Data Mining – Best Practices Part #2 Richard Derrig, PhD, Opal Consulting LLC CAS Spring Meeting June 16-18, 2008

Data Mining  Data Mining, also known as Knowledge- Discovery in Databases (KDD), is the process of automatically searching large volumes of data for patterns. In order to achieve this, data mining uses computational techniques from statistics, machine learning and pattern recognition. 

AGENDA  Predictive v Explanatory Models  Discussion of Methods  Example: Explanatory Models for Decision to Investigate Claims  The “Importance” of Explanatory and Predictive Variables  An Eight Step Program for Building a Successful Model

Predictive v Explanatory Models  Both are of the form: Target or Dependent Variable is a Function of Feature or Independent Variables that are related to the Target Variable  Explanatory Models assume all Variables are Contemporaneous and Known  Predictive Models assume all Variables are Contemporaneous and Estimable

Desirable Properties of a Data Mining Method:  Any nonlinear relationship between target and features can be approximated  A method that works when the form of the nonlinearity is unknown  The effect of interactions can be easily determined and incorporated into the model  The method generalizes well on out-of sample data

Major Kinds of Data Mining Methods  Supervised learning  Most common situation  Target variable  Frequency  Loss ratio  Fraud/no fraud  Some methods  Regression  Decision Trees  Some neural networks  Unsupervised learning  No Target variable  Group like records together-Clustering  A group of claims with similar characteristics might be more likely to be of similar risk of loss  Ex: Territory assignment,  Some methods  PRIDIT  K-means clustering  Kohonen neural networks

The Supervised Methods and Software Evaluated 1) TREENET7) Iminer Ensemble 2) Iminer Tree8) MARS 3) SPLUS Tree9) Random Forest 4) CART10) Exhaustive Chaid 5) S-PLUS Neural11) Naïve Bayes (Baseline) 6) Iminer Neural 12) Logistic reg ( (Baseline)

Decision Trees  In decision theory (for example risk management), a decision tree is a graph of decisions and their possible consequences, (including resource costs and risks) used to create a plan to reach a goal. Decision trees are constructed in order to help with making decisions. A decision tree is a special form of tree structure. 

CART – Example of 1 st split on Provider 2 Bill, With Paid as Dependent  For the entire database, total squared deviation of paid losses around the predicted value (i.e., the mean) is 4.95x1013. The SSE declines to 4.66x10 13 after the data are partitioned using $5,021 as the cutpoint.  Any other partition of the provider bill produces a larger SSE than 4.66x For instance, if a cutpoint of $10,000 is selected, the SSE is 4.76*10 13.

Different Kinds of Decision Trees  Single Trees (CART, CHAID)  Ensemble Trees, a more recent development (TREENET, RANDOM FOREST)  A composite or weighted average of many trees (perhaps 100 or more)  There are many methods to fit the trees and prevent overfitting  Boosting: Iminer Ensemble and Treenet  Bagging: Random Forest

Neural Networks =

 Self-Organizing Feature Maps  T. Kohonen (Cybernetics)  Reference vectors of features map to OUTPUT format in topologically faithful way. Example: Map onto 40x40 2- dimensional square.  Iterative Process Adjusts All Reference Vectors in a “Neighborhood” of the Nearest One. Neighborhood Size Shrinks over Iterations NEURAL NETWORKS

FEATURE MAP SUSPICION LEVELS

FEATURE MAP SIMILIARITY OF A CLAIM

DATA MODELING EXAMPLE: CLUSTERING  Data on 16,000 Medicaid providers analyzed by unsupervised neural net  Neural network clustered Medicaid providers based on 100+ features  Investigators validated a small set of known fraudulent providers  Visualization tool displays clustering, showing known fraud and abuse  Subset of 100 providers with similar patterns investigated: Hit rate > 70% Cube size proportional to annual Medicaid revenues © 1999 Intelligent Technologies Corporation

Multiple Adaptive Regression Splines (MARS)  MARS fits a piecewise linear regression  BF1 = max(0, X – 1,401.00)  BF2 = max(0, 1, X )  BF3 = max(0, X )  Y = E-03 * BF E-03 * BF E-03 * BF3; BF1 is basis function  BF1, BF2, BF3 are basis functions  MARS uses statistical optimization to find best basis function(s)  Basis function similar to dummy variable in regression. Like a combination of a dummy indicator and a linear independent variable

Baseline Methods: Naive Bayes Classifier Logistic Regression  Naive Bayes assumes feature (predictor) variables) independence conditional on each category  Logistic Regression assumes target is linear in the logs of the feature (predictor) variables

REAL CLAIM FRAUD DETECTION PROBLEM  Classify all claims  Identify valid classes  Pay the claim  No hassle  Visa Example  Identify (possible) fraud  Investigation needed  Identify “gray” classes  Minimize with “learning” algorithms

The Fraud Surrogates used as Target Decision Variables  Independent Medical Exam (IME) requested  Special Investigation Unit (SIU) referral  IME successful  SIU successful  DATA: Detailed Auto Injury Closed Claim Database for Massachusetts  Accident Years ( )

DM Databases Scoring Functions Graded Output Non-Suspicious Claims Routine Claims Suspicious Claims Complicated Claims

ROC Curve Area Under the ROC Curve  Want good performance both on sensitivity and specificity  Sensitivity and specificity depend on cut points chosen for binary target (yes/no)  Choose a series of different cut points, and compute sensitivity and specificity for each of them  Graph results  Plot sensitivity vs 1-specifity  Compute an overall measure of “lift”, or area under the curve

True/False Positives and True/False Negatives: The “Confusion” Matrix  Choose a “cut point” in the model score.  Claims > cut point, classify “yes”.

TREENET ROC Curve – IME AUROC = 0.701

Logistic ROC Curve – IME AUROC = 0.643

Ranking of Methods/Software – IME Requested

Variable Importance (IME) Based on Average of Methods

Results for IME Requested

Ranking of Methods/Software – 1 st Two Surrogates

Ranking of Methods/Software – Last Two Surrogates

Plot of AUROC for SIU vs. IME Decision

Plot of AUROC for SIU vs IME Favorable

Claim Fraud Detection Plan  STEP 1:SAMPLE: Systematic benchmark of a random sample of claims.  STEP 2:FEATURES: Isolate red flags and other sorting characteristics  STEP 3:FEATURE SELECTION: Separate features into objective and subjective, early, middle and late arriving, acquisition cost levels, and other practical considerations.  STEP 4:CLUSTER: Apply unsupervised algorithms (Kohonen, PRIDIT, Fuzzy) to cluster claims, examine for needed homogeneity.

Claim Fraud Detection Plan  STEP 5:ASSESSMENT: Externally classify claims according to objectives for sorting.  STEP 6:MODEL: Supervised models relating selected features to objectives (logistic regression, Naïve Bayes, Neural Networks, CART, MARS)  STEP7:STATIC TESTING: Model output versus expert assessment, model output versus cluster homogeneity (PRIDIT scores) on one or more samples.  STEP 8:DYNAMIC TESTING: Real time operation of acceptable model, record outcomes, repeat steps 1-7 as needed to fine tune model and parameters. Use PRIDIT to show gain or loss of feature power and changing data patterns, tune investigative proportions to optimize detection and deterrence of fraud and abuse.