(CI) Predicting Intervention Results & PC Algorithm

Project Overview

This portfolio entry includes two projects that explore different aspects of causal inference. The first project investigates the prediction of intervention results using a Structural Causal Model (SCM), while the second focuses on causal discovery using the PC algorithm.

1. Prediction of Intervention Results Using SCM

This project aims to predict the outcomes of interventions on a causal system by modeling the relationships between variables using a Structural Causal Model (SCM).

Key Components

1. SCM Model Definition:
   • Variables (X), (Y), and (Z) represent dosage, health outcome, and genetic information, respectively.
   • Relationships among variables are defined as:
     • (Z \rightarrow X)
     • (X \rightarrow Y \leftarrow Z)
2. Generating Observational Data:
   • Observational data is generated using the model (P(X, Y, Z)), following the dependencies in the SCM.
3. Intervening on the System:
   • Interventions were made on (X) (dosage) by setting (do(X = x_i)) for specific values of (x), generating new data distributions.
   • The intervention mechanism uses random values (x_i \in {0, 2, 4, 8}) uniformly for each individual.

Comparison of Observational vs Interventional Data:

2. Causal Discovery Using the PC Algorithm

The second project applies the PC algorithm, a well-known method for discovering causal structures from observational data.

Key Components

1. Independence Testing:
   • The algorithm tests conditional independence between variables to prune non-causal edges in the graph.
   • An oracle for conditional independence testing was used to verify results against a known graph.
2. Graph Estimation:
   • The PC algorithm iteratively removes edges by checking conditional independencies.
   • The final output is a partially directed acyclic graph (DAG), which represents causal relationships.
3. Performance Evaluation:
   • The results of the algorithm were validated by comparing the discovered graph against a ground truth causal graph.
   • The accuracy of the PC algorithm was evaluated by the match between the predicted and actual causal structure.

PC Algorithm Summary:

Resources

• Code Repository:

GitHub - Prediction of interventions GitHub - PC Algorithm

• Reference Paper: “Causal Inference in Statistics: A Primer”