Synthetic data for ratemaking: imputation-based methods vs adversarial networks and autoencoders

This paper benchmarks Multivariate Imputation by Chained Equations (MICE) against deep generative models like Variational Autoencoders and Conditional Tabular GANs for synthetic ratemaking data, finding that MICE offers a simpler yet high-fidelity alternative that effectively preserves statistical distributions and supports robust Generalized Linear Model training.

The Gist

Imagine you are an insurance company trying to figure out how much to charge people for car insurance. To do this accurately, you need a massive amount of data: how old the drivers are, what cars they drive, where they live, and how often they crash.

But here's the problem: Real data is hard to get. It's expensive to collect, and companies are terrified of sharing it because of privacy laws and trade secrets. It's like trying to bake a perfect cake but being forbidden from tasting the original recipe or seeing the ingredients.

This paper is about a clever workaround: making up fake data that looks and acts exactly like the real thing. The authors call this "Synthetic Data."

The Big Question: How do we make the best fake data?

The researchers wanted to see which computer program is best at creating this "fake" insurance data. They compared two main types of "fake-data chefs":

1. The High-Tech Chefs (Deep Learning): These are fancy, complex AI models like GANs (Generative Adversarial Networks) and Autoencoders. Think of them as Michelin-star chefs who use molecular gastronomy. They are powerful but require a lot of skill, expensive equipment, and hours of tweaking to get right.
2. The Home Cooks (Imputation/MICE): These are simpler, statistical methods called MICE (Multivariate Imputation by Chained Equations). Think of them as a reliable, well-loved family recipe. They aren't flashy, but they are easy to use, robust, and often produce great results without needing a PhD in computer science.

The Experiment: The "FreMTPL2freq" Kitchen

The researchers took a real, open-source dataset of French car insurance policies (the "original recipe") and asked different computer programs to recreate it.

They tested the fake data in three ways:

• Does it look real? (Do the fake drivers have the same age distribution as real ones?)
• Does it act real? (If you run a standard insurance math model on the fake data, does it give the same answers as the real data?)
• Is it easy to use? (How much time and headache does it take to set up?)

The Results: The Surprise Winner

Here is what they found, translated into everyday terms:

1. The "Home Cook" (MICE) Won the Race
The simple, statistical method (MICE) turned out to be the champion. It created fake data that was almost indistinguishable from the real thing in terms of how insurance models performed.

• Why it won: It was incredibly easy to use. You could just plug it in and go ("out-of-the-box"). It didn't require complex coding or massive computing power.
• The Analogy: It's like using a high-quality, pre-made cake mix. You don't need to be a master baker to get a delicious cake that tastes just like the homemade version.

2. The "Michelin Chefs" (GANs/VAEs) Were Struggling
The fancy, high-tech AI models (like CTGAN and VAEs) did okay, but they had some issues:

• They were finicky: They required a lot of customization and tuning for every new dataset.
• They got confused: They sometimes struggled with variables that had many categories (like car brands), creating weird patterns that didn't match reality.
• The Analogy: These chefs tried to make a cake from scratch using molecular gastronomy. Sometimes it was amazing, but often it was dry, burnt, or took 10 hours to bake when a simple mix would have done the job in 30 minutes.

3. The "Mix-and-Match" Strategy Didn't Help
The researchers also tried "Data Augmentation"—mixing a little bit of fake data in with the real data to see if it made the insurance models smarter.

• The Result: It didn't really help. Adding fake data to real data didn't make the predictions more accurate. It was like adding a cup of fake flour to a bowl of real flour; it didn't make the cake rise any better.

The Big Takeaway

The paper concludes that you don't always need the most expensive, high-tech AI to solve a problem.

For insurance companies and researchers who need to generate fake data to test their models or share data safely, the simple, old-school statistical method (MICE) is often the best choice. It's reliable, easy to implement, and produces high-quality results without the headache of managing complex neural networks.

In short: If you need to bake a cake for a party, sometimes the best tool isn't the most expensive oven; it's the reliable, easy-to-use mixer that just works.

Technical Summary

Here is a detailed technical summary of the paper "Synthetic data for ratemaking: imputation-based methods vs adversarial networks and autoencoders."

1. Problem Statement

Actuarial ratemaking relies heavily on high-quality data to quantify risk and price insurance products accurately. However, access to such data is often restricted due to privacy concerns, security protocols, and competitive advantages, leading to a scarcity of open-access actuarial datasets. Furthermore, insurers entering new markets often lack sufficient historical data.

While synthetic data generation offers a solution to augment or replace real data, existing literature in actuarial science has predominantly focused on deep generative models like Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs). The authors identify two critical gaps in current research:

1. Usability: Deep generative models often require significant customization and fine-tuning for specific datasets, limiting their "out-of-the-box" applicability for practicing actuaries.
2. Data Augmentation Efficacy: Previous studies have not sufficiently investigated whether augmenting real data with synthetic data actually improves the predictive performance of Generalized Linear Models (GLMs), the industry standard for ratemaking.

The paper aims to benchmark Multivariate Imputation by Chained Equations (MICE)—a statistical method traditionally used for missing data—as a synthetic data generator against state-of-the-art deep learning models (CTGAN, VAE, WGAN) in the context of insurance ratemaking.

2. Methodology

Experimental Setup

• Dataset: The study utilizes the freMTPL2freq dataset (French Motor Third-Party Liability), a standard benchmark in actuarial science containing ~678,000 observations with 9 explanatory variables (5 categorical, 4 numerical), exposure, and claim counts.
• Ground Truth Simulation: To rigorously test if generators learn the underlying structural relationships, the authors simulate the response variable ($Y$) using known Poisson GLM formulas:
  • Linear Formula: A standard linear relationship between covariates and claim frequency.
  • Interaction Formula: A complex relationship including pairwise interactions between numerical and categorical variables.
• Evaluation Framework: The study evaluates 10 different generation approaches across two dimensions:
  1. Data Fidelity: How well the synthetic data preserves marginal distributions and multivariate relationships (measured via MAE/MAPE of proportions, correlation structures, and statistical tests).
  2. Model Utility: How well GLMs trained on synthetic (or augmented) data perform compared to those trained on real data. Metrics include:
     • Coefficient Distance ($M_1, M_2$): The deviation of estimated GLM coefficients from the "true" simulated coefficients.
     • Predictive Performance: Poisson deviance and RMSE on a held-out test set.
     • Variable Selection: Accuracy in identifying significant covariates.

Methods Compared

The study benchmarks three categories of methods:

1. Deep Generative Models:
   • CTGAN: Conditional Tabular GAN (standard and with Autoencoder preprocessing for categorical variables).
   • WGAN-GP: Wasserstein GAN with Gradient Penalty (based on Côté et al., 2025).
   • VAE: Variational Autoencoder (based on Jamotton and Hainaut, 2024).
2. Imputation-Based Methods (MICE):
   • MICE Partially Synthetic: Sets 75% of data to missing and imputes using Random Forests (RF) within MICE.
   • MICE Fully Synthetic: Iteratively sets remaining data to missing to generate 100% synthetic data.
   • MICE Tabulator: Inspired by Neves et al. (2022), using random cell masking and MICE-RF.
   • MICE VV: Column-wise imputation as per Volker and Vink (2021).
3. Hybrid Models:
   • CTGAN + MICE: CTGAN generates data, then MICE refines numerical variables.
   • CTGAN + AE + MICE: Combines Autoencoders for categorical encoding, CTGAN, and MICE for numerical refinement.

3. Key Contributions

1. Benchmarking MICE in Actuarial Science: The paper is the first to systematically evaluate MICE-based synthetic data generation against deep learning models specifically for ratemaking. It challenges the assumption that deep learning is always superior for tabular data.
2. Usability Analysis: Beyond statistical metrics, the authors provide a subjective but critical assessment of ease of use, highlighting that MICE-based methods (via the mice R-package) are significantly more accessible and require less preprocessing than deep learning alternatives.
3. Data Augmentation Findings: The study rigorously tests the hypothesis that "more data is better." It demonstrates that generic data augmentation (merging real and synthetic data) generally does not improve the predictive performance or coefficient accuracy of GLMs; in fact, it often degrades performance as the proportion of synthetic data increases.
4. Hybrid Approach Evaluation: The paper investigates whether combining deep learning with imputation (hybrid models) yields the best of both worlds, finding that while AEs help with high-cardinality categorical variables, they do not necessarily improve overall model utility.

4. Key Results

• Performance of MICE vs. Deep Learning:

  • MICE-based methods (specifically MICE Partially and Fully Synthetic) consistently outperformed deep generative models across most metrics. They achieved the lowest error in coefficient estimation ($M_1$ and $M_2$) and the best variable selection accuracy.
  • Deep Learning Models: CTGAN and VAE struggled with preserving the exact structural dependence of the data, leading to higher deviations in GLM coefficients. While CTGAN with Autoencoders improved the generation of high-cardinality categorical variables, it did not compensate for errors in other areas.
  • WGAN-GP: Performed the worst among the tested deep learning models in terms of data fidelity and model utility.

• Data Fidelity:

  • MICE methods preserved marginal distributions and pairwise correlations of numerical variables better than GANs.
  • GANs (specifically CTGAN) were better at maintaining the variance of specific high-cardinality categorical columns (e.g., vehicle density) but failed to capture the joint dependence structure as effectively as MICE.

• Data Augmentation Impact:

  • No Improvement: Augmenting real training data with synthetic data did not improve the GLM's ability to estimate true coefficients or predict claim counts.
  • Linear Degradation: As the proportion of synthetic data increased in the training set, the error in coefficient estimation ($M_1$ metric) increased linearly. The only exception was a minor, isolated case where a small proportion of synthetic data slightly improved results in the interaction scenario, but this was not a generalizable trend.

• Ease of Use:

  • MICE was ranked highest for usability due to its implementation in standard R packages, minimal need for hyperparameter tuning, and lack of complex data preprocessing requirements.
  • Deep Learning models required extensive preprocessing (e.g., one-hot encoding, scaling), complex architecture tuning, and longer training times (up to 10 hours vs. 3 hours for MICE).

5. Significance and Conclusion

The paper concludes that MICE-based methods are a highly competitive, and often superior, alternative to deep generative models for actuarial ratemaking data generation.

• Practical Implication: For actuaries seeking "out-of-the-box" solutions to generate synthetic data for research or privacy-preserving sharing, MICE with Random Forests is the recommended approach. It offers high fidelity in preserving statistical relationships with significantly lower implementation complexity.
• Caution on Augmentation: The study warns against the indiscriminate use of synthetic data augmentation. Simply merging synthetic data with real data does not automatically enhance model performance and may introduce bias if the synthetic data does not perfectly replicate the true underlying distribution.
• Future Directions: The authors suggest future research should focus on integrating business constraints (e.g., logical bounds on age or vehicle value) into the MICE framework and rigorously assessing the disclosure risk (re-identification potential) of these synthetic datasets.

In summary, this work re-evaluates the hierarchy of synthetic data generation in insurance, elevating established statistical imputation techniques above the hype of deep learning for specific tabular tasks where interpretability, ease of use, and coefficient stability are paramount.