Counterfactual Identifiability of Bijective Causal Models

We study counterfactual identifiability in causal models with bijective generation mechanisms (BGM), a class that generalizes several widely used causal models in the literature. We establish their counterfactual identifiability for three common causal structures with unobserved confounding, and propose a practical learning method that casts learning a BGM as structured generative modeling. Learned BGMs enable efficient counterfactual estimation and can be obtained using a variety of deep conditional generative models. We evaluate our techniques in a visual task and demonstrate its application in a real-world video streaming simulation task.

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Requirements

We use Python (3.9.11 tested) for all experiments. Install the following packages:

numpy, tqdm, matplotlib, pyro

Install PyTorch according to the website instructions.

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Counterfactual Ellipse Generation

Create a directory as a workspace for datasets, models and plots. We'll call this directory DIR.

python ellipse/generate_data.py --dir DIR

generates the training data. To train BC and baseline models use the following scripts:

python ellipse/train.py --dir DIR
python ellipse/baseline_x_train.py --dir DIR
python ellipse/baseline_xz_train.py --dir DIR

Table 1's numbers are taken from logs in DIR/logs. Finally, run the following command to generate Figure 4 (DIR/ellipse.png):

python ellipse/generate_ellipse.py --dir DIR

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Video Streaming Simulation

Create a directory as a workspace for datasets, models and plots. We'll call this directory DIR. Move video/simulator_data.tar.gz (generated with this code to DIR and extract it using the following command:

tar -xzvf DIR/simulator_data.tar.gz

For all training runs, we tried seeds (SEED) from 0 to 9.

Markovian

Create the training dataset by running the following command:

python video/create_markovian_data.py --dir DIR

Next, train the model using the following script:

python video/train_markovian.py --dir DIR --seed SEED

The Markovian row in Table 1 was generated using logs in DIR/markovian/logs.

Instrumental Variable (IV)

Create the training dataset by running the following command:

python video/create_IV_data.py --dir DIR

Next, train the IV and CausalSim models using the following scripts:

python video/train_IV.py --dir DIR --seed SEED
python video/train_causalsim.py --dir DIR --seed SEED

The IV and CausalSim rows in Table 1 was generated using logs in DIR/iv/logs.

Backdoor Criterion (BC)

Create the training dataset by running the following command:

python video/create_BC_data.py --dir DIR

Next, train models for both buffer based ABR algorithms (bba and bola) using the following scripts:

python video/train_bc.py --dir DIR --seed SEED --algo bba
python video/train_bc.py --dir DIR --seed SEED --algo bola

The BC row in Table 1 was generated using logs in DIR/bc/logs, by taking the average over Bola and BBA algorithms.

IV + BC

Train the model using the following script:

python video/train_iv_bc_mix.py --dir DIR --seed SEED

The IV+BC row in Table 1 was generated using logs in DIR/mix/logs.