Causal Discovery from Nonstationary/Heterogeneous Data: Skeleton Estimation and Orientation Determination

Local Causal Discovery in Multiple Manipulated Datasets

We consider the problem of distinguishing direct causes from direct effects of a target variable of interest from multiple manipulated datasets with unknown manipulated variables and nonidentical data distributions. Recent studies have shown that datasets attained from manipulated experiments (i.e., manipulated data) contain richer causal information than observational data for causal structure learning. Thus, in this article, we propose a new algorithm, which makes full use of the interventional properties of a causal model to discover the direct causes and direct effects of a target variable from multiple datasets with different manipulations. It is more suited to real-world cases and is also a challenge to be addressed in this article. First, we apply the backward framework to learn parents and children (PC) of a given target from multiple manipulated datasets. Second, we orient some edges connected to the target in advance through the assumption that the target variable is not manipulated and then orient the remaining undirected edges by finding invariant V-structures from multiple datasets. Third, we analyze the correctness of the proposed algorithm. To the best of our knowledge, the proposed algorithm is the first that can identify the local causal structure of a given target from multiple manipulated datasets with unknown manipulated variables. Experimental results on standard Bayesian networks validate the effectiveness of our algorithm.

A Survey on Brain Effective Connectivity Network Learning

Human brain effective connectivity characterizes the causal effects of neural activities among different brain regions. Studies of brain effective connectivity networks (ECNs) for different populations contribute significantly to the understanding of the pathological mechanism associated with neuropsychiatric diseases and facilitate finding new brain network imaging markers for the early diagnosis and evaluation for the treatment of cerebral diseases. A deeper understanding of brain ECNs also greatly promotes brain-inspired artificial intelligence (AI) research in the context of brain-like neural networks and machine learning. Thus, how to picture and grasp deeper features of brain ECNs from functional magnetic resonance imaging (fMRI) data is currently an important and active research area of the human brain connectome. In this survey, we first show some typical applications and analyze existing challenging problems in learning brain ECNs from fMRI data. Second, we give a taxonomy of ECN learning methods from the perspective of computational science and describe some representative methods in each category. Third, we summarize commonly used evaluation metrics and conduct a performance comparison of several typical algorithms both on simulated and real datasets. Finally, we present the prospects and references for researchers engaged in learning ECNs.

Model-Based Transfer Reinforcement Learning Based on Graphical Model Representations

Reinforcement learning (RL) plays an essential role in the field of artificial intelligence but suffers from data inefficiency and model-shift issues. One possible solution to deal with such issues is to exploit transfer learning. However, interpretability problems and negative transfer may occur without explainable models. In this article, we define Relation Transfer as explainable and transferable learning based on graphical model representations, inferring the skeleton and relations among variables in a causal view and generalizing to the target domain. The proposed algorithm consists of the following three steps. First, we leverage a suitable casual discovery method to identify the causal graph based on the augmented source domain data. After that, we make inferences on the target model based on the prior causal knowledge. Finally, offline RL training on the target model is utilized as prior knowledge to improve the policy training in the target domain. The proposed method can answer the question of what to transfer and realize zero-shot transfer across related domains in a principled way. To demonstrate the robustness of the proposed framework, we conduct experiments on four classical control problems as well as one simulation to the real-world application. Experimental results on both continuous and discrete cases demonstrate the efficacy of the proposed method.

Data Integration in Causal Inference

Integrating data from multiple heterogeneous sources has become increasingly popular to achieve a large sample size and diverse study population. This paper reviews development in causal inference methods that combines multiple datasets collected by potentially different designs from potentially heterogeneous populations. We summarize recent advances on combining randomized clinical trial with external information from observational studies or historical controls, combining samples when no single sample has all relevant variables with application to two-sample Mendelian randomization, distributed data setting under privacy concerns for comparative effectiveness and safety research using real-world data, Bayesian causal inference, and causal discovery methods.

Inferring Effective Connectivity Networks From fMRI Time Series With a Temporal Entropy-Score

Inferring brain-effective connectivity networks from neuroimaging data has become a very hot topic in neuroinformatics and bioinformatics. In recent years, the search methods based on Bayesian network score have been greatly developed and become an emerging method for inferring effective connectivity. However, the previous score functions ignore the temporal information from functional magnetic resonance imaging (fMRI) series data and may not be able to determine all orientations in some cases. In this article, we propose a novel score function for inferring effective connectivity from fMRI data based on the conditional entropy and transfer entropy (TE) between brain regions. The new score employs the TE to capture the temporal information and can effectively infer connection directions between brain regions. Experimental results on both simulated and real-world data demonstrate the efficacy of our proposed score function.

Causality in Cognitive Neuroscience: Concepts, Challenges, and Distributional Robustness

Whereas probabilistic models describe the dependence structure between observed variables, causal models go one step further: They predict, for example, how cognitive functions are affected by external interventions that perturb neuronal activity. In this review and perspective article, we introduce the concept of causality in the context of cognitive neuroscience and review existing methods for inferring causal relationships from data. Causal inference is an ambitious task that is particularly challenging in cognitive neuroscience. We discuss two difficulties in more detail: the scarcity of interventional data and the challenge of finding the right variables. We argue for distributional robustness as a guiding principle to tackle these problems. Robustness (or invariance) is a fundamental principle underlying causal methodology. A (correctly specified) causal model of a target variable generalizes across environments or subjects as long as these environments leave the causal mechanisms of the target intact. Consequently, if a candidate model does not generalize, then either it does not consist of the target variable's causes or the underlying variables do not represent the correct granularity of the problem. In this sense, assessing generalizability may be useful when defining relevant variables and can be used to partially compensate for the lack of interventional data.

Learning Markov Blankets From Multiple Interventional Data Sets

Learning Markov blankets (MBs) plays an important role in many machine learning tasks, such as causal Bayesian network structure learning, feature selection, and domain adaptation. Since variables included in the MB of a target variable of interest have causal relationships with the target, the MB can serve as the basis of learning the global structure of a causal Bayesian network or as a reliable and robust feature set for classification, both within the same domain or across domains. In this article, we study the problem of learning the MB of a target variable from multiple interventional data sets. Data sets attained from interventional experiments contain richer causal information than passively observed data (observational data) for MB discovery. However, almost all existing MB discovery methods are designed for learning MBs from a single observational data set. To learn MBs from multiple interventional data sets, we face two challenges: 1) unknown intervention variables and 2) nonidentical data distributions. To address these challenges, we theoretically analyze: 1) under what conditions we can find the correct MB of a target variable and 2) under what conditions we can identify the causes of the target variable via discovering its MB. Based on the theoretical analysis, we propose a new algorithm for learning MBs from multiple interventional data sets, and we present the conditions/assumptions that assure the correctness of the algorithm. To the best of our knowledge, this article is the first to present the theoretical analyses about the conditions for MB discovery in multiple interventional data sets and the algorithm to find the MBs in relation to the conditions. Using benchmark Bayesian networks and real-world data sets, the experiments have validated the effectiveness and efficiency of the proposed algorithm in this article.

Inferring causation from time series in Earth system sciences

The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers.

Review of Causal Discovery Methods Based on Graphical Models

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.

Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models

In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are particularly challenging in such nonstationary environments. In this paper, we study causal discovery and forecasting for nonstationary time series. By exploiting a particular type of state-space model to represent the processes, we show that nonstationarity helps to identify causal structure and that forecasting naturally benefits from learned causal knowledge. Specifically, we allow changes in both causal strengths and noise variances in the nonlinear state-space models, which, interestingly, renders both the causal structure and model parameters identifiable. Given the causal model, we treat forecasting as a problem in Bayesian inference in the causal model, which exploits the timevarying property of the data and adapts to new observations in a principled manner. Experimental results on synthetic and real-world data sets demonstrate the efficacy of the proposed methods.

Multi-domain Causal Structure Learning in Linear Systems

We study the problem of causal structure learning in linear systems from observational data given in multiple domains, across which the causal coefficients and/or the distribution of the exogenous noises may vary. The main tool used in our approach is the principle that in a causally sufficient system, the causal modules, as well as their included parameters, change independently across domains. We first introduce our approach for finding causal direction in a system comprising two variables and propose efficient methods for identifying causal direction. Then we generalize our methods to causal structure learning in networks of variables. Most of previous work in structure learning from multi-domain data assume that certain types of invariance are held in causal modules across domains. Our approach unifies the idea in those works and generalizes to the case that there is no such invariance across the domains. Our proposed methods are generally capable of identifying causal direction from fewer than ten domains. When the invariance property holds, two domains are generally sufficient.

Generalized Score Functions for Causal Discovery

Discovery of causal relationships from observational data is a fundamental problem. Roughly speaking, there are two types of methods for causal discovery, constraint-based ones and score-based ones. Score-based methods avoid the multiple testing problem and enjoy certain advantages compared to constraint-based ones. However, most of them need strong assumptions on the functional forms of causal mechanisms, as well as on data distributions, which limit their applicability. In practice the precise information of the underlying model class is usually unknown. If the above assumptions are violated, both spurious and missing edges may result. In this paper, we introduce generalized score functions for causal discovery based on the characterization of general (conditional) independence relationships between random variables, without assuming particular model classes. In particular, we exploit regression in RKHS to capture the dependence in a non-parametric way. The resulting causal discovery approach produces asymptotically correct results in rather general cases, which may have nonlinear causal mechanisms, a wide class of data distributions, mixed continuous and discrete data, and multidimensional variables. Experimental results on both synthetic and real-world data demonstrate the efficacy of our proposed approach.

Behind Distribution Shift: Mining Driving Forces of Changes and Causal Arrows

We address two important issues in causal discovery from nonstationary or heterogeneous data, where parameters associated with a causal structure may change over time or across data sets. First, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism. That is, given a causal mechanism that varies over time or across data sets and whose qualitative structure is known, we aim to extract from data a low-dimensional and interpretable representation of the main components of the changes. For this purpose we develop a novel kernel embedding of nonstationary conditional distributions that does not rely on sliding windows. Second, the embedding also leads to a measure of dependence between the changes of causal modules that can be used to determine the directions of many causal arrows. We demonstrate the power of our methods with experiments on both synthetic and real data.