoldoutSample
Training Data
Accepts
Population
Accepts + SL
(a) AUC Values
0.00
0.05
0.10
0.15
0 100 200 300
Iteration
PerformanceGap
(b) AUC Gap
0.725
0.750
0.775
0.800
0 100 200 300
Iteration
PerformanceontheHoldoutSample
Training Data
Accepts
Population
Accepts + SL
(a) AUC Values
0.00
0.05
0.10
0.15
0 100 200 300
Iteration
PerformanceGap
(b) AUC Gap
gainfromrejectinferencelossduetobias
AUCValues
Acceptance Cycle Acceptance Cycle
0 300 0 300
.725
0.750
0.775
AUCValues
.800
0
.05
.10
.15
Accepts
Unbiased
Accepts + SL
Training Data
1. Sample Bias17.09.2019

6. Label Noise
Correction
Credit Scoring
Literature
слайд 1/18
Semi-Supervised
Learning
Reject Inference Methods
• label all as BAD
• hard cutoff augmentation
• parcelling
• self-learning
• semi-supervised SVMs
• graph-based methods
• CV-based voting
• neighbor-based labeling
• evolutionary algorithms
Nikita Kozodoi17.09.2019 51. Sample Bias
Empirical results:
• studies provide little evidence of gains from reject inference
• data is often incomplete, low-dimensional or synthetic
(Banasik et al 2005, Chen et al 2001, Cook et al 2004, Verstraeten et al 2005)
(e.g., Bücker et al 2013, Maldonado et al 2010)
Background on Reject Inference

7. слайд 1/18Nikita Kozodoi 6
Reject Inference with Shallow SL
2. Shallow Self-Learning
FACCEPTS REJECTS
train score
Stage I
filtering isolation forest
17.09.2019
FILTERED
REJECTS
• removing rejects whose distribution is most different from the accepts
• reduces the risk of error propagation due to noise in predictions

8. слайд 1/18Nikita Kozodoi 6
Reject Inference with Shallow SL
LACCEPTS FILTERED REJECTS
train score
label & append the most confident cases
Stage II
labeling
FACCEPTS REJECTS
train score
Stage I
filtering
L1 classifier
isolation forest
17.09.2019
FILTERED
REJECTS
2. Shallow Self-Learning
• only label rejects if the model’s confidence is high
• using weak learner (L1) to get well-calibrated probabilities
• imbalance parameter to account for higher BAD rate among rejects
• stopping criteria: confidence threshold & scoring model performance
θ

9. слайд 1/18Nikita Kozodoi 6
Reject Inference with Shallow SL
LACCEPTS FILTERED REJECTS
train score
label & append the most confident cases
ACCEPTS
LABELED
REJECTS
TRAINING
DATA
S NEW APPLICANTS
train score
FACCEPTS REJECTS
train score
Stage II
labeling
Stage III
scoring
Stage I
filtering
FILTERED
REJECTS
L1 classifier
XGB classifier
isolation forest
17.09.2019 2. Shallow Self-Learning

10. слайд 1/18Nikita Kozodoi 7
Illustrative Example on Synthetic Data
Accepts
Accepts + SL
Oracle
Accepts
Labeled Rejects
Rejects
Sample
Model
X1
X2
URL
17.09.2019 2. Shallow Self-Learning

11. слайд 1/18Nikita Kozodoi 8
Illustrative Example on Synthetic Data
X1
17.09.2019
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−2
0
2
−2 0 2 4
X1
X2
Scoring Model
Accepts
Accepts + SL
Population
Labels
●
●
●
Accepts
Labeled Rejects
Rejects
Acceptance Cycle 300/300
Accepts
Accepts + SL
Oracle
Model
Accepts
Labeled Rejects
Rejects
Sample
X2
parallel lines = same ranking
X1
2. Shallow Self-Learning

12. слайд 1/18Nikita Kozodoi 9
B AUC
(accepts)
AUC
(unbiased)
AUC
(accepts)
1
AUC
(unbiased)
0.12 1
Evaluation Problem: Correlation Analysis
3. Evaluation Problem
Data: real-world credit scoring data with synthetic labels (bureau scores)
17.09.2019
• AUC (accepts) = experimental AUC on a biased holdout sample of accepts
• AUC (unbiased) = production AUC on a representative holdout sample of clients

13. слайд 1/18Nikita Kozodoi 10
B AUC
(accepts)
AUC
(unbiased)
Kickout
AUC
(accepts)
1
AUC
(unbiased)
0.12 1
Kickout 0.01 0.30 1
Evaluation Problem: Correlation Analysis
Kickout metric better correlates with performance on unbiased sample
3. Evaluation Problem
Data: real-world credit scoring data with synthetic labels (bureau scores)
17.09.2019

14. слайд 1/18Nikita Kozodoi 114. Kickout Metric
Introducing the Kickout Metric
• KB, KG - kicked-out BADs and GOODs
• p(B) - probability of selecting BAD example
• SB - number of selected BAD examples
Intuition:
• compare two scoring models: before and after reject inference [RI]
• count GOOD and BAD cases that are "kicked out” - rejected after RI
• updated model should kick out more BAD and less GOOD cases
- kicked out cases are replaced by rejects with unknown labels
- kicking out a BAD case has a positive expected value
- kicking out a GOOD case has a negative expected value
17.09.2019

15. слайд 1/18Nikita Kozodoi 12
Experiment on Real-World Data
Data description:
• consumer loans provided by
• contains data on accepted and rejected applicants
• also contains unbiased sample: loans that were randomly accepted
Characteristic Accepts Rejects Unbiased
Number of cases 39,579 18,047 1,967
Number of features 2,410 2,410 2,410
BAD rate 0.39 - 0.66
5. Performance Evaluation17.09.2019

16. слайд 1/18Nikita Kozodoi 13
Experimental Results: Performance
Method
Mean AUC*
(unbiased)
Ignore rejects 0.8007
Label all rejects as BAD 0.6797
Bureau score based inference 0.7911
Hard cutoff augmentation 0.7994
Parceling 0.8041
Shallow Self-Learning + Kickout 0.8072
5. Performance Evaluation
*average across 50 bootstrap samples
17.09.2019

17. слайд 1/18Nikita Kozodoi 14
Experimental Results: Business Value
Assumptions:
• acceptance rate = 30% (applicants with the lowest predicted score)
• average loan amount = $17,100
• average interest rate = 10.36%
• average loss given default = 25%
Business value:
• difference between ignoring rejects and proposed method translates
to 60 less defaulted loans for every 10,000 accepted clients
• potential gains = $1.13 million * 0.25 = $283,073
1 Source: https://www.supermoney.com/studies/personal-loans-industry-study/
1
1
5. Performance Evaluation
2
2 Source: https://www.globalcreditdata.org/system/files/documents/gcd_lgd_report_large_corporates_2018.pdf
17.09.2019

18. слайд 1/18Nikita Kozodoi 15
Summary & Questions
1. Demonstrated the sample bias problem
2. Introduced a new reject inference method
• labeling rejects with shallow self-learning to mitigate bias
3. Introduced a new evaluation metric
• performance on accepts poorly correlates with performance on
the unbiased sample
• kickout metric is a more suitable measure for model selection
4. Evaluated performance gains
• proposed method increases AUC compared to benchmarks
• potential monetary gains are ~ $300k per 10,000 loans
Würzburg17.09.2019

19. слайд 1/18Nikita Kozodoi17.09.2019
APPENDIX
Würzburg

20. слайд 1/18
How to Use Rejects? [1]
• construct features based on full data
• use them to improve a model for accepts
• label rejects using a certain technique
• augment accepts with (labeled) rejects
• filter rejects which are used to augment the data
• can be done both before and after labeling
Nikita KozodoiAppendix17.09.2019
Assign labels to
rejects
Extract information
from rejects
Filter rejects

21. слайд 1/18
How to Use Rejects? [2]
Reject inference in credit scoring
Label noise correction
Semi-supervised learning
Evolutionary algorithms
Active learning
Novelty detection
Autoencoders
Instance selection
Assign labels to
rejects
Extract information
from rejects
Filter rejects
Nikita KozodoiAppendix17.09.2019

22. Label as BAD:
• Label all rejects as BAD risks
• Augment the known data with the labeled rejects
• Retrain the scoring model on the full data
Bureau score based inference:
• Use bureau scores to assign labels to rejects
• e.g., label “A” examples as GOOD, “B” and below - as BAD
• Augment the known data with the labeled rejects
• Retrain the scoring model on the full data
• Can use other informative attributes (e.g., previous loan delinquency)
Reject Inference Techniques [1]
Nikita KozodoiAppendix17.09.2019

23. Hard cutoff augmentation:
• Train a scoring model based on accepts
• Predict default probabilities for rejects using this model
• Assign labels based on a certain threshold
• Augment the known data with the labeled rejects
• Retrain the scoring model on the full data
Parceling:
• Split rejects into groups based on the model score
• Assign labels within groups proportionally to the expected bad rate
• BAD ratio for rejects is usually assumed to be higher
Reject Inference Techniques [2]
Nikita KozodoiAppendix17.09.2019

24. слайд 1/18Nikita Kozodoi
Data Generation & Acceptance Cycle
repeat for g
iterations
1. Initial population
• Create a small (unbiased) sample of applicants from multivariate Gaussians
• Use a simple rule to accept a% applicants (e.g. bureau score > b)
• Partition data into A (accepts) and R (rejects)
2. Updating scorecard
• Train a scoring model f(x) on A
3. New applicants
• Generate a new (unbiased) sample of applicants N
• Score applicants in N using a scoring model f(x)
• Use model scores to accept a% applicants from N
• Partition N into AN (new accepts) and RN (new rejects)
4. Merging data
• append AN (with labels) to A; append RN (no labels) to R
Appendix17.09.2019

25. слайд 1/18Nikita Kozodoi
Sample Bias: Illustration
Data: multivariate Gaussians with class-specific means and covariance
Appendix
0.0
0.2
0.4
0.6
−2 0 2 4 6
V1
density
Population
Accepts
Rejects
Population
0.0
0.1
0.2
0.3
0.4
−2 0 2 4
V2
density
Population
Accepts
Rejects
Population
density
Accepts
Rejects
Unbiased
X2X1
0
0.2
0.4
0.6
0
0.1
0.2
0.4
density
0.3
17.09.2019

26. Reject Inference with Shallow SL
Nikita KozodoiAppendix
Algorithm:
17.09.2019

27. Probability Calibration: L1 vs XG
Nikita KozodoiAppendix
0
40000
80000
120000
0.00 0.25 0.50 0.75 1.00
Predicted Scores
Count
Model
L1
XG
17.09.2019

28. слайд 1/18
Experimental Design: Pipeline
Nikita Kozodoi
FULL DATA
T2 T3 T4V1 R
T1 T3 T4 RV2
T1 T3T2 RV4
… ………
Unbiased (n = 1.967)Accepts (n = 39.579) Rejects (n = 18.047)
50 bootstrap samples
B1 B2 B50…
4-fold CV
Appendix17.09.2019

29. слайд 1/18Nikita Kozodoi
Evaluation Problem: Motivation
Problem:
• Real labels of rejects are unknown
• It is not possible to evaluate performance on an unbiased sample
• Hence, model performance is evaluated on accepts
• Due to sample bias, performance on accepts is a poor indicator of the
production-stage performance
Appendix17.09.2019

30. 0.78
0.79
0.80
0.81
0.728 0.732 0.736 0.740
AUC on Accepts
AUConBaseline
слайд 1/18Nikita Kozodoi
Evaluation Problem: Illustration
Correlation: r = 0.12
Appendix
AUC (Accepts)
.78
.79
.80
.81
AUC(Unbiased)
.728 .732 .736 .740 .744
17.09.2019

31. Using kickout improves AUC by 0.01
0.73
0.75
0.77
0.79
0.728 0.730 0.732
AUC on Accepts
AUContheUnbiasedSample
Models
Best AUC
Best Kickout
Others
0.73
0.75
0.77
0.79
0.02 0.03 0.04 0.05 0.06 0.07
Kickout Metric
AUContheUnbiasedSample
Models
Best AUC
Best Kickout
Others
Kickout Metric: Performance Gains
Nikita KozodoiAppendix17.09.2019

32. слайд 1/18Nikita KozodoiAppendix
Kickout Metric: Computation
• Train initial model on TRAIN and score examples in VALID:
- accepted goods, accepted bads
• Split rejected cases into two subsets: R1 and R2
• Use reject inference to label R1 and append R1 to TRAIN
• Append R2 without labels to VALID
• Train new model on (TRAIN + R1) and score cases from (TEST + R2):
- compare accepted goods and bads to the initial model
ACCEPTS REJECTS
R2
R1
VALID
TRAIN
17.09.2019
• KB, KG - kicked-out BADs and GOODs
• p(B) - probability of selecting BAD example
• SB - number of selected BAD examples