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

Yevhen Havrylenko, Meelis Käärik, Artur Tuttar

TL;DR

This paper assesses the ease of use of each generative approach and study the impact of generically augmenting original data with synthetic data on the performance of GLMs for predicting claim counts and highlights the potential of MICE-based methods in creating high-fidelity tabular data while offering lower implementation complexity compared to deep generative models.

Abstract

Actuarial ratemaking depends on high-quality data, yet access to such data is often limited by the cost of obtaining new data, privacy concerns, etc. In this paper, we explore synthetic-data generation as a potential solution to these issues. In addition to generative methods previously studied in the actuarial literature, we explore and benchmark another class of approaches based on Multivariate Imputation by Chained Equations (MICE). In a comparative study using an open-source dataset, MICE-based models are evaluated against other generative models like Variational Autoencoders and Conditional Tabular Generative Adversarial Networks. We assess how well synthetic data preserves the original marginal distributions of variables as well as the multivariate relationships among covariates. The consistency between Generalized Linear Models (GLMs) trained on synthetic data with GLMs trained on the original data is also investigated. Furthermore, we assess the ease of use of each generative approach and study the impact of generically augmenting original data with synthetic data on the performance of GLMs for predicting claim counts. Our results highlight the potential of MICE-based methods in creating high-fidelity tabular data while offering lower implementation complexity compared to deep generative models.

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

TL;DR

This paper assesses the ease of use of each generative approach and study the impact of generically augmenting original data with synthetic data on the performance of GLMs for predicting claim counts and highlights the potential of MICE-based methods in creating high-fidelity tabular data while offering lower implementation complexity compared to deep generative models.

Abstract

Actuarial ratemaking depends on high-quality data, yet access to such data is often limited by the cost of obtaining new data, privacy concerns, etc. In this paper, we explore synthetic-data generation as a potential solution to these issues. In addition to generative methods previously studied in the actuarial literature, we explore and benchmark another class of approaches based on Multivariate Imputation by Chained Equations (MICE). In a comparative study using an open-source dataset, MICE-based models are evaluated against other generative models like Variational Autoencoders and Conditional Tabular Generative Adversarial Networks. We assess how well synthetic data preserves the original marginal distributions of variables as well as the multivariate relationships among covariates. The consistency between Generalized Linear Models (GLMs) trained on synthetic data with GLMs trained on the original data is also investigated. Furthermore, we assess the ease of use of each generative approach and study the impact of generically augmenting original data with synthetic data on the performance of GLMs for predicting claim counts. Our results highlight the potential of MICE-based methods in creating high-fidelity tabular data while offering lower implementation complexity compared to deep generative models.

Paper Structure

This paper contains 12 sections, 15 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. General setup
  3. Methodology
  4. Multivariate imputation by chained equations
  5. Conditional Tabular GAN
  6. Autoencoders
  7. Case studies
  8. General setting and evaluation metrics
  9. Tested methods and formulas
  10. Case study results
  11. Conclusion
  12. Appendix A

Figures (2)

  • Figure 1: Schematic representation of MICE. $\bm{Y}^{(t - 1)}_{-j} := \left( Y^{(t)}_1,\dots,Y^{(t)}_{j - 1}, Y^{(t-1)}_{j+1}, \dots, Y^{(t-1)}_p \right)$, $Y^{(t)}_{j,mis}$ denotes the elements of the column corresponding to $Y^{(t)}_{j}$ that must be imputed $\Bigl($i.e., missing in the column corresponding to $Y^{(0)}_{j}\Bigr)$, $Y^{(t)}_{j,obs}$ denotes the elements in the respective column that were originally observed in $Y^{(0)}_{j}$, $f_j$ is an imputation model (e.g., a GLM, a random forest, etc.), $\bm{\theta}^{(t)}_j$ is the vector of parameters of $f_j$ in MICE iteration $t$.
  • Figure 2: $M_1$ metric results as a function of synthetic data proportion. "All synthetic" represents the cases where only synthetic data is used and are treated as "asymptotic" estimation of the shown relationship. The "All synthetic" metric values are scaled 1:2 (right side axis) compared to the other presented values (left side axis). The dotted lines represent the corresponding asymptotic trends.