More Like this

1. Identification of Nonlinear Latent Hierarchical Models

   Kong Lingjing, Huang Biwei ( July 2023 , arXivorg)

   Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be highly challenging, especially when observed variables are generated by causally related latent variables and the relationships are nonlinear. In this work, we investigate the identification problem for nonlinear latent hierarchical causal models in which observed variables are generated by a set of causally related latent variables, and some latent variables may not have observed children. We show that the identifiability of both causal structure and latent variables can be achieved under mild assumptions: on causal structures, we allow for the existence of multiple paths between any pair of variables in the graph, which relaxes latent tree assumptions in prior work; on structural functions, we do not make parametric assumptions, thus permitting general nonlinearity and multi-dimensional continuous variables. Specifically, we first develop a basic identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. Leveraging this criterion, we show that both causal structures and latent variables of the hierarchical model can be identified asymptotically by explicitly constructing an estimation procedure. To the best of our knowledge, our work is the first to establish identifiability guarantees for both causal structures and latent variables in nonlinear latent hierarchical models. 

   more » « less
2. Triad Constraints for Learning Causal Structure of Latent Variables

   Ruichu Cai, Feng Xie ( December 2019 , Advances in neural information processing systems)

   Learning causal structure from observational data has attracted much attention,and it is notoriously challenging to find the underlying structure in the presenceof confounders (hidden direct common causes of two variables). In this paper,by properly leveraging the non-Gaussianity of the data, we propose to estimatethe structure over latent variables with the so-called Triad constraints: we design a form of "pseudo-residual" from three variables, and show that when causal relations are linear and noise terms are non-Gaussian, the causal direction between the latent variables for the three observed variables is identifiable by checking a certain kind of independence relationship. In other words, the Triad constraints help us to locate latent confounders and determine the causal direction between them. This goes far beyond the Tetrad constraints and reveals more information about the underlying structure from non-Gaussian data. Finally, based on the Triad constraints, we develop a two-step algorithm to learn the causal structure corresponding to measurement models. Experimental results on both synthetic and real data demonstrate the effectiveness and reliability of our method. 

   more » « less
3. A Computational Framework for Solving Nonlinear Binary Optimization Problems in Robust Causal Inference

   https://doi.org/10.1287/ijoc.2022.1226  

   Islam, Md Saiful ; Morshed, Md Sarowar ; Noor-E-Alam, Md. ( November 2022 , INFORMS Journal on Computing)

   Identifying cause-effect relations among variables is a key step in the decision-making process. Whereas causal inference requires randomized experiments, researchers and policy makers are increasingly using observational studies to test causal hypotheses due to the wide availability of data and the infeasibility of experiments. The matching method is the most used technique to make causal inference from observational data. However, the pair assignment process in one-to-one matching creates uncertainty in the inference because of different choices made by the experimenter. Recently, discrete optimization models have been proposed to tackle such uncertainty; however, they produce 0-1 nonlinear problems and lack scalability. In this work, we investigate this emerging data science problem and develop a unique computational framework to solve the robust causal inference test instances from observational data with continuous outcomes. In the proposed framework, we first reformulate the nonlinear binary optimization problems as feasibility problems. By leveraging the structure of the feasibility formulation, we develop greedy schemes that are efficient in solving robust test problems. In many cases, the proposed algorithms achieve a globally optimal solution. We perform experiments on real-world data sets to demonstrate the effectiveness of the proposed algorithms and compare our results with the state-of-the-art solver. Our experiments show that the proposed algorithms significantly outperform the exact method in terms of computation time while achieving the same conclusion for causal tests. Both numerical experiments and complexity analysis demonstrate that the proposed algorithms ensure the scalability required for harnessing the power of big data in the decision-making process. Finally, the proposed framework not only facilitates robust decision making through big-data causal inference, but it can also be utilized in developing efficient algorithms for other nonlinear optimization problems such as quadratic assignment problems. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: This work was supported by the Division of Civil, Mechanical and Manufacturing Innovation of the National Science Foundation [Grant 2047094]. Supplemental Material: The online supplements are available at https://doi.org/10.1287/ijoc.2022.1226 . 

   more » « less
4. Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models

   Biwei Huang, Kun Zhang ( January 2019 , Proceedings of the 36th International Conference on Machine Learning)

   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 the 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 time-varying 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. 

   more » « less
5. One-Class Order Embedding for Dependency Relation Prediction

   https://doi.org/10.1145/3331184.3331249  

   Chiang, Meng-Fen ; Lim, Ee-Peng ; Lee, Wang-Chien ; Ashok, Xavier Jayaraj ; Prasetyo, Philips Kokoh ( July 2019 , Proceedings of the 42nd International ACM SIGIR Conference on Research and Development in Information Retrieval)

   Learning the dependency relations among entities and the hierarchy formed by these relations by mapping entities into some order embedding space can effectively enable several important applications, including knowledge base completion and prerequisite relations prediction. Nevertheless, it is very challenging to learn a good order embedding due to the existence of partial ordering and missing relations in the observed data. Moreover, most application scenarios do not provide non-trivial negative dependency relation instances. We therefore propose a framework that performs dependency relation prediction by exploring both rich semantic and hierarchical structure information in the data. In particular, we propose several negative sampling strategies based on graph-specific centrality properties, which supplement the positive dependency relations with appropriate negative samples to effectively learn order embeddings. This research not only addresses the needs of automatically recovering missing dependency relations, but also unravels dependencies among entities using several real-world datasets, such as course dependency hierarchy involving course prerequisite relations, job hierarchy in organizations, and paper citation hierarchy. Extensive experiments are conducted on both synthetic and real-world datasets to demonstrate the prediction accuracy as well as to gain insights using the learned order embedding. 

   more » « less