用混合高斯耦合模型更准确建模驾驶场景参数联合概率。
Estimating the Joint Probability of Scenario Parameters with Gaussian Mixture Copula Models
- 结合高斯混合与耦合机制，分别建模参数分布与依赖关系。
- 在1800万条真实数据上，性能优于高斯耦合模型，接近高斯混合模型。
- 适合自动驾驶安全评估，尤其需要精准概率估计的场景验证。
本文首次将高斯混合耦合模型应用于自动驾驶系统安全验证中的驾驶场景统计建模。掌握场景参数的联合概率分布对基于场景的安全评估至关重要，风险量化依赖于具体参数组合的出现概率。高斯混合耦合模型融合了高斯混合模型的多模态表达能力与耦合模型的灵活性，可独立建模边缘分布与依赖结构。我们基于联合国第157号法规定义的两个场景的真实驾驶数据，对高斯混合耦合模型与先前方法（高斯混合模型、高斯耦合模型）进行对比。在约1800万实例上的评估表明，高斯混合耦合模型在对数似然和Sinkhorn距离指标上均持续优于高斯耦合模型，并与高斯混合模型表现相当，相对性能因场景而异。结果表明该模型有望成为未来基于场景验证框架的统计基础。
原文摘要 · Abstract (English)
This paper presents the first application of Gaussian Mixture Copula Models to the statistical modeling of driving scenarios for the safety validation of automated driving systems. Knowledge of the joint probability distribution of scenario parameters is essential for scenario-based safety assessment, where risk quantification depends on the likelihood of concrete parameter combinations. Gaussian Mixture Copula Models bring together the multimodal expressivity of Gaussian Mixture Models and the flexibility of copulas, enabling separate modeling of marginal distributions and dependence. We benchmark Gaussian Mixture Copula Models against previously proposed approaches - Gaussian Mixture Models and Gaussian Copula Models - using real-world driving data drawn from two scenarios defined in United Nations Regulation No. 157. Our evaluation on approximately 18 million instances of these two scenarios demonstrates that Gaussian Mixture Copula Models consistently surpass Gaussian Copula Models and perform competitively with Gaussian Mixture Models, as measured by both log-likelihood and Sinkhorn distance, with relative performance depending on the scenario. The results are promising for the adoption of Gaussian Mixture Copula Models as a statistical foundation for future scenario-based validation frameworks.
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