Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discovery
Conditional independence (CI) testing is frequently used in data analysis and machine learning for various scientific fields and it forms the basis of constraint-based causal discovery. Oftentimes, CI testing relies on strong, rather unrealistic assumptions. One of these assumptions is homoskedasticity, in other words, a constant conditional variance is assumed. We frame heteroskedasticity in a structural causal model framework and present an adaptation of the partial correlation CI test that works well in the presence of heteroskedastic noise, given that expert knowledge about the heteroskedastic relationships is available. Further, we provide theoretical consistency results for the proposed CI test which carry over to causal discovery under certain assumptions. Numerical causal discovery experiments demonstrate that the adapted partial correlation CI test outperforms the standard test in the presence of heteroskedasticity and is on par for the homoskedastic case. Finally, we discuss the general challenges and limits as to how expert knowledge about heteroskedasticity can be accounted for in causal discovery.
Code (0)
등록된 구현이 없습니다.
Tasks
Causal DiscoverySimilar Papers 제목 키워드 기반
Recurrent Conditional Heteroskedasticity
We propose a new class of financial volatility models, called the REcurrent Conditional Heteroskedastic (RECH) models, to improve both in-sample analysis and out-ofsample forecasting of the traditional conditional hetero…
Testing for Threshold Effects in Presence of Heteroskedasticity and Measurement Error with an application to Italian Strikes
Many macroeconomic time series are characterised by nonlinearity both in the conditional mean and in the conditional variance and, in practice, it is important to investigate separately these two aspects. Here we address…
Time SeriesConditional Independence Test Based on Transport Maps
Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional s…
Kernel-based Conditional Independence Test and Application in Causal Discovery
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is …
Causal DiscoveryConditional Local Independence Testing with Application to Dynamic Causal Discovery
In this note, we extend the conditional local independence testing theory developed in Christgau et al. (2024) to Ito processes. The result can be applied to causal discovery in dynamic systems.
Causal Discovery