Hi Prof 👋: High-Probability Falsifier

We formalize verification in causal graphical models: deciding whether a given observational formula identifies a target interventional distribution. This opens a problem complementary to identification, asking not whether any identifying formula exists, but whether the given formula is identifying. We show that even sound and complete solutions to identification do not solve verification. We propose a falsifier as a first practical route forward, prove that it induces an almost-surely correct verifier for regular exponential-family models, and describe the gateway test, a natural application of the resulting verifier that finds all sets admissible for use in a front-door formula.

If you publish research using hiprof, please cite our paper introducing verification:

@article{hiprof2026,
  author  = {Francesco Freni and Leonard Henckel and Sebastian Weichwald},
  title   = {{Verifying formulas for interventional distributions}},
  journal = {{arXiv preprint arXiv:2607.13883}},
  year    = {2026}
}

Feedback very welcome!

⚙️ Installation

Install hiprof from PyPI using pip:

# create virtual environment (optional)
python -m venv venv_hiprof
source venv_hiprof/bin/activate

# install hiprof
python -m pip install hiprof

Alternatively, using uv:

# create virtual environment (optional)
uv venv

# install hiprof
uv pip install hiprof

Two optional feature gates provide additional functionality:

• identification installs y0 and enables IDAlgorithm, which derives an identifying formula when one is available;
• nonidentifiability installs ananke-causal and enables verification of non-identifiability claims.

Install optional features individually:

python -m pip install "hiprof[identification]"
python -m pip install "hiprof[nonidentifiability]"

or install all optional features:

python -m pip install "hiprof[all]"

The same requirement strings can be used with uv pip install.

🚀 Quick start

from hiprof import HPFalsifier

falsifier = HPFalsifier(
    graph="T -> M; M -> Y; T <-> Y",
    treatments="T",
    outcomes="Y",
)

formula = """
sum_{M} {
    p(M | T)
    sum_{T'} { p(Y | M, T') p(T') }
}
"""

falsifier.check(formula)
# Output:
# True
# False-acceptance bound: 5.421e-18

Adjacency matrices can be translated as follows (numpy arrays and pandas DataFrames are accepted as well):

from hiprof import adjacency_to_graph

adjacency = [
    [0, 1, 1],
    [0, 0, 1],
    [1, 0, 0],
]

graph = adjacency_to_graph(
    adjacency,
    nodes=["T", "M", "Y"],
    edge_direction="from row to column",
)
# T -> M
# T <-> Y
# M -> Y

📚 Examples

For a concise introduction, see notebooks/demo.ipynb.

After cloning and installing the repository, the standalone examples in examples/ can be run from the repository root:

python examples/frontdoor.py
python examples/napkin.py
python examples/cross_graph_verification.py

cross_graph_verification.py uses IDAlgorithm and therefore requires the identification feature.

🛠️ Local development

Clone the repository and install it in editable mode:

git clone git@github.com:francescofreni/hiprof.git
cd hiprof
python -m pip install -e ".[dev]"

To include all optional features as well as the development tools:

python -m pip install -e ".[dev,all]"

Run the test suite with

pytest