Causal Discovery Toolbox: Uncover causal relationships in Python

This paper presents a new open source Python framework for causal discovery from observational data and domain background knowledge, aimed at causal graph and causal mechanism modeling. The 'cdt' package implements the end-to-end approach, recovering the direct dependencies (the skeleton of the causal graph) and the causal relationships between variables. It includes algorithms from the 'Bnlearn' and 'Pcalg' packages, together with algorithms for pairwise causal discovery such as ANM. 'cdt' is available under the MIT License at https://github.com/Diviyan-Kalainathan/CausalDiscoveryToolbox.

SAM: Structural Agnostic Model, Causal Discovery and Penalized Adversarial Learning

We present the Structural Agnostic Model (SAM), a framework to estimate end-to-end non-acyclic causal graphs from observational data. In a nutshell, SAM implements an adversarial game in which a separate model generates each variable, given real values from all others. In tandem, a discriminator attempts to distinguish between the joint distributions of real and generated samples. Finally, a sparsity penalty forces each generator to consider only a small subset of the variables, yielding a sparse causal graph. SAM scales easily to hundreds variables. Our experiments show the state-of-the-art performance of SAM on discovering causal structures and modeling interventions, in both acyclic and non-acyclic graphs.

Causal Generative Neural Networks

We present Causal Generative Neural Networks (CGNNs) to learn functional causal models from observational data. CGNNs leverage conditional independencies and distributional asymmetries to discover bivariate and multivariate causal structures. CGNNs make no assumption regarding the lack of confounders, and learn a differentiable generative model of the data by using backpropagation. Extensive experiments show their good performances comparatively to the state of the art in observational causal discovery on both simulated and real data, with respect to cause-effect inference, v-structure identification, and multivariate causal discovery.

Learning Functional Causal Models with Generative Neural Networks

We introduce a new approach to functional causal modeling from observational data. The approach, called Causal Generative Neural Networks (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. First, we apply CGNN to the problem of cause-effect inference, where two CGNNs model $P(Y|X,\textrm{noise})$ and $P(X|Y,\textrm{noise})$ identify the best causal hypothesis out of $X\rightarrow Y$ and $Y\rightarrow X$. Second, CGNN is applied to the problem of identifying v-structures and conditional independences. Third, we apply CGNN to problem of multivariate functional causal modeling: given a skeleton describing the dependences in a set of random variables $\{X_1, \ldots, X_d\}$, 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, we extend CGNN to handle the case of confounders, where latent variables are involved in the overall causal model.