causal_inference_public

Some of the non-proprietary work and exploration I did while at Perimeter

Overview

This repository contains research on causal inference using nonconvex quadratic programming (Gurobi) to estimate causal effects, test graphical model compatibility, and perform counterfactual reasoning when hidden confounders exist.

Main Research Areas (Favourites/)

1. Unpacking DAGs (Favourites/Unpacking DAGs/)

Transforms causal DAGs into counterfactual graphs to estimate causal intervention effects with hidden confounders. Nodes are "unpacked" into counterfactual versions (e.g., $A \rightarrow {A_0, A_1}$), using quadratic separability constraints to compute bounds on causal effects $P(Y | \text{do}(A=a))$.

Key files:

• unpacking_front_door_confounded.ipynb - Main implementation with full documentation
• GearingDemo_FrontDoorConfounded.py/ipynb - Alternative "gearing" approach
• interuption_dag_dvirs*.ipynb - Interruption DAG scenarios

2. Compatibility Testing (Favourites/Compatibility/)

Tests if observed probability distributions are compatible with specific causal graph structures (Bell DAG). Determines whether correlations $P(A,B|X,Y)$ can be explained by a classical hidden common cause using the structural equation: $P(A,B|X,Y) = \sum_\lambda P(A|X,\lambda) \cdot P(B|Y,\lambda) \cdot P(\lambda)$.

Key files:

• bell_compatibility_class.py - Reusable class for Bell compatibility testing
• Bell Compatibility.ipynb - Full implementation
• Latent Var Min Card/ - Find minimum cardinality of hidden variable needed

3. Inflation (Favourites/Inflation/)

Creates copies of a causal DAG to derive new testable constraints on probability distributions. Used for compatibility testing and causal effect estimation by relating inflated graphs back to the original via constraints.

Key files:

• ring_inflation_of_triangle_compatibility_matrix_form.ipynb - Triangle DAG ring inflation
• triangle_inflation_do_cond_diff.ipynb - Estimating intervention effects using inflation
• cut_inflation_of_triangle_compatibility_test.ipynb - Alternative inflation schemes

4. Distribution Generation (Favourites/Dist_Generation from DAG/)

Generates probability distributions compatible with specific DAG structures using deterministic strategies. Uses the 16 deterministic strategies for binary Bell scenarios as extremal points to create convex combinations.

Key files:

• generating_compatible_dists_w_Bell.ipynb - Generate Bell-compatible distributions
• generate_convex_points_for_funcs.ipynb - Generate extremal points (deterministic strategies)
• v_checker.py - Parameterized compatibility checker