- The paper introduces RegressGAN, a novel regression framework using conditional GANs to approximate the target variable's full conditional distribution instead of optimizing traditional loss functions.
- By employing adversarial training, RegressGAN effectively captures complex target distributions, particularly heavy-tailed or zero-inflated data, without requiring explicit specification of the likelihood function.
- Experiments demonstrate RegressGAN consistently outperforms traditional methods like FNN-MSE and GP on real-world datasets with challenging distributions, achieving significantly lower MAE.
The paper presents a novel regression framework that leverages conditional generative adversarial networks (CGANs) to perform regression tasks on tabular data. Instead of optimizing conventional loss functions such as mean squared error (MSE), the proposed approach—termed RegressGAN—aims to approximate the full conditional distribution of the target variable by training a generator and discriminator pair adversarially. This framework allows the model to bypass strict assumptions regarding the likelihood function, drawing an analogy to how generalized linear models (GLMs) extend linear regression through the use of link functions.
The method is motivated by the observation that traditional regression modeling often fails to capture complex distributional characteristics, especially in contexts where the response variable exhibits heavy-tailed or zero-inflated behavior. By optimizing against an adversarial loss, RegressGAN inherently minimizes a divergence (in particular, an approximation to the Jensen–Shannon divergence) between the generator’s output distribution and the empirical distribution of the target, conditioned on the inputs. This setup permits the neural network to adapt the likelihood function implicitly given sufficient data.
Key aspects of the methodology include:
- Adversarial Formulation: The generator predicts target values given covariates, while the discriminator is trained to distinguish between real (observed) and generated target values. This dual training mitigates overfitting by forcing the generator to capture the entire conditional distribution.
- Theoretical Justification: The approach leverages classical GAN theory to justify the optimization of distributional divergence measures without requiring an explicit specification of the likelihood function. This offers a flexible alternative to relying on preset closed-form loss functions.
- Heavy-Tailed Data Handling: Extensive experiments demonstrate that while traditional feed-forward networks trained with MSE and Gaussian process regression perform adequately on simulated “normal” data, RegressGAN exhibits considerable advantages on datasets with heavy-tailed and skewed distributions. The improvement is particularly pronounced on real-world datasets such as Car Insurance, Health Insurance, and E-commerce, where the target variables naturally possess properties such as zero-inflation.
In the experimental evaluation, several datasets were utilized:
- Synthetic Datasets: RegressGAN consistently matched or outperformed baseline methods, even in scenarios where the underlying distribution was Gaussian. This unexpected outcome is attributed to the generator’s necessity to learn the entire conditional distribution, rendering it inherently more resilient to overfitting.
- Real-World Datasets: In domains characterized by heavy-tailed responses, RegressGAN achieved markedly lower mean absolute error (MAE) when compared to both a feed-forward neural network with MSE (FNN-MSE) and Gaussian process regression (GP). For instance, in the Car Insurance dataset, MAE was reduced from 0.358 (FNN-MSE) and 0.420 (GP) to 0.261 for RegressGAN, underscoring the method’s capability to capture complex target distributions.
The paper also includes an ablation analysis pertaining to strategies commonly employed to accelerate convergence in image-based GAN training. The results indicate that many of these conventional training “tricks” are unnecessary when applying CGANs to tabular regression, thereby simplifying the deployment of RegressGAN in practice.
Overall, the paper provides a comprehensive treatment of employing GAN technology for regression, extending the flexibility and representational power of GLMs to deep neural networks. The empirical results emphasize that, especially in cases of heavy-tailed regression tasks, the RegressGAN framework not only achieves superior performance but also converges more reliably without extensive hyperparameter tuning—making it a compelling alternative for regression problems in industrial applications.