mixpc

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).

Key Features

• PC-stable skeleton discovery with deterministic, order-independent edge removal
• Three v-structure orientation strategies: conservative, majority, and PC-Max
• Automatic dispatch to the appropriate correlation measure per variable pair
• Prior knowledge support: required/forbidden edges and directions, partial temporal layering
• Full Meek rule application (R1–R4) for maximal orientation of remaining edges

Supported Data Types

• Continuous–continuous: nonparanormal Spearman sin-transform (Liu et al., 2009)
• Ordinal–ordinal: polychoric MLE (Brent or Newton-Fisher solver)
• Mixed continuous–ordinal: ad-hoc polyserial correlation

Methods

The package combines order-independent skeleton discovery with conservative, majority, and PC-Max v-structure orientation rules, integrating optional prior knowledge — including partial temporal layering — across all three PC phases. Mixed data are handled through a latent Gaussian copula view, with pairwise correlations chosen automatically based on variable types.

Citation

Göbler, K. (2026). mixpc: Mixed PC Algorithm for Causal Discovery (Version 0.1.1) [Computer software]. https://github.com/konstantingoe/mixed-pc