Session 5 A brief introduction to Predictive Modeling Lichen Bao, - - PDF document
SOA Predictive Analytics Seminar Malaysia 27 Aug. 2018 | Kuala Lumpur, Malaysia Session 5 A brief introduction to Predictive Modeling Lichen Bao, Ph.D A Brief Introduction to Predictive Modeling LICHEN BAO Data Scientist, RGA Reinsurance
SOA Predictive Analytics Seminar – Malaysia
27 Aug. 2018 | Kuala Lumpur, Malaysia
Session 5 A brief introduction to Predictive Modeling
Lichen Bao, Ph.D
LICHEN BAO
Data Scientist, RGA Reinsurance Company
August 27, 2018
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Data
High quality data
Modeling
Statistical model
Prediction
Business decisions
Modeling
Statistical model
Modeling covers the statistics models and algorithms.
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Linear regression model
Underlying Assumptions for a Valid LM
Observation independence
Linear regression and OLS may sound familiar …
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Linear regression and OLS may sound familiar …
Ordinary Least Squares(OLS)
Identical to Maximum likelihood estimator
Use adj R2 to compare fitness of models
1 = 𝑆𝑇𝑇
𝑈𝑇𝑇 + 𝐹𝑇𝑇 𝑈𝑇𝑇
Define 𝑆2 = 𝑆𝑇𝑇
𝑈𝑇𝑇 = 1 − 𝐹𝑇𝑇 𝑈𝑇𝑇 = 𝑗(𝑍𝑗− 𝑍𝑗)2 𝑗(𝑍𝑗− 𝑍)2 , but it is biased
Adjusted 𝑆2 = 1 − 𝐹𝑇𝑇
𝑈𝑇𝑇 ∗ 𝑜−1 𝑜−𝑙 = 1 − (1−𝑆2)∗ 𝑜−1 𝑜−𝑙
β = 𝑏𝑠 min 𝑆𝑇𝑇 = 𝑏𝑠 min 𝑗( 𝑧𝑗 − 𝑧𝑗)2 = 𝑏𝑠 min 𝑗(𝑘𝛾𝑘𝑌𝑗𝑘 − 𝑧𝑗)2 β1 = (𝑦𝑗𝑧𝑗 − 1
𝑜𝑦𝑗𝑧𝑗) (𝑦𝑗
2 − 1
𝑜(𝑦𝑗)2),
β0 = 𝑧 − β1 𝑦 β = 𝑏𝑠 m𝑏𝑦 𝑀(𝑌, 𝑍, 𝛾) = 𝑏𝑠 min −ln(𝑀 𝑌, 𝑍, 𝛾 ) = 𝑏𝑠 min 𝑗(𝑧𝑗 − 𝑧𝑗(𝜈𝑗))2
if normal distribution
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We barely see any real application of OLS in life insurance because of the constraints.
Features of OLS
Validation of assumptions - Normal w/ constant σ2 Non-linear relationship,
Unbounded data, non- negative value
Applications in Insurance
Binomial for rate (mortality/lapse/UW, etc.), σ2 ~ r(1-r) Poisson for claim count, ~ mean Gamma for claim amount, ~ mean2
Unmatched
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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
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GLM is extensively used in insurance industry.
Random component Systematic component Link function
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Random component Observations Y1, . . . , Yn are independent w/ density from the exponential family From maximum likelihood theory, Each distribution is specified in terms of mean & variance Variance is a function of mean 𝑔
𝑗 𝑧𝑗; 𝜄𝑗, = 𝑓𝑦𝑞 𝑧𝑗𝜄𝑗 − 𝑐(𝜄𝑗)
𝑏𝑗() + 𝑑(𝑧𝑗, ) 𝐹 𝑍 = 𝜈 = 𝑐′ 𝜄 , 𝑤𝑏𝑠 𝑍 = 𝑐′′ 𝜄 𝑏 = 𝑏 𝑊(𝜈)
Norm
al Poiss
Bin inomial Gam amma InverseGauss ssian Name 𝑂(𝜈, 2) 𝑄(𝜈) 𝐶(𝑛, 𝜌) 𝑛 𝐻(𝜈, ) 𝐽𝐻(𝜈, 2) Range (-,+) (0,+) (0,1) (0,+) (0,+) b(𝜄) 2 e ln(1+e) − ln −𝜄 −(−2𝜄)1/2 𝜈(𝜄) 𝜄 e e/(1+e) − 1/ 𝜄 (−2𝜄)−1/2 𝑊(𝜈) 1 𝜈 𝜈(1 − 𝜈) 𝜈2 𝜈3
GLM is extensively used in insurance industry.
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Systematic component A linear predictor 𝑗 = 𝑘 𝑦𝑗𝑘𝛾𝑘 = 𝑌𝛾 for observation i link function 𝑗 = (𝜈𝑗), random & systematic are connected by a smooth & invertible function Log is unique in insurance application s.t. all parameters are multiplicative
𝑦𝑗𝑘 = 𝑘 𝑔 𝑘 𝑦𝑗𝑘
Ide dentity Log Log Log Logit Rec eciprocal (𝜈𝑗) 𝑦 ln(𝑦) ln( 𝑦 1 − 𝑦) 1/𝑦 −1(𝑗) 𝑦 𝑓𝑦
𝑓𝑦 1+𝑓𝑦
1/𝑦
GLM is extensively used in insurance industry.
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Inclusion of most distributions related to insurance data
GLM is extensively used in insurance industry.
Random Systematic Link OLS Normal only 𝑗 =
𝑘
𝑦𝑗𝑘𝛾𝑘 𝐹 𝑧𝑗 = 𝑗 GLM Various distribution 𝐹(𝑧𝑗) = 𝑗
Comparison with OLS
Link function Application sample Normal General Application Poisson Claim frequency, counts Bernoulli Retention, cross-sell, underwriting rates Negative Binomial Claim severity Gamma Claim severity Tweedie Claim cost Inverse Gaussian Claim severity
Machine Learning & Statistical Techniques Ensemble method Random Forest Gradient Boosting Survey Data Analysis Genetic Algorithms Markov chain Monte Carlo Optimization Methods Sentiment Analysis Support vector machine Neural Networks / Deep learning Ada Boosting XG-boost machine Feature engineering Classification/Association Bayesian Analysis Mixed Models Analysis of Variance Multivariate Analysis Categorical Data Analysis Cluster Analysis Survival Analysis Decision Trees Non-Parametric Analysis Text mining There are plenty of statistical modeling methods out there.
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There are different terminologies regarding predictive modeling.
Supervised vs. Unsupervised Learning
expected value of Y given values of X. GLM, Cox, CART, MARS, Random Forests, SVM, NN, etc.
interesting patterns amongst X; no target variable Y Clustering, Correlation / Principal Components / Factor Analysis Classification vs. Regression
segment observations into 2 or more
legitimate, lapsed vs. retained, UW class
a continuous amount. Dollars of loss for a policy, ultimate size of claim Parametric vs. Non- Parametric
probabilistic model of data Poisson Regression(claims count), Gamma (claim amount)
Statistics: no probability model specified Classification trees, NN
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There is always the trade-off between interpretability and flexibility.
GLM Models
Interpretability Flexibility
This is just a sample of many algorithms available
Trade-Off Between Interpretability and Flexibility
Random Forest Gradient Boosted Trees Decision Trees
Often referred to as simple, transparent models Often referred to as “machine learning”, black-box models
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There is always the trade-off between interpretability and flexibility.
Interpretability “Transparent” Algorithms Flexibility “Black-box” Algorithms More human intervention Less human intervention More interpretable Less interpretable Require less data Require more data Faster to estimate a model Slower to estimate a model Good at handling smooth effects (e.g., age, income, etc.) Not 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. Higher predictive accuracy because functional form is derived from the data, not assumed. Less likely to overfit the data More likely to overfit the data
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Choosing the right algorithm is a combination of statistical and business considerations.
Business Considerations
Some business problems are well-defined and are historically modeled a specific way successfully. Example: Poisson Regression for Experience Studies
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.
Sometimes the increased accuracy in more complex models doesn’t warrant the additional technical difficulties.
Statistical Considerations
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.
Powerful algorithms (e.g., random forest) require more data to work well.
Data Scientists build many models, and pick the champion model based on which model predicts new data the best (e.g., higher accuracy)
Level
demand
Hig igh Low Medium Pre-sale Und nderw rwri riti ting In In-force man anagement Cl Claims
New rating factors Multivariate analysis Cross- sell/upsell Fraud/non- disclosure Preferred risk selection Predictive underwriting Propensity to apply & triggers Distributor quality control Propensity to complete purchase Underwriting triage Determine underwriting ratings Proactive lapse management Claims triage Customer lifetime value Competitive pricing strategy
As long as there is data, there is potential to capitalize on it by predictive modeling.
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Set
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
model for target variable; choose explanatory variables; determine if cross- terms are needed; assess model
model Understand model (e.g. A/E); extract business insights; implement in business process Monitor the performance and update when necessary
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.
understand risk over conventional method
Objectives
Person Info
Data
Modeling & Lift Plot
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 basis, such as BMI, etc. Pricing
provided for customers with relatively lower risk selected by model
uninsurable, e.g., particularly to some disease Product Redefinition
Business Goals Data Environment
The success of a PM project needs considering many factors.
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Advantages
knowledge - domain knowledge is a key in modeling process
process - data is always #1 issue in data-driven application
data analytics Opportunities
statistics
experience in modeling (OLS)
new skills & thinking by education, training, and experience Outlook
here to stay; it is changing insurance industry, and will fundamentally change how we run insurance business
and should be on top of it and lead the change Actuaries are good candidates for predictive modeling practitioners.
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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