Journal of Data Science

Causal inference can estimate causal effects, but unless data are collected experimentally, statistical analyses must rely on pre-specified causal models. Causal discovery algorithms are empirical methods for constructing such causal models from data. Several asymptotically correct discovery methods already exist, but they generally struggle on smaller samples. Moreover, most methods focus on very sparse causal models, which may not always be a realistic representation of real-life data generating mechanisms. Finally, while causal relationships suggested by the methods often hold true, their claims about causal non-relatedness have high error rates. This non-conservative error trade off is not ideal for observational sciences, where the resulting model is directly used to inform causal inference: A causal model with many missing causal relations entails too strong assumptions and may lead to biased effect estimates. We propose a new causal discovery method that addresses these three shortcomings: Supervised learning discovery (SLdisco). SLdisco uses supervised machine learning to obtain a mapping from observational data to equivalence classes of causal models. We evaluate SLdisco in a large simulation study based on Gaussian data and we consider several choices of model size and sample size. We find that SLdisco is more conservative, only moderately less informative and less sensitive towards sample size than existing procedures. We furthermore provide a real epidemiological data application. We use random subsampling to investigate real data performance on small samples and again find that SLdisco is less sensitive towards sample size and hence seems to better utilize the information available in small datasets.

A graphical tool for choosing the number of nodes for a neural network is introduced. The idea is to fit the neural network with a range of numbers of nodes at first, and then generate a jump plot using a transformation of the mean square errors of the resulting residuals. A theorem is proven to show that the jump plot will select several candidate numbers of nodes among which one is the true number of nodes. Then a single node only test, which has been theoretically justified, is used to rule out erroneous candidates. The method has a sound theoretical background, yields good results on simulated datasets, and shows wide applicability to datasets from real research.