Distinguishing the cause and effect from bivariate observational data is the foundational problem that finds applications in many scientific disciplines. One solution to this problem is assuming that cause and effect are generated from a structural causal model, enabling identification of the causal direction after estimating the model in each direction. The heteroscedastic noise model is a type of structural causal model where the cause can contribute to both the mean and variance of the noise. Current methods for estimating heteroscedastic noise models choose the Gaussian likelihood as the optimization objective which can be suboptimal and unstable when the data has a non-Gaussian distribution. To address this limitation, we propose a novel approach to estimating this model with Student's $t$-distribution, which is known for its robustness in accounting for sampling variability with smaller sample sizes and extreme values without significantly altering the overall distribution shape. This adaptability is beneficial for capturing the parameters of the noise distribution in heteroscedastic noise models. Our empirical evaluations demonstrate that our estimators are more robust and achieve better overall performance across synthetic and real benchmarks.

翻译：从双变量观测数据中区分因果关系是许多科学学科中的基础问题。解决该问题的一种方法是假设因果关系由结构因果模型生成，从而在估计每个方向的模型后识别因果方向。异方差噪声模型是一种结构因果模型，其中原因可同时影响噪声的均值和方差。当前估计异方差噪声模型的方法以高斯似然为优化目标，但该目标在数据分布非高斯时可能次优且不稳定。针对这一局限，我们提出基于学生t分布的新颖模型估计方法——该分布以鲁棒性著称，能在样本量较小或存在极端值时有效处理采样变异性，且不显著改变整体分布形态。这种适应性有助于捕捉异方差噪声模型中的噪声分布参数。实验表明，我们的估计器在合成与真实基准测试中均表现出更强的鲁棒性及更优的整体性能。