Synthetic Dataset Generation of Driver Telematics
Abstract
:1. Background
1.1. Literature
1.2. Motivation
2. Related Work
2.1. Extended SMOTE
2.2. Feedforward Neural Network
3. The Synthetic Output: File Description
- Duration is the period that policyholder is insured in days, with values in [22, 366].
- Insured.age is the age of insured driver in integral years, with values in [16, 103].
- Car.age is the age of vehicle, with values in [−2, 20]. Negative values are rare but are possible as buying a newer model can be up to two years in advance.
- Years.noclaims is the number of years without any claims, with values in [0, 79] and always less than Insured.age.
- Territory refers to the territorial location code of vehicle, which has 55 labels in {11, 12, 13, …, 91}.
- Annual.pct.driven is the number of day a policyholder uses vehicle divided by 365, with values in [0, 1].
- Pct.drive.mon, ⋯, Pct.drive.sun are compositional variables meaning that the sum of seven (days of the week) variables is 100%.
- Pct.drive.wkday and Pct.drive.wkend are clearly compositional variables too.
- NB_Claim refers to the number of claims, with values in {0, 1, 2, 3}; 95.72% observations with zero claim, 4.06% with exactly one claim, and merely 0.20% with two claim and 0.01% with three claim. Real NB_Claim has the following proportions; zero claim: 95.60%, one claim: 4.19%, two claim: 0.20%, three claim: 0.007%.
- AMT_Claim is the aggregated amount of claims, with values in [0, 138766.5]. Table 3 shows summary statistics of synthetic and real data.
4. The Data Generating Process
4.1. The Detailed Simulation Procedures
4.1.1. Synthetic Portfolio Generation
- integer features are rounded up;
- for categorical features, only Car.use are multi-class. Car.use is converted by one-hot coding before applying extended SMOTE so that every categorical feature variable has the value 0 or 1. After the generation, they are rounded up; and,
- for compositional features, Pct.drive.sun and Pct.drive.wkend are not involved in the generation process, but are calculated by ‘1 − the rest of related features.’
4.1.2. The Simulation of Number of Claims
- Sub-simulation 1: . Corresponding instance index is. The data is given as the following:
- Sub-simulation 2: . Corresponding instance index is. The data is given as the following:
- Sub-simulation 3: . Corresponding instance index is. The data is given as the following:
4.1.3. The Simulation of Aggregated Amount of Claims
4.2. Comparison: Poisson and Gamma Regression
5. Concluding Remarks
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Graphical Display of Distributions of Selected Variables between Synthetic and Real Datasets
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Data Source | Reference | Sample | Period | Analytical Techniques | Research Synthesis |
---|---|---|---|---|---|
Belgium | Verbelen et al. (2018) | 10,406 drivers (33,259 obs.) | 2010–2014 | Poisson GAM, Negative binomial GAM | Shows that the presence of telematics variables are better important predictors of driving habits |
Canada | So et al. (2020) | 71,875 obs. | 2013–2016 | Adaboost, SAMME.C2 | Demonstrates telematics information improves the accuracy of claims frequency prediction with a new boosting algorithm |
China | Gao et al. (2019) | 1478 drivers | 2014.01–2017.06 | Poisson GAM | Shows the relevance of telematics covariates extracted from speed-acceleration heatmaps in a claim frequency model |
Europe | Baecke and Bocca (2017) | 6984 drivers (<age 30) | 2011–2015 | Logistic regression, Random forests, Neural networks | Illustrates the importance of telematics variables for pricing UBI products and shows that as few as three months of data may already be enough to obtain efficient risk estimates |
Greece | Guillen et al. (2020) | 157 drivers (1225 obs.) | 2016– 2017 | Negative binomial reg. | Demonstrates how the information drawn from telematics can help predict near-miss events |
Japan | Osafune et al. (2017) | 809 drivers | 2013.12–2015.02 | Support Vector Machines | Investigates accident risk indices that statistically separate safe and risky drivers |
Spain | Ayuso et al. (2014) | 15,940 drivers (<age 30) | 2009–2011 | Weibull regression | Compares driving behaviors of novice and experienced young drivers with PAYD policies |
Ayuso et al. (2016) | 8198 drivers (<age 30) | 2009–2011 | Weibull regression | Determines the use of gender becomes irrelevant in the presence of sufficient telematics information | |
Boucher et al. (2017) | 71,489 obs. | 2011 | Poisson GAM | Offers the benefits of using generalized additive models (GAM) to gain additional insights as to how premiums can be more dynamically assessed with telematics information | |
Guillen et al. (2019) | 25,014 drivers (<age 40) | 2011 | Zero-inflated Poisson | Investigates how telematics information helps explain part of the occurrence of zero accidents not typically accounted by traditional risk factors | |
Ayuso et al. (2019) | 25,014 drivers (<age 40) | 2011 | Poisson regression | Incorporates information drawn from telematics metrics into classical frequency model for tariff determination | |
Pérez-Marín et al. (2019) | 9614 drivers (<age 35) | 2010 | Quantile regression | Demonstrates that the use of quantile regression allows for better identification of factors associated with risky drivers | |
Pesantez-Narvaez et al. (2019) | 2767 drivers (<age 30) | 2011 | XGBoost | Examines and compares the performance of XGBoost algorithm against the traditional logistic regression |
Type | Variable | Description |
---|---|---|
Traditional | Duration | Duration of the insurance coverage of a given policy, in days |
Insured.age | Age of insured driver, in years | |
Insured.sex | Sex of insured driver (Male/Female) | |
Car.age | Age of vehicle, in years | |
Marital | Marital status (Single/Married) | |
Car.use | Use of vehicle: Private, Commute, Farmer, Commercial | |
Credit.score | Credit score of insured driver | |
Region | Type of region where driver lives: rural, urban | |
Annual.miles.drive | Annual miles expected to be driven declared by driver | |
Years.noclaims | Number of years without any claims | |
Territory | Territorial location of vehicle | |
Telematics | Annual.pct.driven | Annualized percentage of time on the road |
Total.miles.driven | Total distance driven in miles | |
Pct.drive.xxx | Percent of driving day xxx of the week: mon/tue/…/sun | |
Pct.drive.xhrs | Percent vehicle driven within x hrs: 2hrs/3hrs/4hrs | |
Pct.drive.xxx | Percent vehicle driven during xxx: wkday/wkend | |
Pct.drive.rushxx | Percent of driving during xx rush hours: am/pm | |
Avgdays.week | Mean number of days used per week | |
Accel.xxmiles | Number of sudden acceleration 6/8/9/…/14 mph/s per 1000 miles | |
Brake.xxmiles | Number of sudden brakes 6/8/9/…/14 mph/s per 1000 miles | |
Left.turn.intensityxx | Number of left turn per 1000 miles with intensity 08/09/10/11/12 | |
Right.turn.intensityxx | Number of right turn per 1000 miles with intensity 08/09/10/11/12 | |
Response | NB_Claim | Number of claims during observation |
AMT_Claim | Aggregated amount of claims during observation |
Synthetic | NB_Claim | Mean | Std Dev | Min | Q1 | Median | Q3 | Max |
---|---|---|---|---|---|---|---|---|
AMT_Claim | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 4062 | 6767 | 0 | 670 | 2191 | 4776 | 138,767 | |
2 | 8960 | 9554 | 0 | 2350 | 7034 | 11,225 | 56,780 | |
3 | 5437 | 2314 | 2896 | 3620 | 5372 | 5698 | 9743 | |
Real | NB_Claim | Mean | Std Dev | Min | Q1 | Median | Q3 | Max |
AMT_Claim | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 4646 | 8387 | 0 | 659 | 2238 | 5140 | 145,153 | |
2 | 8643 | 10,920 | 0 | 1739 | 5184 | 11,082 | 62,259 | |
3 | 5682 | 2079 | 3253 | 4540 | 5416 | 5773 | 9521 |
Category | Continuous/Integer | Percentage | Compositional |
---|---|---|---|
Marital | Duration | Annual.pct.driven | Pct.drive.mon |
Insured.sex | Insured.age | Pct.drive.xhrs | Pct.drive.tue |
Car.use | Car.age | Pct.drive.rushxx | . |
Region | Credit.score | . | |
Territory | Annual.miles.drive | Pct.drive.sun | |
NB_Claim | Years.noclaims | Pct.drive.wkday | |
Total.miles.driven | Pct.drive.wkend | ||
Avgdays.week | |||
Accel.xxmiles | |||
Brake.xxmiles | |||
Left.turn.intensityxx | |||
Right.turn.intensityxx | |||
AMT_Claim |
Architecture | N.Hidden L. | N.Nodes_First Hidden L. | N.Nodes_Rest Hidden L. | Activation | BatchSize | Learning R. |
---|---|---|---|---|---|---|
sub-sim1 | 3 | 353 | 68 | ReLU | 85 | 0.000667 |
sub-sim2 | 3 | 473 | 67 | ReLU | 18 | 0.001019 |
sub-sim3 | 2 | 60 | 60 | ReLU | 16 | 0.001922 |
Architecture | N.Hidden L. | N.Nodes_First Hidden L. | N.Nodes_Rest Hidden L. | Activation | BatchSize | Learning R. |
---|---|---|---|---|---|---|
6 | 344 | 67 | ReLU | 3 | 0.000526 |
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So, B.; Boucher, J.-P.; Valdez, E.A. Synthetic Dataset Generation of Driver Telematics. Risks 2021, 9, 58. https://doi.org/10.3390/risks9040058
So B, Boucher J-P, Valdez EA. Synthetic Dataset Generation of Driver Telematics. Risks. 2021; 9(4):58. https://doi.org/10.3390/risks9040058
Chicago/Turabian StyleSo, Banghee, Jean-Philippe Boucher, and Emiliano A. Valdez. 2021. "Synthetic Dataset Generation of Driver Telematics" Risks 9, no. 4: 58. https://doi.org/10.3390/risks9040058