Causal Inference - MSML610 -- Tutorials

Imports¶

%load_ext autoreload
%autoreload 2

import logging

import matplotlib.pyplot as plt
import seaborn as sns

# Set plotting style.
# TODO(gp): Is this needed?
sns.set_style("whitegrid")
plt.rcParams["figure.figsize"] = (12, 6)

# import helpers.hmodule as hmodule

# hmodule.install_module_if_not_present(
#     "networkx",
#     use_activate=True,
# )
# hmodule.install_module_if_not_present(
#     "pgmpy",
#     use_activate=True,
# )

Module 'networkx' is already installed.
Module 'pgmpy' is already installed.

import msml610_utils as ut
import L08_04_02_causal_inference_utils as mtl0cireout

ut.config_notebook()

# Initialize logger.
logging.basicConfig(level=logging.INFO)
_LOG = logging.getLogger(__name__)

pymc is not installed
arviz is not installed
preliz is not installed
sns is not installed

Python 3.12.13
Linux 38584b25ad22 6.12.67-linuxkit #1 SMP Sun Jan 25 02:26:28 UTC 2026 aarch64 GNU/Linux

import networkx as nx

import pgmpy.base as pgmpy_base

Cell 1: Causal Roles Explorer¶

Goal:

Visualize which nodes in a DAG play the role of confounders, mediators, or colliders relative to a selected treatment-outcome pair
Build intuition for how graph structure determines causal relationships

Plots:

A DAG with nodes color-coded by their causal role:
- Treatment: green
- Outcome: blue
- Confounders: orange (common ancestors of treatment and outcome)
- Mediators: purple (on a directed path from treatment to outcome)
- Colliders: red (receives arrows from both neighbors on some path)
- Other: light blue

Parameters:

Graph: select a predefined causal graph (Confounder, Mediator, Collider, etc.)
Treatment: the treatment node
Outcome: the outcome node

Key observations:

The same node can play different roles depending on the treatment-outcome pair
Conditioning on a collider opens a previously closed path (collider bias)
Conditioning on a mediator blocks the causal path from treatment to outcome

# Display interactive causal roles explorer: select a graph, treatment, and
# outcome to highlight confounders, mediators, and colliders.
mtl0cireout.cell1_causal_roles_explorer()

Cell 2: D-Separation Graph Analysis¶

Build a specific DAG and manually query d-separation properties
Demonstrate how conditioning on a node can open or close paths between nodes

model = nx.DiGraph(
    [
        ("C", "A"),
        ("C", "B"),
        ("D", "A"),
        ("B", "E"),
        ("F", "E"),
        ("A", "G"),
    ]
)

mtl0cireout.plot_graph_highlight(model)

# Convert your NetworkX graph to pgmpy DAG.
dag = pgmpy_base.DAG(model.edges())

print("Are D and C dependent?")
print(not dag.is_dconnected("D", "C"))

Are D and C dependent?
True

subgraph = mtl0cireout.reachable_subgraph(model, ["A", "D", "C"])
mtl0cireout.plot_graph_highlight(
    subgraph,
    node1="D",
    node2="C",
    conditioning_node_set=["A"],
)

print("Are D and C dependent given A?")
print(not dag.is_dconnected("D", "C", observed={"A"}))

Are D and C dependent given A?
False

print("Are D and C dependent given G?")
print(not dag.is_dconnected("D", "C", observed={"G"}))

Are D and C dependent given G?
False

print("Are G and D dependent?")
print(not dag.is_dconnected("G", "D"))

Are G and D dependent?
False

print("Are G and D dependent given A?")
print(not dag.is_dconnected("G", "D", observed=["A"]))

Are G and D dependent given A?
True

print("Are G and F dependent?")
print(dag.is_dconnected("G", "F"))

Are G and F dependent?
False

print("Are G and F dependent given E?")
print(dag.is_dconnected("G", "F", observed=["E"]))

Are G and F dependent given E?
True

Cell 3: Interactive D-Separation Explorer¶

Goal:

Interactively explore d-separation for any pair of nodes in the DAG built in Cell 2
See how adding nodes to the conditioning set opens or closes paths

Plots:

The reachable subgraph containing the selected nodes and their descendants
Nodes color-coded: node1 green, node2 blue, conditioning nodes red
Paths between node1 and node2 highlighted in orange

Parameters:

Node 1: first node to query
Node 2: second node to query
Conditioning: set of nodes to condition on (shift-click to select multiple)

Key observations:

Two nodes that are marginally independent can become dependent when conditioning on a collider between them
Two nodes that are marginally dependent can become independent when conditioning on a confounder or mediator

# Display interactive d-separation explorer for node1, node2, and conditioning
# set (use shift to select multiple conditioning nodes).
mtl0cireout.cell3_d_separation_explorer(
    model,
    dag,
)