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Introduction to CART Decision Tree Analysis for Data Mining and Predictive Modeling

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Matthew Magistrado
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Data Mining with Decision Trees: An Introduction to CART ® Dan Steinberg Mikhail Golovnya [email_address] http://www.salford-systems.com
In The Beginning… ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Years of Struggle ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Final Triumph ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
So What is CART? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Typical CART Solution ,[object Object],[object Object],[object Object],PATIENTS = 215 SURVIVE 178 82.8% DEAD 37 17.2% Is BP<=91? Terminal Node A SURVIVE 6 30.0% DEAD 14 70.0% NODE = DEAD Terminal Node B SURVIVE 102 98.1% DEAD 2 1.9% NODE = SURVIVE PATIENTS = 195 SURVIVE 172 88.2% DEAD 23 11.8% Is AGE<=62.5? Terminal Node C SURVIVE 14 50.0% DEAD 14 50.0% NODE = DEAD PATIENTS = 91 SURVIVE 70 76.9% DEAD 21 23.1% Is SINUS<=.5? Terminal Node D SURVIVE 56 88.9% DEAD 7 11.1% NODE = SURVIVE <= 91 > 91 <= 62.5 > 62.5 >.5 <=.5
How to Read It ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Decision Questions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Tree is a Classifier ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Importance of Binary Splits ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Accuracy of a Tree ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Prediction Success Table ,[object Object],[object Object],Classified As TRUE Class 1 Class 2 &quot;Survivors&quot; &quot;Early Deaths&quot; Total % Correct Class 1 &quot;Survivors&quot; 158 20 178 88% Class 2 &quot;Early Deaths&quot; 9 28 37 75% Total 167 48 215 86.51%
Tree Interpretation and Use ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Binary Recursive Partitioning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Three Major Stages ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
General Workflow Stage 1 Stage 2 Stage 3 Historical Data Learn Test Validate Build a Sequence of Nested Trees Monitor Performance Best Confirm Findings
Large Trees and Nearest Neighbor Classifier ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Derivation ,[object Object],[object Object],[object Object],[object Object],[object Object]
Illustration ,[object Object]
Impact on the Relative Error ,[object Object],[object Object]
Searching All Possible Splits ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Split Tables ,[object Object],[object Object],Sorted by Age Sorted by Blood Pressure
Categorical Predictors ,[object Object],[object Object],[object Object],[object Object],Left Right 1 A B, C, D 2 B A, C, B 3 C A, B, D 4 D A, B, C 5 A, B C, D 6 A, C B, D 7 A, D B, C
Binary Target Shortcut ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
GYM Model Example ,[object Object],[object Object],[object Object],[object Object],[object Object]
Variable Definitions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],predictors not used target
Initial Runs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Pruning Multiple Nodes ,[object Object],[object Object],[object Object]
Pruning Weaker Split First ,[object Object],[object Object]
Understanding Variable Importance ,[object Object],[object Object],[object Object],[object Object]
Competitors and Surrogates ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Utility of Surrogates ,[object Object],[object Object],[object Object],[object Object],[object Object]
Competitors and Surrogates Are Different ,[object Object],[object Object],[object Object],[object Object],A B C A B C Split X A B C A C B Split Y ,[object Object],[object Object],[object Object]
Calculating Association ,[object Object],[object Object],[object Object],[object Object],          Split X Split Y           Default           ,[object Object]
Notes on Association ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Calculating Variable Importance ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Mystery Solved ,[object Object],[object Object]
Penalizing Individual Variables ,[object Object],[object Object],[object Object]
Penalizing Missing and Categorical Predictors ,[object Object],[object Object],[object Object],[object Object]
Splitting Rules - Introduction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Priors Adjusted Probabilities ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
GINI Splitting Rule ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Illustration
GINI Properties ,[object Object],[object Object],[object Object]
Example ,[object Object],[object Object]
ENTROPY Splitting Rule ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example ,[object Object],[object Object]
TWOING Splitting Rule ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example ,[object Object],[object Object]
Best Possible Split ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example ,[object Object],A 40 B 30 C 20 D 10 A 40 B 30 C 20 D 10 GINI Best Split A 40 B 30 C 20 D 10 A 40 D 10 B 30 C 20 TWOING Best Split
Symmetric GINI ,[object Object],[object Object],[object Object],[object Object]
Ordered TWOING ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Class Probability Rule ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example
Favor Even Splits Control ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Fundamental Tree Building Mechanisms ,[object Object],[object Object],[object Object]
Key Players ,[object Object],DM Engine Analyst Model Dataset Priors  i Costs C i  j Population
Fraud Example ,[object Object],[object Object],[object Object],[object Object]
Fraud Example – PRIORS EQUAL (0.5, 0.5) ,[object Object],[object Object],[object Object],[object Object]
Fraud Example – PRIORS SPECIFY (0.9, 0.1) ,[object Object],[object Object],[object Object],[object Object]
Fraud Example – PRIORS DATA (0.98, 0.02) ,[object Object],[object Object],[object Object],[object Object]
Internal Class Assignment Rule ,[object Object],[object Object],[object Object],[object Object]
Putting It All Together ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Impact of Priors ,[object Object],[object Object],[object Object], r =0.1 ,  b =0.9  r =0.9 ,  b =0.1  r =0.5 ,  b =0.5
Model Evaluation ,[object Object],Evaluator Analyst Expected Cost Dataset Priors  i Costs C i  j Model PS Table Cells n i  j Population
Estimating Expected Cost ,[object Object],[object Object],[object Object],[object Object]
PRIORS DATA – Relative Cost ,[object Object],[object Object],[object Object],[object Object],[object Object]
PRIORS EQUAL – Relative Cost ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Using Equivalent Costs ,[object Object],[object Object]
Automated CART Runs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
More Batteries ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Battery MCT ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Battery MVI ,[object Object],[object Object],[object Object],[object Object],[object Object]
Battery PRIOR ,[object Object],[object Object],[object Object],[object Object],[object Object]
Battery SHAVING ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Battery SAMPLE ,[object Object],[object Object],[object Object]
Battery TARGET ,[object Object],[object Object],[object Object],[object Object]
Recommended Reading ,[object Object],[object Object],[object Object],[object Object]

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Introduction to CART Decision Tree Analysis for Data Mining and Predictive Modeling

  • 1. Data Mining with Decision Trees: An Introduction to CART ® Dan Steinberg Mikhail Golovnya [email_address] http://www.salford-systems.com
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  • 16. General Workflow Stage 1 Stage 2 Stage 3 Historical Data Learn Test Validate Build a Sequence of Nested Trees Monitor Performance Best Confirm Findings
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