Identifying Cause and Effect on Discrete Data using Additive Noise Models

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Causal Inference by Stochastic Complexity (2017, methodology): “Altogether we can compute the multinomial stochastic complexity in O(n).”
Origo: causal inference by compression (2016, background): “[20] proposes an ANM for discrete numeric data.”
Telling Cause from Effect Using MDL-Based Local and Global Regression (2017, background): “There exist many approaches based on this framework that try to exploit linear [25] or non-linear functions [8] and can be applied to real valued [25], [8], [31], [20] as well as discrete data [19].”
Identiﬁability of Causal Graphs using Functional Models (background): “Hoyer et al. [2009], Peters et al. [2010] show a similar result for non-linear additive functions f ( x, n ) = g ( x ) + n , and Zhang and Hyv¨arinen [2009] for post-nonlinear models f ( x, n ) = h g ( x ) + n with invertible h .”
Discovering Cyclic Causal Models with Latent Variables: A General SAT-Based Procedure (2013, background): “…to this causal discovery problem have been suggested (Spirtes et al., 1999; Richardson and Spirtes, 1999; Schmidt and Murphy, 2009; Claassen and Heskes, 2010; Peters et al., 2010; Triantaﬁllou et al., 2010), building on the framework of causal Bayes networks (Spirtes et al., 1993; Pearl, 2000).”