EFSC — Exponential Family Synthetic Controls

Probabilistic imputation and causal analysis for panels of datasets

• Each unit-time cell contains a distribution of observations from an exponential family.
• An intervention at a specific time perturbs the distributions of a subset of units.
• Information sharing via probabilistic exponential-family matrix factorization.
• Black-box variational inference with automatic differentiation in PyTorch.
• Estimation of distributional counterfactuals and treatment effects.
• Dual functionality: probabilistic completion and synthetic controls.

Input	Mode	Purpose
Long-format observations	Imputation	Fit the panel and infer missing unit-time datasets
Long-format observations plus causal metadata—treated units and each unit's first treated period	Causal/SC	Estimate untreated counterfactual distributions

Without causal metadata, EFSC performs probabilistic matrix completion using the factorization underlying the model. With causal metadata, EFSC estimates untreated counterfactual distributions and treatment effects using the synthetic-control design described in the paper. See the currently available distributions and the guides to imputation and causal/SC modes. Users can provide their own long-format CSV files or pandas DataFrames, and configure model fitting through the available inference settings. The documentation index and example index collect the complete guides and runnable scripts; see the imputation examples and causal/SC examples.

Code to reproduce the manuscript results is maintained in the companion efsc-paper-reproduction repository.

Citation

If you use EFSC in your research, please cite:

@article{rodriguezdeniz2026efsc,
  author = {Rodriguez-Deniz, Hector and Blei, David M.},
  title = {Exponential Family Synthetic Controls},
  journal = {arXiv preprint arXiv:2609.23970},
  year = {2026},
  url = {https://arxiv.org/abs/2609.23970}
}

Installation

EFSC requires Python 3.10 or newer. To install the current source:

git clone https://github.com/blei-lab/efsc.git
cd efsc
python -m venv myenv
source myenv/bin/activate
python -m pip install --upgrade pip
python -m pip install --editable .

For a CPU-only installation, install the CPU build of PyTorch first. This avoids downloading CUDA libraries on machines that will not use a GPU:

python -m pip install torch --index-url https://download.pytorch.org/whl/cpu
python -m pip install --editable .

To run examples that generate figures, install the optional plotting dependencies:

python -m pip install --editable ".[examples]"

For development and testing:

python -m pip install --editable ".[test,examples]"
python -W error -m pytest -p no:cacheprovider

Quick start

This example simulates an 8-by-24 Poisson panel and treats its final two units from period 20 onward. Each unit-time cell contains 32 observations. EFSC then estimates the untreated counterfactual rates and distributional treatment effects:

from efsc import EFSC, InferenceConfig
from examples.poisson_synthetic_control import simulate_panel

panel, adoption = simulate_panel(random_state=123)

result = EFSC(
    family="poisson",
    rank=1,
    random_state=123,
    inference_config=InferenceConfig(epochs=2000, device="cpu"),
).fit(
    panel,
    outcome="outcome",
    unit="unit",
    time="time",
    causal_metadata=adoption,
)

effects = result.causal.effects
print(
    effects.groupby("unit", as_index=False)[
        ["counterfactual_rate", "treated_rate", "difference_rate", "ecd"]
    ].mean()
)

unit  counterfactual_rate  treated_rate  difference_rate      ecd
  U7             3.144352      6.167707         3.023355 1.267228
  U8             3.768525      7.799882         4.031357 1.740297

The dashed lines mark the treated units and the first treated period. The complete runnable script can also regenerate the figure when Matplotlib is installed; see examples/poisson_synthetic_control.py.