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Identification of causal direction between a causal-effect pair from observed data has recently attracted much attention. Various methods based on functional causal models have been proposed to solve this problem, by assuming the causal process satisfies some (structural) constraints and showing that the reverse direction violates such constraints. The nonlinear additive noise model has been demonstrated to be effective for this purpose, but the model class is not transitive--even if each direct causal relation follows this model, indirect causal influences, which result from omitted intermediate causal variables and are frequently encountered in practice, do not necessarily follow the model constraints; as a consequence, the nonlinear additive noise model may fail to correctly discover causal direction. In this work, we propose a cascade nonlinear additive noise model to represent such causal influences--each direct causal relation follows the nonlinear additive noise model but we observe only the initial cause and final effect. We further propose a method to estimate the model, including the unmeasured intermediate variables, from data, under the variational auto-encoder framework. Our theoretical results show that with our model, causal direction is identifiable under suitable technical conditions on the data generation process. Simulation results illustrate the power of the proposed method in identifying indirect causal relations across various settings, and experimental results on real data suggest that the proposed model and method greatly extend the applicability of causal discovery based on functional causal models in nonlinear cases.
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Causal Discovery from Discrete Data using Hidden Compact Representation
Causal discovery from a set of observations is one of the fundamental problems across several disciplines. For continuous variables, recently a number of causal discovery methods have demonstrated their effectiveness in distinguishing the cause from effect by exploring certain properties of the conditional distribution, but causal discovery on categorical data still remains to be a challenging problem, because it is generally not easy to find a compact description of the causal mechanism for the true causal direction. In this paper we make an attempt to find a way to solve this problem by assuming a two-stage causal process: the first stage maps the cause to a hidden variable of a lower cardinality, and the second stage generates the effect from the hidden representation. In this way, the causal mechanism admits a simple yet compact representation. We show that under this model, the causal direction is identifiable under some weak conditions on the true causal mechanism. We also provide an effective solution to recover the above hidden compact representation within the likelihood framework. Empirical studies verify the effectiveness of the proposed approach on both synthetic and real-world data.
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- Award ID(s):
- 1829681
- PAR ID:
- 10125694
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- ISSN:
- 1049-5258
- Page Range / eLocation ID:
- 2666 - 2674
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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