mixpc 0.1.1

This package provides an implementation of the Mixed PC algorithm for learning causal graphical models from data with mixed variable types.

mixpc: Mixed PC Algorithm for Causal Discovery

mixpc is a Python library for learning causal graphical models from data with mixed variable types (continuous and ordinal). It implements the PC algorithm with the PC-stable skeleton discovery variant (Colombo & Maathuis 2014) and three v-structure orientation strategies from Ramsey et al. (2016).

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Features

• PC-stable skeleton discovery — deterministic edge removal order, independent of variable ordering.
• Three orientation strategies — conservative, majority, and PC-Max v-structure rules.
• Mixed data support — automatic dispatch to the right correlation measure per variable pair:
  • Both continuous → nonparanormal Spearman sin-transform (Liu et al. 2009)
  • Both ordinal → polychoric MLE (Brent or Newton-Fisher solver)
  • Mixed → ad-hoc polyserial correlation
• Prior knowledge — required/forbidden edges, required/forbidden directions, and partial temporal layering (e.g. production-line stations) integrated into all three PC phases.
• Full Meek rule application — R1–R4 applied to maximally orient remaining undirected edges.

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Installation

pip install mixpc

From source

git clone https://github.com/konstantingoe/mixed-pc.git
cd mixed-pc
pip install -e .

Development installation

git clone https://github.com/konstantingoe/mixed-pc.git
cd mixed-pc
make sync-venv

make sync-venv creates a virtual environment, installs all pinned dev dependencies via uv pip sync, and installs the package in editable mode.

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Quick Start

Continuous data (Nonparanormal Fisher Z test)

import numpy as np
from mixpc import PC

rng = np.random.default_rng(42)
n = 2000

# Ground truth: X0 -> X2 <- X1, X2 -> X3
x0 = rng.normal(size=(n, 1))
x1 = rng.normal(size=(n, 1))
x2 = x0 + x1 + 0.5 * rng.normal(size=(n, 1))
x3 = x2 + 0.3 * rng.normal(size=(n, 1))

data = {"X0": x0, "X1": x1, "X2": x2, "X3": x3}

pc = PC(alpha=0.05)
pdag = pc.learn_graph(data, v_structure_rule="conservative")

print("Directed edges:", pdag.dir_edges)
# → [('X0', 'X2'), ('X1', 'X2'), ('X2', 'X3')]

Mixed data (continuous + ordinal)

import numpy as np
from mixpc import PC, MixedFisherZ

rng = np.random.default_rng(0)
n = 3000

x0 = rng.normal(size=(n, 1))
x1 = rng.normal(size=(n, 1))
x2 = x0 + x1 + 0.5 * rng.normal(size=(n, 1))

# X3 is ordinal. The polyserial CI test assumes a latent continuous z3
# of which the observed ordinal X3 is a thresholded version.
z3 = x2 + 0.5 * rng.normal(size=(n, 1))
thresholds = np.percentile(z3, [20, 40, 60, 80])
x3 = np.searchsorted(thresholds, z3).reshape(n, 1).astype(float)

data = {"X0": x0, "X1": x1, "X2": x2, "X3": x3}

pc = PC(alpha=0.05, test=MixedFisherZ)
pdag = pc.learn_graph(data, v_structure_rule="majority")

print("Directed edges:", pdag.dir_edges)
# → [('X0', 'X2'), ('X1', 'X2'), ('X2', 'X3')]

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Orientation strategies

Pass v_structure_rule to learn_graph:

Strategy	Behaviour
"conservative"	Orient as v-structure only if all separating sets exclude the middle node
"majority"	Orient if majority of separating sets exclude the middle node
"pc-max"	Orient based on the highest p-value across separating sets

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Prior knowledge

Encode domain constraints with PriorKnowledge and pass it to learn_graph. All five hint types compose: required/forbidden edges, required/forbidden directions, and a partial temporal layering.

from mixpc import PC, PriorKnowledge

# Production-line example: three stations, intra-station ordering unknown
prior = PriorKnowledge(
    layering=[["X0", "X1"], ["X2"], ["X3"]],   # X0,X1 precede X2 precedes X3
    forbidden_directions=[("X3", "X2")],       # explicit override (redundant with layering here)
    required_edges=[("X0", "X2")],             # never tested for removal
)

pc = PC(alpha=0.05)
pdag = pc.learn_graph(data, v_structure_rule="majority", prior_knowledge=prior)

Layering is consulted in all three PC phases: it prunes conditioning sets during skeleton discovery, blocks impossible v-structures, and propagates orientations through the Meek rules.

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Project Structure

.
├── mixpc/
│   ├── __init__.py
│   ├── pc_algorithm.py
│   ├── independence_tests.py
│   ├── correlations.py
│   ├── prior_knowledge.py
│   ├── graphs.py
│   └── py.typed
├── tests/
├── docs/
├── pyproject.toml
├── Makefile
├── mkdocs.yml
└── .pre-commit-config.yaml

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Testing

make test       # plain pytest
make coverage   # pytest with coverage + missing-line report

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Development

Managing dependencies

make requirements        # re-pin without upgrading existing deps
make update-requirements # re-pin and upgrade all deps
make sync-venv           # apply the lock files to the venv

Pre-commit hooks

pre-commit install          # enable hooks (run automatically on git commit/push)
pre-commit run --all-files  # run all hooks manually

Linting and type checking

ruff check mixpc/
mypy mixpc/

Documentation

source venv_mixed-pc/bin/activate
mkdocs serve   # live preview at http://127.0.0.1:8000
mkdocs build   # static site in site/

Deploy to GitHub Pages

mike deploy --push --update-aliases 0.1.1 latest
mike set-default --push latest   # first time only

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References

• Spirtes, P., Glymour, C. & Scheines, R. (2000). Causation, Prediction, and Search. MIT Press.
• Colombo, D. & Maathuis, M.H. (2014). Order-independent constraint-based causal structure learning. JMLR 15, 3741–3782.
• Ramsey, J., Zhang, J. & Spirtes, P. (2016). Adjacency-faithfulness and conservative causal inference. UAI.
• Liu, H., Lafferty, J. & Wasserman, L. (2009). The nonparanormal. JMLR 10, 2295–2328.
• Göbler, K., Drton, M., Mukherjee, S. & Miloschewski, A. (2024). High-dimensional undirected graphical models for arbitrary mixed data. Electronic Journal of Statistics 18(1). doi:10.1214/24-EJS2254.

License

MIT License — see LICENSE for details.