Compare two graphs

The fastest path to a full comparison is bnmetrics.compare, which runs every comparative metric and packages the results into a Comparison value object.

Worked example: the diamond fixture

The canonical pedagogical fixture is the four-node diamond DAG \(A \to B,\; A \to C,\; B \to D,\; C \to D\). Its CPDAG keeps the v-structure into \(D\) directed but leaves the upper edges \(A - B\) and \(A - C\) undirected (they lie in the Markov-equivalence class). A common recovery error at moderate sample sizes is to flip these upper edges, returning \(B \to A\) and \(C \to A\) — two reversals.

import numpy as np
import bnmetrics

# True CPDAG of the diamond.
true_cpdag = bnmetrics.to_graphlike(
    np.array([
        # cols A  B  C  D
        [0, 1, 1, 0],   # A
        [1, 0, 0, 2],   # B
        [1, 0, 0, 2],   # C
        [0, 1, 1, 0],   # D
    ], dtype=np.int8),
    var_names=("A", "B", "C", "D"),
)

# Recovered CPDAG with both upper edges reversed.
recovered = bnmetrics.to_graphlike(
    np.array([
        # cols A  B  C  D
        [0, 1, 1, 0],   # A
        [2, 0, 0, 2],   # B
        [2, 0, 0, 2],   # C
        [0, 1, 1, 0],   # D
    ], dtype=np.int8),
    var_names=("A", "B", "C", "D"),
)

Single-metric calls

For interactive inspection of one metric, the standalone functions are equivalent to (and faster than) extracting the same field from a Comparison:

bnmetrics.shd(true_cpdag, recovered)               # 2
bnmetrics.hd(true_cpdag, recovered)                # 0   — skeleton-only
bnmetrics.f1(true_cpdag, recovered)                # 0.5
bnmetrics.precision(true_cpdag, recovered)         # 0.5
bnmetrics.recall(true_cpdag, recovered)            # 0.5
bnmetrics.count_reversals(true_cpdag, recovered)   # 2

The Hamming distance is zero because both graphs share the same skeleton; all error is concentrated in orientation. SHD = 2 and \(F_1 = 0.5\) together localise the discrepancy to two reversals.

Multi-metric Comparison

comp = bnmetrics.compare(true_cpdag, recovered)
comp.comparative["shd"]        # 2.0
comp.comparative["f1"]         # 0.5
comp.comparative["reversals"]  # 2.0

comp.comparative is a dictionary keyed by metric name; the available keys are additions, deletions, reversals, shd, hd, tp, fp, fn, precision, recall, f1. Descriptive metrics for each input graph are exposed on comp.g1_descriptive and comp.g2_descriptive.

Tidy DataFrame export

bnmetrics.to_dataframe flattens a Comparison into a single-row pandas.DataFrame combining descriptive and comparative metrics (requires the pandas extra):

df = bnmetrics.to_dataframe(comp)
df[["shd", "hd", "f1", "precision", "recall",
    "additions", "deletions", "reversals"]]

 shd  hd   f1  precision  recall  additions  deletions  reversals
 2.0 0.0  0.5        0.5     0.5        0.0        0.0        2.0

Variable-name alignment

bnmetrics aligns variables by name when both inputs expose var_names; otherwise it aligns positionally. A BNMDataError is raised if the two graphs have different variable counts or non-matching name sets, since silent positional alignment of inconsistently-named graphs is the most common source of subtle metric bugs.