Distinguishing Cause and Effect via Second Order Exponential Models

By Dominik Janzing, Xiaohai Sun, B. Schoelkopf. 2009

18 citations recorded by the source corpus.

We propose a method to infer causal structures containing both discrete and continuous variables. The idea is to select causal hypotheses for which the conditional density of every variable, given its causes, becomes smooth. We define a family of smooth densities and conditional densities by second order exponential models, i.e., by maximizing conditional entropy subject to first and second statistical moments. If some of the variables take only values in proper subsets of R^n, these conditionals can induce different families of joint distributions even for Markov-equivalent graphs. We consider the case of one binary and one real-valued variable where the method can distinguish between cause and effect. Using this example, we describe that sometimes a causal hypothesis must be rejected because P(effect|cause) and P(cause) share algorithmic information (which is untypical if they are chosen independently). This way, our method is in the same spirit as faithfulness-based causal inference because it also rejects non-generic mutual adjustments among DAG-parameters.

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Citations in the corpus

Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, background): “Some approaches, instead, define certain classes of “simple” conditionals, e.g., Additive Noise Models (Hoyer et al., 2009) and second-order exponential models (Sun et al., 2006; Janzing et al., 2009), and infer X to be the cause of Y whenever PY”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, background): “Some approaches, instead, define certain classes of “simple” conditionals, e.g., Additive Noise Models (Hoyer et al., 2009) and second-order exponential models (Sun et al., 2006; Janzing et al., 2009), and infer X to be the cause of Y whenever PY”
Identifying Cause and Effect on Discrete Data using Additive Noise Models (2010, methodology): “Sun et al. (2006); Janzing et al. (2009b) fit joint distributions of cause and effect with conditional densities whose logarithm is a second order polynomial (up to the log-partition function) and show that this often makes causal directions identifiable when some or all variables are discrete.”