A fundamental task in various disciplines of science, including biology, is to find underlying causal relations and make use of them. Causal relations can be seen if interventions are properly applied; however, in many cases they are difficult or even impossible to conduct. It is then necessary to discover causal relations by analyzing statistical properties of purely observational data, which is known as causal discovery or causal structure search. This paper aims to give a introduction to and a brief review of the computational methods for causal discovery that were developed in the past three decades, including constraint-based and score-based methods and those based on functional causal models, supplemented by some illustrations and applications.

This paper aims to give a broad coverage of central concepts and principles involved in automated causal inference and emerging approaches to causal discovery from i.i.d data and from time series. After reviewing concepts including manipulations, causal models, sample predictive modeling, causal predictive modeling, and structural equation models, we present the constraint-based approach to causal discovery, which relies on the conditional independence relationships in the data, and discuss the assumptions underlying its validity. We then focus on causal discovery based on structural equations models, in which a key issue is the identifiability of the causal structure implied by appropriately defined structural equation models: in the two-variable case, under what conditions (and why) is the causal direction between the two variables identifiable? We show that the independence between the error term and causes, together with appropriate structural constraints on the structural equation, makes it possible. Next, we report some recent advances in causal discovery from time series. Assuming that the causal relations are linear with nonGaussian noise, we mention two problems which are traditionally difficult to solve, namely causal discovery from subsampled data and that in the presence of confounding time series. Finally, we list a number of open questions in the field of causal discovery and inference.

Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting, but many investigators cannot use KCIT with large datasets because the test scales at least quadratically with sample size. We therefore devise two relaxations called the Randomized Conditional Independence Test (RCIT) and the Randomized conditional Correlation Test (RCoT) which both approximate KCIT by utilizing random Fourier features. In practice, both of the proposed tests scale linearly with sample size and return accurate p-values much faster than KCIT in the large sample size context. CCD algorithms run with RCIT or RCoT also return graphs at least as accurate as the same algorithms run with KCIT but with large reductions in run time.

Causality is a fundamental notion in science, and plays an important role in explanation, prediction, decision making and control. Recently, with the rapid accumulation of huge volumes of data, it is even more desirable to abstract causal knowledge from data. Furthermore, such data are usually time series measured over a relatively long time period or aggregated data from multiple data sets collected in different environments or under different experimental conditions, leading to the issue of data heterogeneity. Causality also provides a way to understand and tackle data heterogeneity, while traditional machine learning typically assumes that the given data follow a fixed distribution.

Recent years have witnessed tremendous interest in deep learning on graph-structured data. Due to the high cost of collecting labeled graph-structured data, domain adaptation is important to supervised graph learning tasks with limited samples. However, current graph domain adaptation methods are generally adopted from traditional domain adaptation tasks, and the properties of graph-structured data are not well utilized. For example, the observed social networks on different platforms are controlled not only by the different crowds or communities but also by domain-specific policies and background noise. Based on these properties in graph-structured data, we first assume that the graph-structured data generation process is controlled by three independent types of latent variables, i.e., the semantic latent variables, the domain latent variables, and the random latent variables. Based on this assumption, we propose a disentanglement-based unsupervised domain adaptation method for the graph-structured data, which applies variational graph auto-encoders to recover these latent variables and disentangles them via three supervised learning modules. Extensive experimental results on two real-world datasets in the graph classification task reveal that our method not only significantly outperforms the traditional domain adaptation methods and the disentangled-based domain adaptation methods but also outperforms the state-of-the-art graph domain adaptation algorithms. The code is available at https://github.com/rynewu224/GraphDA .

We review and reflect on fairness notions proposed in machine learning literature and make an attempt to draw connections to arguments in moral and political philosophy, especially theories of justice. We survey dynamic fairness inquiries and further consider the long-term impact induced by current prediction and decision. We present a flowchart that encompasses implicit assumptions and expected outcomes of different fairness inquiries on the data-generating process, the predicted outcome, and the induced impact, respectively. We demonstrate the importance of matching the mission (what kind of fairness to enforce) and the means (which appropriate fairness spectrum to analyze) to fulfill the intended purpose.