Interactive Causal Structure Discovery

Multiple algorithms exist for the detection of causal relations from observational data but they are limited by their required assumptions regarding the data or by available computational resources. Only limited amount of information can be extracted from finite data but domain experts often have some knowledge of the underlying processes. We propose combining an expert’s prior knowledge with data likelihood to find models with high posterior probability. Our high-level procedure for interactive causal structure discovery contains three modules: discovery of initial models, navigation in the space of causal structures, and validation for model selection and evaluation. We present one manner of formulating the problem and implementing the approach assuming a rational, Bayesian expert which assumption we use to model the user in simulated experiments. The expert navigates greedily in the structure space using their prior information and the structures’ fit to data to find a local maximum a posteriori structure. Existing algorithms provide initial models for the navigation. Through simulated user experiments with synthetic data and use cases with real-world data, we find that the results of causal analysis can be improved by adding prior knowledge. Additionally, different initial models can lead to the expert finding different causal models and model validation helps detect overfitting and concept drift

Joint Learning of Label and Environment Causal Independence for Graph Out-of-Distribution Generalization

We tackle the problem of graph out-of-distribution (OOD) generalization. Existing graph OOD algorithms either rely on restricted assumptions or fail to exploit environment information in training data. In this work, we propose to simultaneously incorporate label and environment causal independence (LECI) to fully make use of label and environment information, thereby addressing the challenges faced by prior methods on identifying causal and invariant subgraphs. We further develop an adversarial training strategy to jointly optimize these two properties for casual subgraph discovery with theoretical guarantees. Extensive experiments and analysis show that LECI significantly outperforms prior methods on both synthetic and real-world datasets, establishing LECI as a practical and effective solution for graph OOD generalization

Technical note: Incorporating expert domain knowledge into causal structure discovery workflows

In this note, we argue that the outputs of causal discovery algorithms should not usually be considered end results but rather starting points and hypotheses for further study. The incentive to explore this topic came from a recent study by Krich et al. (2020), which gives a good introduction to estimating causal networks in biosphere–atmosphere interaction but confines the scope by investigating the outcome of a single algorithm. We aim to give a broader perspective to this study and to illustrate how not only different algorithms but also different initial states and prior information of possible causal model structures affect the outcome. We provide a proof-of-concept demonstration of how to incorporate expert domain knowledge with causal structure discovery and remark on how to detect and take into account over-fitting and concept drift.Peer reviewe

Simple low cost causal discovery using mutual information and domain knowledge

PhDThis thesis examines causal discovery within datasets, in particular observational datasets where normal experimental manipulation is not possible. A number of machine learning techniques are examined in relation to their use of knowledge and the insights they can provide regarding the situation under study. Their use of prior knowledge and the causal knowledge produced by the learners are examined. Current causal learning algorithms are discussed in terms of their strengths and limitations. The main contribution of the thesis is a new causal learner LUMIN that operates with a polynomial time complexity in both the number of variables and records examined. It makes no prior assumptions about the form of the relationships and is capable of making extensive use of available domain information. This learner is compared to a number of current learning algorithms and it is shown to be competitive with them

Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data

Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when the underlying graph involving the multivariate functions may have cycles. To enhance interpretability, our model involves a low-dimensional causal embedded space such that all the relevant causal information in the multivariate functional data is preserved in this lower-dimensional subspace. We prove that the proposed model is causally identifiable under standard assumptions that are often made in the causal discovery literature. To carry out inference of our model, we develop a fully Bayesian framework with suitable prior specifications and uncertainty quantification through posterior summaries. We illustrate the superior performance of our method over existing methods in terms of causal graph estimation through extensive simulation studies. We also demonstrate the proposed method using a brain EEG dataset.Comment: 36 pages, 2 figures, 7 table

Learning Large Causal Structures from Inverse Covariance Matrix via Matrix Decomposition

Learning causal structures from observational data is a fundamental yet highly complex problem when the number of variables is large. In this paper, we start from linear structural equation models (SEMs) and investigate ways of learning causal structures from the inverse covariance matrix. The proposed method, called $\mathcal{O}$-ICID (for {\it Independence-preserving} Decomposition from Oracle Inverse Covariance matrix), is based on continuous optimization of a type of matrix decomposition that preserves the nonzero patterns of the inverse covariance matrix. We show that $\mathcal{O}$-ICID provides an efficient way for identifying the true directed acyclic graph (DAG) under the knowledge of noise variances. With weaker prior information, the proposed method gives directed graph solutions that are useful for making more refined causal discovery. The proposed method enjoys a low complexity when the true DAG has bounded node degrees, as reflected by its time efficiency in experiments in comparison with state-of-the-art algorithms

Causally Invariant Predictor with Shift-Robustness

This paper proposes an invariant causal predictor that is robust to distribution shift across domains and maximally reserves the transferable invariant information. Based on a disentangled causal factorization, we formulate the distribution shift as soft interventions in the system, which covers a wide range of cases for distribution shift as we do not make prior specifications on the causal structure or the intervened variables. Instead of imposing regularizations to constrain the invariance of the predictor, we propose to predict by the intervened conditional expectation based on the do-operator and then prove that it is invariant across domains. More importantly, we prove that the proposed predictor is the robust predictor that minimizes the worst-case quadratic loss among the distributions of all domains. For empirical learning, we propose an intuitive and flexible estimating method based on data regeneration and present a local causal discovery procedure to guide the regeneration step. The key idea is to regenerate data such that the regenerated distribution is compatible with the intervened graph, which allows us to incorporate standard supervised learning methods with the regenerated data. Experimental results on both synthetic and real data demonstrate the efficacy of our predictor in improving the predictive accuracy and robustness across domains