On the identifiability of the post-nonlinear causal model

ABSTRACT

By taking into account the nonlinear effect of the cause, the inner noise effect, and the measurement distortion effect in the observed variables, the post-nonlinear (PNL) causal model has demonstrated its excellent performance in distinguishing the cause from effect. However, its identifiability has not been properly addressed, and how to apply it in the case of more than two variables is also a problem. In this paper, we conduct a systematic investigation on its identifiability in the two-variable case. We show that this model is identifiable in most cases; by enumerating all possible situations in which the model is not identifiable, we provide sufficient conditions for its identifiability. Simulations are given to support the theoretical results. Moreover, in the case of more than two variables, we show that the whole causal structure can be found by applying the PNL causal model to each structure in the Markov equivalent class and testing if the disturbance is independent of the direct causes for each variable. In this way the exhaustive search over all possible causal structures is avoided.

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Index Terms

• Computing methodologies

  • Artificial intelligence

    • Knowledge representation and reasoning

      • Probabilistic reasoning

      • Vagueness and fuzzy logic

  • Modeling and simulation

    • Model development and analysis

      • Modeling methodologies

• Mathematics of computing

  • Probability and statistics

    • Probabilistic algorithms

    • Probabilistic reasoning algorithms

      • Markov-chain Monte Carlo methods

      • Sequential Monte Carlo methods

    • Probabilistic representations

      • Markov networks

    • Stochastic processes

      • Markov processes

• Theory of computation

  • Theory and algorithms for application domains

    • Machine learning theory

      • Markov decision processes