Inferring deterministic causal relations

By Povilas Daniusis, Dominik Janzing, Joris M. Mooij, Jakob Zscheischler, Bastian Steudel, Kun Zhang, Bernhard Schölkopf. 2010

202 citations recorded by the source corpus.

We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the deterministic (noise-free) case, there are asymmetries that can be exploited for causal inference. Our method is based on the idea that if the function and the probability density of the cause are chosen independently, then the distribution of the effect will, in a certain sense, depend on the function. We provide a theoretical analysis of this method, showing that it also works in the low noise regime, and link it to information geometry. We report strong empirical results on various real-world data sets from different domains.

Subfields: Artificial Intelligence, Causal Inference & Discovery, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Causal Inference & Discovery

In Signal Processing

Citations in the corpus

Toward Causal Representation Learning (2021, methodology): “To see this, we refer to Daniušis et al. [50] who deﬁne a measure of dependence between input P ( X ) and conditional P ( Y | X ) .”
Discovering Causal Signals in Images (2016, background): “Again, this asymmetry renders the cause distinguishable from the effect [3].”
Towards Causal Representation Learning (2021, background): “[49] who define a measure of dependence between input P (X) and conditional P (Y |X).”
Causality for Machine Learning (2019, methodology): “should be possible in that case? It turns out the answer was yes, due to the work on cause-effect inference using independent causal mechanisms mentioned in Section 5. This work was done with Povilas Daniušis et al. (2010).15 It introduced a measure of dependence between the input and the conditiona”
Learning Neural Causal Models from Unknown Interventions (2019, methodology): “…based on observational data (Chickering, 2002; Tsamardinos et al., 2006; Goudet et al., 2017; Hauser & Bühlmann, 2012; Spirtes et al., 2000; Sun et al., 2007; Zhang et al., 2012; Shimizu et al., 2006; Hoyer et al., 2009; Daniusis et al., 2012; Budhathoki & Vreeken, 2017; Kalainathan et al., 2018).”
Generalization in anti-causal learning (2018, background): “While the ICM principle might provide some justiﬁcation for such expectations in the causal direction, these do not hold for the anti-causal direction.”
Learning Independent Causal Mechanisms (2017, methodology): “The IM assumption discussed in the introduction can be used for identiﬁcation of causal models (Daniuˇsis et al., 2010; Zhang et al., 2015), but causality has also proven a useful tool for discussing and understanding machine learning in the non-i.i.d. regime.”
Causal Generative Neural Networks (2017, background): “…rely on different but equally strong assumptions, such as linearity [Shimizu et al. , 2006], additive noise [Zhang and Hyv¨arinen, 2009; Peters et al. , 2014], determinism [Daniusis et al. , 2012], or a large corpus of annotated causal relations [Lopez-Paz et al. , 2015; Fonollosa, 2016].”
Group invariance principles for causal generative models (2017, background): “(8) which corresponds exactly to the orthogonality postulate exploited in Information Geometric Causal Inference (IGCI) (Daniusis et al., 2010; Janzing et al., 2012).”
Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference (2015, methodology): “Second, consider the information-geometric approach to causal inference [40, 41].”
Telling cause from effect in deterministic linear dynamical systems (2015, methodology): “The idea behind SIC, as well as several new approaches to causal inference (Daniusis et al., 2010; Janzing et al., 2010; Mooij et al., 2010; Zscheischler et al., 2011; Janzing et al., 2012; Sgouritsa et al., 2015), is to rely on the “philosophical” principle that the cause and”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, methodology): “There should be better ways of dealing with discretization effects, but we nevertheless include this particular estimator for comparison, as it was also used in previous implementations of the entropy-based IGCI method (Daniušis et al., 2010; Janzing et al., 2012).”
Testing whether linear equations are causal: A free probability theory approach (2011, background): “In particular one can infer – with some reliability – whether X causes Y or Y causes X, given that either statement is true (e.g. Friedman and Nachman (2000); Kano and Shimizu (2003); Sun et al. (2006); Hoyer et al. (2009); Daniušis et al. (2010); Mooij et al. (2009)).”
Causal Discovery via Reproducing Kernel Hilbert Space Embeddings (2014, background): “Note that the causal relations among the stock indices in different regions are more likely to be nonlinear, and thus methods such as ANM and IGCI seem to be more appropriate than LiNGAM.”
Towards a Learning Theory of Cause-Effect Inference (2015, background): “Figure 1 plots the classification accuracy of RCC, IGCI (Daniusis et al., 2012), and ANM (Mooij et al., 2014) versus the fraction of decisions that the algorithms are forced to make out of the 82 scalar Tüebingen cause-effect pairs.”
Automated Machine Learning: Methods, Systems, Challenges (2019, unknown): “It is not a formal proof of causality, as it comes from an “Occam razor principle” that favors a simple explanation with the prior assumption that an additive noise model is simpler than a non additive noise model [12].”