On the Identifiability of Poisson Branching Structural Causal Model Under Latent Confounding

The Python implementation of the paper On the Identifiability of Poisson Branching Structural Causal Model Under Latent Confounding (ICML 2026).

Usage

The running example of LC-PB-SCM is given below.

import numpy as np
from eq_search import eq_search_v2, mag2graph
from pgf_confounder_partial import pgf_confounder_partial
from util import pbscm, graph2pgf
from PGF import PGF
case_graph =(
    3,
    [.02, .03, .04, .05],
    [
        [0, 0, 0.3, 0],
        [0, 0, 0.4, 0],
        [0, 0, 0, 0],
        [0.5, 0.6, 0, 0],
    ]
)
n = case_graph[0]
mu = case_graph[1]
graph = case_graph[2]
print(np.array(graph))

pgf = PGF(graph)
expr = pgf.compute(mu, s=[pgf.s[k] if k < n else 1 for k in range(len(mu))])
print("True PGF expression:")
print(expr.as_expr())

data = pbscm(graph=graph, mu=mu, sample=10000)
data = data[:, :n]

terms, mag = pgf_confounder_partial(data, bootstrap_round=200, p_value=.05, verbose=True)
print("Learned PPADMG:")
print(mag2graph(mag))

Requirements

The requirements are given in requirements.txt. You can install them using the following command:

pip install -r requirements.txt