Session 5. A brief introduction to Predictive Modeling

Transcription

1 SOA Predictive Analytics Seminar Malaysia 27 Aug Kuala Lumpur, Malaysia Session 5 A brief introduction to Predictive Modeling Lichen Bao, Ph.D

2 A Brief Introduction to Predictive Modeling LICHEN BAO Data Scientist, RGA Reinsurance Company August 27, 2018

3 Agenda Overview of Predictive Modeling (PM) A Case Study PM for Actuaries

4 Overview of Predictive Modeling (PM)

5 What is Predictive Modeling? Modeling covers the statistics models and algorithms. Data High quality data Modeling Statistical model Prediction Business decisions 4

6 Review of Predictive Modeling Linear regression and OLS may sound familiar Linear regression model Y target/response variable; Xi explanatory/predictor variable βi parameters to be estimated ε error term/noise Underlying Assumptions for a Valid LM Normality, ε ~ N(0,σ 2 ) Linearity; Homogeneity-Y for population; Fixed X, error-free; Observation independence 5

7 Review of Predictive Modeling Linear regression and OLS may sound familiar Ordinary Least Squares(OLS) β = arg min RSS = arg min i ( y i y i ) 2 = arg min i ( j β j X ij y i ) 2 For a simple regression β 1 = ( x i y i 1 x n i y i ) ( x 2 i 1 ( x n i) 2 ), β 0 = y β 1 x Identical to Maximum likelihood estimator More robust and consistent approach β = arg max L(X, Y, β) = arg min ln(l X, Y, β ) = arg min i (y i y i (μ i )) 2 Use adj R 2 to compare fitness of models 1 = RSS + ESS TSS TSS Define R 2 = RSS TSS = 1 ESS portion that has been explained by OLS model portion of TSS for the error TSS = i(y i Y i ) 2 i (Y i Y) Adjusted R 2 = 1 ESS TSS n 1 n k = 1 (1 R2 ) n 1 n k 2, but it is biased if normal distribution 6

8 Review of Predictive Modeling We barely see any real application of OLS in life insurance because of the constraints. Features of OLS Applications in Insurance Validation of assumptions - Normal w/ constant σ 2 Binomial for rate (mortality/lapse/uw, etc.), σ 2 ~ r(1-r) Non-linear relationship, esp. for extrapolation Unmatched Poisson for claim count, ~ mean Unbounded data, nonnegative value Gamma for claim amount, ~ mean 2 7

9 Generalized Linear Model (GLM) GLM is extensively used in insurance industry. Major focus of PM in insurance industry Includes most distributions related to insurance Great flexibility in variance structure OLS model is a special case of GLM (Relatively) Easy to understand and communicate Multiplicative model intuitive & consistent with insurance practice 8

10 Generalized Linear Model (GLM) GLM is extensively used in insurance industry. Random component Systematic component Link function 9

11 Generalized Linear Model (GLM) GLM is extensively used in insurance industry. Random component Observations Y 1,..., Y n are independent w/ density from the exponential family f i y i ; θ i, = exp y iθ i b(θ i ) + c(y a i ( ) i, ) From maximum likelihood theory, E Y = μ = b θ, var Y = b θ a = a V(μ) Each distribution is specified in terms of mean & variance Variance is a function of mean Normal Poisson Binomial Gamma InverseGaussian Name N(μ, 2 ) P(μ) B(m, π) m G(μ, ) IG(μ, 2 ) Range (-,+ ) (0,+ ) (0,1) (0,+ ) (0,+ ) b(θ) 2 e ln(1+e ) ln θ ( 2θ) 1/2 μ(θ) θ e e /(1+e ) 1/ θ ( 2θ) 1/2 V(μ) 1 μ μ(1 μ) μ 2 μ 3 10

12 Generalized Linear Model (GLM) GLM is extensively used in insurance industry. Systematic component A linear predictor i = j x ij β j = Xβ for observation i link function i = g(μ i ), random & systematic are connected by a smooth & invertible function Identity Log Logit Reciprocal g(μ i ) x ln(x) x ln( 1 x ) 1/x g 1 ( i ) x e x e x 1/x Log is unique in insurance application s.t. all parameters are multiplicative y = exp( j x ij β j ) = j exp x ij β j = j exp β j x ij = j f j x ij Consistent with most insurance practices Intuitively easy to understand and communicate 1+e x 11

13 Generalized Linear Model (GLM) GLM is extensively used in insurance industry. Comparison with OLS Random Systematic Link OLS Normal only E y i = x ij β i = i j GLM Various distribution j g E(y i ) = i Inclusion of most distributions related to insurance data Normal, binomial, Poisson, Gamma, inverse-gaussian, Tweedie Link function Normal Poisson Bernoulli Negative Binomial Gamma Tweedie Inverse Gaussian Application sample General Application Claim frequency, counts Retention, cross-sell, underwriting rates Claim severity Claim severity Claim cost Claim severity 12

14 An Inventory of the Methods There are plenty of statistical modeling methods out there. Random Forest XG-boost machine Gradient Boosting Support vector machine Ada Boosting Ensemble method Survey Data Analysis Sentiment Analysis Genetic Algorithms Markov chain Monte Carlo Optimization Methods Bayesian Analysis Decision Trees Feature engineering Neural Networks / Deep learning Analysis of Variance Classification/Association Mixed Models Categorical Data Analysis Survival Analysis Multivariate Analysis Non-Parametric Analysis Cluster Analysis Text mining Machine Learning & Statistical Techniques

15 Predictive Modeling by Classes There are different terminologies regarding predictive modeling. Supervised vs. Unsupervised Learning Classification vs. Regression Parametric vs. Non- Parametric Supervised: estimate expected value of Y given values of X. GLM, Cox, CART, MARS, Random Forests, SVM, NN, etc. Unsupervised: find interesting patterns amongst X; no target variable Y Clustering, Correlation / Principal Components / Factor Analysis Classification: to segment observations into 2 or more categories. Fraud vs. legitimate, lapsed vs. retained, UW class Regression: to predict a continuous amount. Dollars of loss for a policy, ultimate size of claim Parametric Statistics: probabilistic model of data Poisson Regression(claims count), Gamma (claim amount) Non-Parametric Statistics: no probability model specified Classification trees, NN 14

16 Choosing the Right Method There is always the trade-off between interpretability and flexibility. Trade-Off Between Interpretability and Flexibility Decision Trees Interpretability GLM Models Logistic Regression Poisson Regression Often referred to as simple, transparent models Often referred to as machine learning, black-box models Random Forest Gradient Boosted Trees Flexibility This is just a sample of many algorithms available 15

17 Choosing the Right Method There is always the trade-off between interpretability and flexibility. Interpretability Transparent Algorithms More human intervention More interpretable Require less data Faster to estimate a model Good at handling smooth effects (e.g., age, income, etc.) The model we choose might not be a good match to reality, resulting in poor predictions. Less likely to overfit the data Flexibility Black-box Algorithms Less human intervention Less interpretable Require more data Slower to estimate a model Not good at handling smooth effects (e.g., age, income, etc.) Higher predictive accuracy because functional form is derived from the data, not assumed. More likely to overfit the data 16

18 Choosing the Right Method Choosing the right algorithm is a combination of statistical and business considerations. Business Considerations Experience Some business problems are well-defined and are historically modeled a specific way successfully. Example: Poisson Regression for Experience Studies Know your audience The successful business implementation of a model may require buy-in from many different groups throughout an organization. Model interpretability may be critical, particularly for analyzing experience study data. Technical Implementation Sometimes the increased accuracy in more complex models doesn t warrant the additional technical difficulties. Statistical Considerations Dependent Variable Knowing whether the dependent variable is available (or not), if available whether its continuous, binary, or a count helps us narrow down the appropriate algorithm. Amount of Data Powerful algorithms (e.g., random forest) require more data to work well. Model Validation Data Scientists build many models, and pick the champion model based on which model predicts new data the best (e.g., higher accuracy) 17

19 A Case Study

20 Predictive Modeling on Value Chain As long as there is data, there is potential to capitalize on it by predictive modeling. Pre-sale Underwriting In-force management Claims High Predictive underwriting Preferred risk selection Crosssell/upsell Fraud/nondisclosure Multivariate analysis New rating factors Medium Propensity to apply & triggers Distributor quality control Propensity to complete purchase Underwriting triage Determine underwriting ratings Proactive lapse management Low Competitive pricing strategy Customer lifetime value Claims triage Level of client demand

21 Process of Predictive Modeling Projects Set objective Process data Fit a model Interpret model & implement Monitor & Update What to achieve by PM Same as traditional one: understand business & data; clean & process data - Select proper model for target variable; choose explanatory variables; determine if crossterms are needed; assess model Understand model (e.g. A/E); extract business insights; implement in business process Monitor the performance and update when necessary - Validate the model 20

22 Multivariate Experience Study The client would like to conduct multivariate experience study for their CI products, where predictive model is built and tested to better understand risk and explore for additional business insights. Objectives Modeling & Lift Plot To use advanced statistical model to better understand risk over conventional method To identify true risk drivers and their effects To gain additional business insights 20 statistical significant variables in the built model Income, Occupation, Marital Status, BMI Data In traditional experience study format, covering o o 7 calendar years 10 products About 30 variables available for modeling o For ex. Policy Info, Demographic Info and Sales Person Info

23 Multivariate Experience Study The client would like to conduct multivariate experience study for their CI products, where predictive model are built and tested to better understand risk and explore for additional business insights. Pricing Benchmark the traditional pricing methods Could introduce new factors previously not in the pricing basis, such as BMI, etc. Product Redefinition Products of simpler underwriting process could be provided for customers with relatively lower risk selected by model Better use the data, and might ensure previously uninsurable, e.g., particularly to some disease

24 Predictive Modeling Considerations The success of a PM project needs considering many factors. Business Goals Objective to support the profitable growth of your business Resources available & strong support from senior executives Data Sufficient quantity & high quality of data to support modeling Satisfactory data depth & width Able & willing to obtain data, knowledge to understand & clean data Environment Local regulatory environment & privacy laws will allow such models Distribution channel can support data-driven analytic solution

25 PM for Actuaries

26 Predictive Modeling to Actuaries Actuaries are good candidates for predictive modeling practitioners. Advantages Opportunities Outlook Industry knowledge - domain knowledge is a key in modeling process Expertise in data process - data is always #1 issue in data-driven application Unique position in data analytics Solid foundation in statistics Education experience in modeling (OLS) Need to pick up new skills & thinking by education, training, and experience Data analytics is here to stay; it is changing insurance industry, and will fundamentally change how we run insurance business Actuaries could and should be on top of it and lead the change 25

27 Predictive Modeling to Actuaries Actuaries could master predictive modeling through different study activities. Refresh yourself with the basics of modeling Learn a modeling application / language & practice with examples Attend seminar, conference, training program, etc. Link your new skills with your job & practice if possible 26

28 Thank You.

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