This paper studies automated machine learning (AutoML) for causal discovery, the process of uncovering cause-and-effect relationships within data. Causal discovery is an unsupervised learning problem, as the target (the underlying ground truth causal model) is typically unknown. Therefore, the loss functions commonly used as an optimisation objective in AutoML systems developed for supervised learning problems are not applicable. We propose AutoCD, the first AutoML system utilising Bayesian optimisation based on a search space of causal discovery algorithms. In designing AutoCD, we study and compare the applicability of two different loss functions and post-hoc corrections. Additionally, based on the analysis of the performance of AutoCD, we propose an improved version called AutoCD(PC) by warm-starting the search from the PC algorithm. Results from our experiments on datasets simulated from 45 graphical models demonstrate that AutoCD PC performs better than the baselines by ranking the highest (avg. rank 3.69) compared to the best causal tuning baseline (avg. rank 5.21) and the best fine-tuned individual algorithm (avg. rank 4.36).
Many Bayesian Network structure learning algorithms are unstable in that the learnt graph is sensitive to arbitrary artefacts of the dataset, such as the ordering of columns (i.e., variable order). PC-Stable, developed by Colombo and Maathuis (2014), attempts to address this issue for the widely-used PC algorithm, prompting researchers to use the 'stable' version instead. However, this problem seems to have been overlooked for score-based algorithms. In this study, we show that some widely-used score-based algorithms suffer from the same issue and that PC-Stable, although less sensitive than most of the score-based algorithms tested, is not completely stable. We also present a solution to score-based greedy hill-climbing that completely eliminates this instability, and provide two implementations: the HC-Stable and Tabu-Stable algorithms, the latter of which learns more accurate graphs than all the well-known algorithms we compared it to.
A frequent goal in healthcare is to estimate personalized causal effects in order to select the best treatment for a patient from observational or experimental (RCT) data (or both), where "best" is defined in terms of maximizing the expectation of the desired outcome. The first task in estimating personalized effects is selecting the optimal set of personalization covariates (causal feature selection). This set of covariates is the Markov Boundary of the outcome in the experimental distribution, also known as the Interventional Markov Boundary (IMB), and can be identified from RCT data using methods for finding Markov Boundaries. However, most RCT data are very limited in sample size and do not work well with these methods. In this work, we develop methods that combine limited experimental and large observational data to identify the IMB, and improve the estimation of conditional (personalized) causal effects. These methods extend recent results (Triantafillou et al., 2021), which were limited to discrete data, to mixed data with binary and ordinal outcomes. The methods are based on Bayesian regression models. In simulated data, we show that our methods identify the correct IMB and improve causal effect estimation.
A common approach to learning Bayesian networks involves specifying an appropriately chosen family of parameterized probability density such as Gaussian. However, the distribution of most real-life data is leptokurtic and may not necessarily be best described by a Gaussian process. In this work we introduce Cauchy Graphical Models (CGM), a class of multivariate Cauchy densities that can be represented as directed acyclic graphs with arbitrary network topologies, the edges of which encode linear dependencies between random variables. We develop CGLearn, the resultant algorithm for learning the structure and Cauchy parameters based on Minimum Dispersion Criterion (MDC). Experiments using simulated datasets on benchmark network topologies demonstrate the efficacy of our approach when compared to Gaussian Graphical Models (GGM).
