GuidesDiscover a graph

Discover a graph

Learn a causal graph from a table of observations, then read what the result can and can't tell you. You'll run one search and check it against a network whose true graph is known.

Run the program#

The Asia network (Lauritzen and Spiegelhalter, 1988) is a teaching model of a chest clinic: a visit to Asia, smoking, tuberculosis, lung cancer, bronchitis, an x-ray and shortness of breath (dysp). either is true when the patient has tuberculosis or lung cancer. load_asia samples patients from the network's own probability tables, so you know the answer in advance.

from ergodic import discover
from ergodic.datasets import load_asia
from ergodic.graph import cpdag_of_dag, dag

# 1. Sample 5,000 patients from the Asia network.
asia = load_asia(n=5_000, seed=0)
print(asia.data.variables)

# 2. Learn the graph with greedy equivalence search (GES).
result = discover(asia.data, method="ges")
print(result.method, result.score, result.n)
print(result.graph)

# 3. Build the class of graphs the data could reveal: the truth's CPDAG.
truth = cpdag_of_dag(dag(asia.target["edges"]))
found = {edge.glyph() for edge in result.graph.edges}
expected = {edge.glyph() for edge in truth.edges}

# 4. Compare edge by edge, marks included.
print("right:", len(found & expected), "of", len(expected))
print("missed:", sorted(expected - found))
print("extra:", sorted(found - expected))

('asia', 'tub', 'smoke', 'lung', 'bronc', 'either', 'xray', 'dysp')
ges bic_discrete 5000
MixedGraph(kind=cpdag, nodes=8, edges=[bronc --> dysp, bronc --- smoke, dysp <-- either, either <-- lung, either <-- tub, either --> xray, lung --- smoke])
right: 7 of 8
missed: ['asia --- tub']
extra: []

• Step 2. discover picked the discrete BIC score because every column is categorical. The result is a CPDAG: some edges have a direction, some don't.
• Step 3. No method can orient more than the data allows. cpdag_of_dag turns the true graph into the class of graphs that fit the same independences. That class is the fair target.
• Step 4. GES found 7 of the 8 edges with the right marks and added none. It missed asia --- tub: only 1 patient in 100 visited Asia, and a visit raises the chance of tuberculosis from 1% to 5%. In 5,000 rows that signal is too weak to see.

Read the result#

discover returns a DiscoveryResult. The graph is the headline; the other fields say how it was found.

Each edge prints as a glyph. The marks at the two ends carry the meaning:

Circle marks come from FCI and RFCI. Graphs and edge marks covers each graph kind in full.

Pick a method#

method= takes a name. Every method except "pcmci" reads a TabularData and refuses time series, whose rows aren't independent.

Choose a method and test lists the assumptions behind each one and shows how to swap the independence test or the score.

The scores are score-equivalent: every DAG in an equivalence class gets the same score. So A* and HillClimb return one member of a class, picked by tie-breaking, and some of its directions are arbitrary. Before you identify an effect, turn the result back into its class with ergodic.graph.cpdag_of_dag(result.graph).

Next steps#