CSuite: A Suite of Benchmark Datasets for Causality

CSuite is a collection of synthetic datasets for benchmarking causal machine learning algorithms. Each dataset consists of

• the true causal graph, for benchmarking causal discovery;
• 4000 rows of observational training data;
• 2000 rows of observational test data;
• interventional test data, for benchmarking estimation of average treatment effect (ATE) and conditional average treatment effect (CATE), 2000 rows per interventional environment.

The data was generated from known hand-crafted structural equation models (SEMs). Different datasets are intended to test different features of causal discovery and inference algorithms. CSuite was originally introduced in this paper. The data generation code for CSuite is publicly available.

Versioning

CSuite datasets are versioned so that we can amend and add datasets, whilst ensuring backwards compatibility with older versions of the data. Full reproducibility with CSuite requires specifying the correct version.

Summary of datasets

The download URLs here are for the latest version.

Dataset	No. nodes	No. edges	Additive noise model?	Discrete/continuous	ATE benchmarking	CATE benchmarking	Download link
lingauss	2	1	Y	Continuous	Y	N	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_lingauss.zip
linexp	2	1	Y	Continuous	Y	N	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_linexp.zip
nonlingauss	2	1	Y	Continuous	Y	N	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_nonlingauss.zip
nonlin_simpson	4	4	Y	Continuous	Y	Y	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_nonlin_simpson.zip
symprod_simpson	4	4	Y	Continuous	Y	Y	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_symprod_simpson.zip
large_backdoor	9	10	Y	Continuous	Y	Y	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_large_backdoor.zip
weak_arrows	9	15	Y	Continuous	Y	N	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_weak_arrows.zip
cat_to_cts	2	1	N	Mixed	Y	N	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_cat_to_cts.zip
cts_to_cat	2	1	N	Mixed	Y	N	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_cts_to_cat.zip
mixed_simpson	4	4	N	Mixed	Y	N	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_mixed_simpson.zip
large_backdoor_binary_t	9	10	N	Mixed	Y	Y	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_large_backdoor_binary_t.zip
weak_arrows_binary_t	9	15	N	Mixed	Y	N	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_weak_arrows_binary_t.zip
mixed_confounding	12	15	N	Mixed	Y	N	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_mixed_confounding.zip
cat_chain	3	2	N	Discrete	Y	N	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_cat_chain.zip
cat_collider	3	2	N	Discrete	Y	N	https://github.com/microsoft/csuite/releases/download/v0.1/csuite_cat_collider.zip

Data format

Each dataset consists of the following files

• adj_matrix.csv, which describes the causal graph used to generate the data; a value 1 in row i, column j indicates an edge from node i to node j;
• train.csv, the observational training data;
• test.csv, the observational test data;
• interventions.json, a JSON containing interventional test data.

The interventional data JSON consists of pairs of interventional environments, which can be used to estimate (C)ATE. The two environments are the 'primary' and 'reference' environments. Conditional data was generating using HMC. The format of the interventional data is

{
    "environments": [
        {
            "conditioning_idxs": <optional list containing indices of nodes to that were conditioned on>,
            "conditioning_values": <list of values set on the conditioning nodes>,
            "effect_idxs": <list containing indices of nodes to be considered effect variables>,
            "intervention_idxs": <list of indices of nodes that were acted on with do-intervention>,
            "intervention_values": <list of values set on the intervention nodes in the primary do-intervention: for example, receiving a medicine>,
            "intervention_reference": <list of values set on the intervention nodes in the reference do-intervention: for example, not receiving the medicine>,
            "test_data": <array of data from the primary do-intervention, same number of columns as train.csv>,
            "reference_data": <array of data from the reference do-intervention>
        },
        ...
    ],
    "metadata": {
        "columns_to_nodes": <matches to columns to their corresponding nodes, only important for vector-values nodes>
    }
}

Download

From the terminal

You can download CSuite datasets from any previous version using the following URL pattern

$ curl -O https://github.com/microsoft/csuite/releases/download/v<version>/csuite_<name>.zip

where <name> and <version> should be set appropriately.

From Python

The uncompressed files listed under Data format are also directly available from a public storage account. These may either be accessed through their HTTP links, e.g. https://azuastoragepublic.blob.core.windows.net/datasets/csuite_linexp/train.csv or their equivalent Azure blob storage paths. To load these directly in python:

import pandas as pd

# Load over HTTP
df = pd.read_csv("https://azuastoragepublic.blob.core.windows.net/datasets/csuite_linexp/train.csv")

# Load using `adlfs` (`pip install adlfs`)
df = pd.read_csv("az://[email protected]/csuite_linexp/train.csv")

Citation

If you use CSuite datasets in your work, please cite the following paper which originally introduced these datasets

@article{geffner2022deep,
    title={Deep End-to-end Causal Inference},
    author={Geffner, Tomas and Antoran, Javier and Foster, Adam and Gong, Wenbo and Ma, Chao and Kiciman, Emre and Sharma, Amit and Lamb, Angus and Kukla, Martin and Pawlowski, Nick and  Allamanis, Miltiadis and Zhang, Cheng},
    journal={arXiv preprint arXiv:2202.02195},
    year={2022}
}

Detailed descriptions of datasets

lingauss

A two node linear Gaussian system. The structural equations are

$$ \begin{align} X_0 &\sim N(0, 1) \\ X_1 &= \frac{1}{2}X_0 + \frac{\sqrt{3}}{2}Z_1 \end{align} $$

where $Z_1 \sim N(0,1)$ is independent of $X_0$. The dataset is constructed so that the observational distribution is the same if $X_0$ and $X_1$ are swapped and both nodes have the same marginal variance of 1. This model is not structural identifiable from observational data.

linexp

A two node linear system with exponentially distributed noise. The structural equations are

$$ \begin{align} X_0 &= Z_0 - 1 \\ X_1 &= \frac{1}{2}X_0 + \frac{\sqrt{3}}{2}(Z_1-1) \end{align} $$

where $Z_0, Z_1 \sim \textup{Exp}(1)$ are independent variables. The dataset is constructed so that both nodes have the same marginal variance of 1. This model is structural identifiable given a non-Gaussian additive noise assumption.

nonlingauss

A two node non-linear system with Gaussian distributed noise. The structural equations are

$$ \begin{align} X_0 &\sim N(0,1) \\ X_1 &= \sqrt{6} \exp(-X_0^2) + \alpha Z_1 \end{align} $$

where $Z_1 \sim N(0,1)$ is independent of $X_0$ and

$$ \alpha^2 = 1 - 6 \left(\frac{1}{\sqrt{5}} - \frac{1}{3} \right). $$

The dataset is constructed so that $\textup{Var}(X_0) = \textup{Var}(X_1) = 1$ and $\textup{Cov}(X_0,X_1)=0$. This model is structural identifiable given a nonlinear additive noise assumption.

nonlin_simpson

An example of Simpson's Paradox using a continuous SEM. The dataset is constructed so that $\textup{Cov}(X_1,X_2)$ has the opposite sign to $\textup{Cov}(X_1,X_2\mid X_0)$. Estimating the treatment effects correctly in this SEM is highly sensitive to accurate causal discovery.

The structural equations are

$$ \begin{align} X_0 &\sim N(0,1) \\ X_1 &= s(1 - X_0) + \sqrt{\frac{3}{20}} Z_1\\ X_2 &= \tanh(2X_1) + \frac{3}{2}X_0 -1 + \tanh(Z_2)\\ X_3 &= 5 \tanh\left(\frac{X_2 - 4}{5}\right) + 3 + \frac{1}{\sqrt{10}} Z_3 \end{align} $$

where $Z_1,Z_2 \sim N(0,1)$ and $Z_3 \sim \textup{Laplace}(1)$ are mutually independent and independent of $X_0$, $s(x) = \log(1+\exp(x))$ is the softplus function. Constants were chosen so that each variable has a marginal variance of (approximately) 1.

symprod_simpson

A dataset exhibiting multi-modality that is suitable for benchmarking CATE estimation. Nonlinear function estimation is important since $\textup{Cov}(X_0,X_2)=\textup{Cov}(X_1,X_2)=0$.

The structural equations are

$$ \begin{align} X_0 &\sim N(0,1) \\ X_1 &= 2\tanh(2X_0) + \frac{1}{\sqrt{10}} Z_1\\ X_2 &= \frac{1}{2}X_0 X_1 + \frac{1}{\sqrt{2}} Z_2\\ X_3 &= \tanh\left(\frac{3}{2} X_0\right) + \sqrt{\frac{3}{10}} Z_3 \end{align} $$

where $Z_1 \sim t_3,Z_2 \sim \textup{Laplace}(1)$ and $Z_3 \sim N(0,1)$ are mutually independent and independent of $X_0$. Constants were chosen so that each variable has a marginal variance of (approximately) 1.

large_backdoor

A larger dataset with a pyramidal graph structure. This dataset is constructed so that there are many possible choices of backdoor adjustment set for estimating the treatment effect of $X_7$ on $X_8$. While both minimal and maximal adjustment sets can result in a correct solution, the a minimal adjustment set results in a much lower-dimensional adjustment problem and thus will result in lower variance solutions.

A complete description of the structural equations can be found in the data generation code for CSuite.

weak_arrows

A larger dataset that is similar to large_backdoor, but with many additional edges. The causal discovery challenge revolves around finding all arrows, which are scaled to be relatively weak, but which have significant predictive power for $X_8$ in aggregate.

A complete description of the structural equations can be found in the data generation code for CSuite.

cat_to_cts

Variable	Discrete/continuous
$X_0$	Discrete on $\{0,1,2\}$
$X_1$	Continuous

A two node system with one categorical and one continuous variable. The structural equations are

$$ \begin{align} X_0 &\sim \text{Cat}\left(\frac{1}{4}, \frac{1}{4}, \frac{1}{2}\right)\\ X_1 &= \frac{1}{2}(X_0-1) + \frac{9}{25}\mathbf{1}_{\{X_0=2\}} + \frac{8}{5}(s(Z_1) - 1) \end{align} $$

where $s(x) = \log(1+\exp(x))$ is the softplus function, and $Z_1 \sim N(0,1)$ is independent of $X_0$.

cts_to_cat

Variable	Discrete/continuous
$X_0$	Continuous
$X_1$	Discrete on $\{0,1,2\}$

A two node system with one categorical and one continuous variable. The structural equations are

$$ \begin{align} X_0 &\sim U(-\sqrt{3},\sqrt{3})\\ p(X_1|X_0=x) &= \begin{cases} \left(\tfrac{6}{13},\tfrac{6}{13},\tfrac{1}{13} \right) & \text{ if } x < -\tfrac{\sqrt{3}}{3} \\ \left(\tfrac{1}{8},\tfrac{3}{4},\tfrac{1}{8} \right) & \text{ if } -\tfrac{\sqrt{3}}{3} \le x < \tfrac{\sqrt{3}}{3} \\ \left(\tfrac{1}{3},\tfrac{1}{3},\tfrac{1}{3} \right) & \text{ if } x > \tfrac{\sqrt{3}}{3} \\ \end{cases} \end{align} $$

mixed_simpson

Variable	Discrete/continuous
$X_0$	Discrete on $\{0,1\}$
$X_1$	Continuous
$X_2$	Discrete on $\{0,1,2,3,4,5\}$
$X_3$	Continuous

Another example of Simpson's Paradox using a mixed-type SEM. The dataset is constructed so that $\textup{Cov}(X_0,X_1)$ has the opposite sign to $\textup{Cov}(X_0,X_1\mid X_2)$. Estimating the treatment effects correctly in this SEM is highly sensitive to accurate causal discovery.

The structural equations are

$$ \begin{align} X_2 &\sim \text{Cat}\left(\frac{1}{6},\frac{1}{6},\frac{1}{6},\frac{1}{6},\frac{1}{6},\frac{1}{6}\right) \\ p(X_0|X_2=x) &= \begin{cases} \left(\tfrac{1}{12},\tfrac{11}{12} \right) & \text{ if } x < 3 \\ \left(\tfrac{11}{12},\tfrac{1}{12} \right) & \text{ if } x \ge 3 \\ \end{cases} \\ X_1 &= \frac{7}{10}\left(X_0 + X_2 - 4\right) + s\left(\frac{1}{2} Z_1 \right) \\ X_3 &= \frac{10}{3} \tanh\left(\frac{X_1}{3}\right) + \frac{1}{10}(Z_3 -1) \end{align} $$

where $Z_1 \sim N(0,1),Z_3\sim \textup{Exp}(1)$ are independent noise random variables and $s(x)=\log(1+\exp(x))$.

large_backdoor_binary_t

Variable	Discrete/continuous
$X_0$	Continuous
$X_1$	Continuous
$X_2$	Continuous
$X_3$	Continuous
$X_4$	Continuous
$X_5$	Continuous
$X_6$	Continuous
$X_7$	Discrete on $\{0,1\}$
$X_8$	Continuous

An adaptation of large_backdoor with a binary variable $X_7$ which is considered the treatment variable.

A complete description of the structural equations can be found in the data generation code for CSuite.

weak_arrow_binary_t

Variable	Discrete/continuous
$X_0$	Continuous
$X_1$	Continuous
$X_2$	Continuous
$X_3$	Continuous
$X_4$	Continuous
$X_5$	Continuous
$X_6$	Continuous
$X_7$	Discrete on $\{0,1\}$
$X_8$	Continuous

An adaptation of weak_arrows with a binary variable $X_7$ which is considered the treatment variable.

A complete description of the structural equations can be found in the data generation code for CSuite.

mixed_confounding

Variable	Discrete/continuous
$X_0$	Discrete on $\{0,1\}$
$X_1$	Continuous
$X_2$	Continuous
$X_3$	Continuous
$X_4$	Discrete on $\{0,1\}$
$X_5$	Discrete on $\{0,1,2\}$
$X_6$	Continuous
$X_7$	Discrete on $\{0,1,2\}$
$X_8$	Continuous
$X_9$	Continuous
$X_{10}$	Continuous
$X_{11}$	Continuous

A larger dataset with treatment node $X_0$ and outcome node $X_1$. There are different variables that are: confounders, causes of $X_0$ only, causes of $X_1$ only, downstream of $X_0$, downstream of $X_1$, collider caused by $X_0$ and $X_1$.

A complete description of the structural equations can be found in the data generation code for CSuite.

cat_chain

Variable	Discrete/continuous
$X_0$	Discrete on $\{0,1,2\}$
$X_1$	Discrete on $\{0,1,2\}$
$X_2$	Discrete on $\{0,1\}$

A chain graph with discrete variables. The structural equations are

$$ \begin{align} X_0 &\sim \text{Cat}\left(\frac{1}{4}, \frac{1}{4}, \frac{1}{2}\right)\\ p(X_1|X_0=x) &= \begin{cases} \left(\tfrac{3}{4},\tfrac{1}{8},\tfrac{1}{8} \right) & \text{ if } x=0 \\ \left(\tfrac{1}{8},\tfrac{3}{4},\tfrac{1}{8} \right) & \text{ if } x=1 \\ \left(\tfrac{1}{8},\tfrac{1}{8},\tfrac{3}{4} \right) & \text{ if } x=2 \\ \end{cases} \\ p(X_2|X_1=y) &= \begin{cases} \left(\tfrac{6}{7},\tfrac{1}{7} \right) & \text{ if } y=0 \\ \left(\tfrac{6}{7},\tfrac{1}{7} \right) & \text{ if } y=1 \\ \left(\tfrac{1}{7},\tfrac{6}{7} \right) & \text{ if } y=2. \\ \end{cases} \\ \end{align} $$

cat_collider

Variable	Discrete/continuous
$X_0$	Discrete on $\{0,1,2\}$
$X_1$	Discrete on $\{0,1,2\}$
$X_2$	Discrete on $\{0,1\}$

A collider graph with discrete variables. The structural equations are

$$ \begin{align} X_0 &\sim \text{Cat}\left(\frac{1}{4}, \frac{1}{4}, \frac{1}{2}\right)\\ X_2 &\sim \text{Cat}\left(\frac{1}{2}, \frac{1}{2}\right) \\ p(X_1|X_0=x,X_1=y) &= \begin{cases} \left(\tfrac{11}{13},\tfrac{1}{13},\tfrac{1}{13} \right) & \text{ if } x=0,y=0 \\ \left(\tfrac{1}{13},\tfrac{11}{13},\tfrac{1}{13} \right) & \text{ if } x=1,y=0 \\ \left(\tfrac{1}{13},\tfrac{1}{13},\tfrac{11}{13} \right) & \text{ if } x=2,y=0 \\ \left(\tfrac{31}{43},\tfrac{11}{43},\tfrac{1}{43} \right) & \text{ if } x=0,y=1 \\ \left(\tfrac{21}{43},\tfrac{21}{43},\tfrac{1}{43} \right) & \text{ if } x=1,y=1 \\ \left(\tfrac{21}{43},\tfrac{11}{43},\tfrac{11}{43} \right) & \text{ if } x=2,y=1. \\ \end{cases} \end{align} $$

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