Women in Machine Learning Workshop 12 th of December 2011 Ina Fiterau, Carnegie Mellon University Artur Dubrawski, Carnegie Mellon University E XPLAINING D ATASETS THROUGH H IGH -A CCURACY R EGIONS 1 Work under review at the SIAM Data Mining Conference
2 O UTLINE Motivation of need for interpretability Explanation-Oriented Partitioning (EOP) Evaluation of EOP
3 E XAMPLE A PPLICATION : N UCLEAR T HREAT D ETECTION Border control: vehicles are scanned Human in the loop interpreting results prediction feedback vehicle scan
4 B OOSTED D ECISION S TUMPS Accurate, but hard to interpret How is the prediction derived from the input? Image obtained with the Adaboost applet.
5 D ECISION T REE – M ORE I NTERPRETABLE yes no Radiation > x% no yes Payload type = ceramics yes no Uranium level > max. Consider balance admissible for ceramics of Th232, Ra226 and Co60 Threat Clear
6 M OTIVATION Many users are willing to trade accuracy to better understand the system-yielded results Need : simple, interpretable model Need : explanatory prediction process
7 E XPLANATION -O RIENTED P ARTITIONING (EOP)
8 E XPLANATION -O RIENTED P ARTITIONING (EOP) E XECUTION E XAMPLE – 3D DATA Uniform cube 2 Gaussians 5 4 3 2 1 0 -1 -2 -3 5 4 3 2 5 4 5 1 3 2 0 4 1 -1 0 3 -1 -2 -2 2 -3 -3 -4 1 0 -1 -2 -3 -4 -3 -2 -1 0 1 2 3 4 5 (X,Y) plot
9 EOP E XECUTION E XAMPLE – 3D DATA Step 1: Select a projection - (X 1 ,X 2 )
10 EOP E XECUTION E XAMPLE – 3D DATA Step 1: Select a projection - (X 1 ,X 2 )
11 EOP E XECUTION E XAMPLE – 3D DATA h 1 Step 2: Choose a good classifier - call it h 1
12 EOP E XECUTION E XAMPLE – 3D DATA Step 2: Choose a good classifier - call it h 1
13 EOP E XECUTION E XAMPLE – 3D DATA OK NOT OK Step 3: Estimate accuracy of h 1 at each point
14 EOP E XECUTION E XAMPLE – 3D DATA Step 3: Estimate accuracy of h 1 for each point
15 EOP E XECUTION E XAMPLE – 3D DATA Step 4: Identify high accuracy regions
16 EOP E XECUTION E XAMPLE – 3D DATA Step 4: Identify high accuracy regions
17 EOP E XECUTION E XAMPLE – 3D DATA Step 5:Training points - removed from consideration
18 EOP E XECUTION E XAMPLE – 3D DATA Step 5:Training points - removed from consideration
19 EOP E XECUTION E XAMPLE – 3D DATA Finished first iteration
20 EOP E XECUTION E XAMPLE – 3D DATA Iterate until all data is accounted for or error cannot be decreased
21 L EARNED M ODEL – P ROCESSING QUERY [ X 1 X 2 X 3 ] yes h 1 (x 1 x 2 ) [x 1 x 2 ] in R 1 ? no yes h 2 (x 2 x 3 ) [x 2 x 3 ] in R 2 ? no yes h 3 (x 1 x 3 ) [x 1 x 3 ] in R 3 ? no Default Value
22 PARAMETRIC R EGIONS OF HIGH CONFIDENCE (B OUNDING P OLYHEDRA ) Enclose points in simple convex shapes (multiple per iteration) Grow contour while train error is ≤ ε decision Incorrectly classified Correctly classified
23 PARAMETRIC R EGIONS OF HIGH CONFIDENCE (B OUNDING P OLYHEDRA ) Enclose points in simple convex shapes (multiple per iteration) Grow contour while train error is ≤ ε decision Incorrectly classified Correctly classified Calibration on hold out set - remove shapes that: do not contain calibration points over which the classifier is not accurate
24 PARAMETRIC R EGIONS OF HIGH CONFIDENCE (B OUNDING P OLYHEDRA ) Enclose points in simple convex shapes (multiple per iteration) Grow contour while train error is ≤ ε decision Incorrectly classified Correctly classified Calibration on hold out set - remove shapes that: do not contain calibration points over which the classifier is not accurate Intuitive, visually appealing - hyper-rectangles/spheres
25 O UTLINE Motivation of need for interpretability Explanation-Oriented Partitioning (EOP) Evaluation of EOP Summary
26 B ENEFITS OF EOP - A VOIDING N EEDLESS C OMPLEXITY - Typical XOR dataset
27 B ENEFITS OF EOP - A VOIDING N EEDLESS C OMPLEXITY - Typical XOR dataset CART • is accurate • takes many iterations • does not uncover or leverage structure of data
28 B ENEFITS OF EOP - A VOIDING N EEDLESS C OMPLEXITY - Typical XOR dataset EOP • equally accurate CART • uncovers structure • is accurate + o • takes many iterations • does not uncover or leverage structure of data Iteration 1 o + Iteration 2
29 C OMPARISON T O B OOSTING What is the price of understandability? Why boosting? It is an [arguably] good black-box classifier Learns an ensemble using any type of classifier Iteratively targets data misclassified earlier Criterion: Complexity of the resulting model = number of vector operations to make a prediction
30 C OMPARISON TO BOOSTING - S ETUP Problem: Binary classification 10D Gaussians/uniform cubes for each class Statistical significance: repeat experiment with several datasets and compute paired t-test p-values Results obtained through 5-fold cross validation
31 EOP VS A DA B OOST - SVM BASE CLASSIFIERS EOP is often less accurate, but not significantly the reduction of complexity is statistically significant 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0.85 0.9 0.95 1 0 100 200 300 Accuracy Complexity Boosting EOP (nonparametric) Accuracy p-value: 0.832 Complexity p-value: 0.003
32 EOP ( STUMPS AS BASE CLASSIFIERS ) VS CART D ATA FROM THE UCI REPOSITORY CART EOP N. BT EOP P. V MB BCW 0 0.2 0.4 0.6 0.8 1 0 1.2 10 20 30 40 Accuracy Complexity CART is Parametric the most EOP yields Dataset # of Features # of Points accurate the simplest Breast Tissue 10 1006 models Vowel 9 990 MiniBOONE 10 5000 Breast Cancer 10 596
33 E XPLAINING R EAL D ATA - S PAMBASE 1 st Iteration classier labels everything as spam high confidence regions do enclose mostly spam and Incidence of the word ‘your’ is low Length of text in capital letters is high
34 E XPLAINING R EAL D ATA - S PAMBASE 2 nd Iteration the threshold for the incidence of `your' is lowered the required incidence of capitals is increased the square region on the left also encloses examples that will be marked as `not spam'
35 E XPLAINING R EAL D ATA - S PAMBASE 3 rd Iteration Classifier marks everything as spam Frequency of ‘your’ and ‘hi’ determine the regions
36 S UMMARY EOP maintains classification accuracy but uses less complex models when compared to Boosting EOP with decision stumps finds less complex models than CART at the price of a small decrease in accuracy EOP gives interpretable high accuracy regions We are currently testing EOP in a range of practical application scenarios
37 T HANK Y OU
38 E XTRA R ESULTS
39 E XPLAINING REAL DATA - FUEL
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