Quantifying causal influences

By Dominik Janzing, David Balduzzi, Moritz Grosse-Wentrup, Bernhard Schölkopf. 2012

239 citations recorded by the source corpus.

Many methods for causal inference generate directed acyclic graphs (DAGs) that formalize causal relations between $n$ variables. Given the joint distribution on all these variables, the DAG contains all information about how intervening on one variable changes the distribution of the other $n-1$ variables. However, quantifying the causal influence of one variable on another one remains a nontrivial question. Here we propose a set of natural, intuitive postulates that a measure of causal strength should satisfy. We then introduce a communication scenario, where edges in a DAG play the role of channels that can be locally corrupted by interventions. Causal strength is then the relative entropy distance between the old and the new distribution. Many other measures of causal strength have been proposed, including average causal effect, transfer entropy, directed information, and information flow. We explain how they fail to satisfy the postulates on simple DAGs of $\leq3$ nodes. Finally, we investigate the behavior of our measure on time-series, supporting our claims with experiments on simulated data.

Subfields: Sociology and Political Science

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Citations in the corpus

Causal Discovery from Nonstationary/Heterogeneous Data: Skeleton Estimation and Orientation Determination (2017, background): “The contribution from θ ′ 1 to V1 has been derived in [Janzing et al., 2013]: Sθ′ 1→V1 =”
Algorithmic Transparency via Quantitative Input Influence: Theory and Experiments with Learning Systems (2016, background): “[35] use interventions to assess the causal importance of relations between variables in causal graphs; in order to assess the causal effect of a relation between two variables, X → Y (assuming that both take on specific values X = x and Y = y), a new causal model is constructed, where the value of ”
Discovery and Visualization of Nonstationary Causal Models (2015, unknown): “The contribution from θ ′ 1 to V1 has been derived in [22]: Sθ′ 1→V1 = E [ log P (V1 |V2,θ 1) ∫ P (V1 |V2,θ̃′ 1)P (θ̃′ 1)dθ̃ 1 ] , where θ̃′ 1 is an independent copy of θ′ 1.”
Causal Discovery with Attention-Based Convolutional Neural Networks (2019, unknown): “Instead of intervening on variables, the “destruction of edges” [56] (intervening on the edges) in a Bayesian network can be used to validate and quantify causal strength by calculating the relative entropy between the old and intervened distribution.”
Demystifying fixed k-nearest neighbor information estimators (2016, methodology): “Equation (9) in [20]) and widely studied in the information theory community due to its invariance to scaling (cf.”
Alignment for Advanced Machine Learning Systems (2020, methodology): “Janzing et al. (2013) define a framework for quantifying the causal influence between variables in a causal network, which could be used to selectively report only the most causally relevant factor in some judgment. Sparse models offer another approach to ensure transparency, by simplifying the mode”
Estimating Causal Effects by Bounding Confounding (2014, background): “[Janzing et al., 2013] proposed a definition for the causal strength of a set of arrows in a causal DAG.”
Generative causal explanations of black-box classifiers (2020, methodology): “compute the average causal effect (ACE) of human-interpretable concepts on the classifier [50], but require labeled examples of the concepts and suffer from limitations of the ACE metric [8].”
CXPlain: Causal Explanations for Model Interpretation under Uncertainty (2019, background): “More sophisticated feature masking schemes that consider the masked feature’s distribution [38, 39] could be a more principled alternative to masking with point-wise estimates.”
Detecting Confounding in Multivariate Linear Models via Spectral Analysis (2017, background): “2 Note that quantifying causal influence in causal Bayesian networks is non-trivial and there exists no generally accepted measure [8].”