Error asymmetry in causal and anticausal regression

By Patrick Blöbaum, Takashi Washio, Shohei Shimizu. 2016

13 citations recorded by the source corpus.

It is generally difficult to make any statements about the expected prediction error in an univariate setting without further knowledge about how the data were generated. Recent work showed that knowledge about the real underlying causal structure of a data generation process has implications for various machine learning settings. Assuming an additive noise and an independence between data generating mechanism and its input, we draw a novel connection between the intrinsic causal relationship of two variables and the expected prediction error. We formulate the theorem that the expected error of the true data generating function as prediction model is generally smaller when the effect is predicted from its cause and, on the contrary, greater when the cause is predicted from its effect. The theorem implies an asymmetry in the error depending on the prediction direction. This is further corroborated with empirical evaluations in artificial and real-world data sets.

Subfields: Artificial Intelligence, Statistics and Probability, Causal Inference & Discovery

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Citations in the corpus

Toward Causal Representation Learning (2021, background): “It also led to a range of follow-up work [32], [78], [97], [114], [115], [152], [153], [156], [167], [195], [204], [243], [263], [267], [277], [278], [281], complementing the studies of Bareinboim and Pearl [14], [185], and it inspired a thread of work in the statistics community exploiting…”
Causality for Machine Learning (2019, background): “The line of work provided rather fruitful (Zhang et al., 2013; Weichwald et al., 2014; Zhang et al., 2015; Gong et al., 2016; Huang et al., 2017; Blöbaum et al., 2016; Guo et al., 2018; Wang et al., 2019; Subbaswamy et al., 2018; Rabanser et al., 2018; Li et al., 2018a; Lipton et al., 2018; Li et al”
Detecting non-causal artifacts in multivariate linear regression models (2018, methodology): “…assumption Spirtes et al. (1993); Pearl (2000), researchers have also stated assumptions that admit causal inference when no conditional statistical independences hold, e.g., Kano and Shimizu (2003); Sun et al. (2006); Hoyer et al. (2009); Zhang and Hyvärinen (2009); Blöbaum et al. (2017).”
Cause-Effect Inference by Comparing Regression Errors (2018, background): “A preliminary version of this idea can be found in [20, 21] but in these works the analysis is based on a simple heuristic assuming that the regression of Y on X and the regression of X on Y yield functions that are inverse to each other, which holds approximately in the limit of small noise.”