Robust Estimation of Causal Heteroscedastic Noise Models
Quang-Duy Tran Bao Duong Phuoc Nguyen Thin Nguyen
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.