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Book Sections Year : 2018

## Learning Functional Causal Models with Generative Neural Networks

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Olivier Goudet
Diviyan Kalainathan
Philippe Caillou
David Lopez-Paz
• Function : Author
Isabelle Guyon
• Function : Author
• PersonId : 963159
Michèle Sebag
• Function : Author
• PersonId : 836537

#### Abstract

We introduce a new approach to functional causal modeling from observational data, called Causal Generative Neural Networks (CGNN). CGNN leverages the power of neural networks to learn a generative model of the joint distribution of the observed variables, by minimizing the Maximum Mean Discrepancy between generated and observed data. An approximate learning criterion is proposed to scale the computational cost of the approach to linear complexity in the number of observations. The performance of CGNN is studied throughout three experiments. Firstly, CGNN is applied to cause-effect inference, where the task is to identify the best causal hypothesis out of $X\rightarrow Y$ and $Y\rightarrow X$. Secondly, CGNN is applied to the problem of identifying v-structures and conditional independences. Thirdly, CGNN is applied to multivariate functional causal modeling: given a skeleton describing the direct dependences in a set of random variables $\textbf{X} = [X_1, \ldots, X_d]$, CGNN orients the edges in the skeleton to uncover the directed acyclic causal graph describing the causal structure of the random variables. On all three tasks, CGNN is extensively assessed on both artificial and real-world data, comparing favorably to the state-of-the-art. Finally, CGNN is extended to handle the case of confounders, where latent variables are involved in the overall causal model.

#### Domains

Statistics [stat] Other Statistics [stat.ML]

### Dates and versions

hal-01649153 , version 1 (27-11-2017)

### Identifiers

• HAL Id : hal-01649153 , version 1
• ARXIV :
• DOI :

### Cite

Olivier Goudet, Diviyan Kalainathan, Philippe Caillou, David Lopez-Paz, Isabelle Guyon, et al.. Learning Functional Causal Models with Generative Neural Networks. Explainable and Interpretable Models in Computer Vision and Machine Learning, Springer International Publishing, 2018, Springer Series on Challenges in Machine Learning, 978-3-319-98131-4. ⟨10.1007/978-3-319-98131-4⟩. ⟨hal-01649153⟩

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