Primary Submission Category: Causal Discovery
Towards Causal Discovery with Statistical Guarantees
Authors: Shreya Prakash, Fan Xia, Elena Erosheva,
Presenting Author: Shreya Prakash*
Causal discovery methods aim to determine the causal direction between variables using data, such as whether sleep problems cause depression or vice versa. Causal discovery algorithms, like LiNGAM, use structural and distributional assumptions to estimate the causal direction. However, these algorithms often lack a way to measure uncertainty in their estimates or their finite-sample performance when assumptions are violated. We introduce the True Direction Detection Rate (TDDR) metric and a TDDR-based procedure to quantify uncertainty and assess the finite sample performance of causal discovery methods. The TDDR calculates the probability of accurately predicting the true causal direction as a function of sample size. We demonstrate the TDDR in a bivariate linear causal discovery setting and show its applicability to various causal discovery methods. These include methods based on independence measure comparisons like LiNGAM and those based on hypothesis testing like our proposed test-based method, which provides more statistical guarantees compared to the former. Through simulations, we validate asymptotic normality for the TDDR and demonstrate its use for causal discovery methods like LiNGAM and the test-based method when linearity and non-Gaussianity assumptions are violated. Our work provides insights into assessing the finite-sample performance and uncertainty of causal discovery methods, especially when assumptions are not met.