Causal Structure & Dynamic Matrices

Stage II, Course 6 · 4 credits · 14 weeks · Formalize causality and prove non-collapsibility

Course Purpose

Students learn to formalize causality mathematically. Every causal relationship can be represented as a directed edge in a graph, and every causal graph can be represented as a matrix. The lower-triangular form of this matrix mathematically proves non-collapsibility.

By end: Students can translate from system description to causal graph to matrix, understand topological ordering, prove stability from eigenvalues, and verify mathematically that channel separation is maintained.

Learning Outcomes

1. Draw causal graphs — edges as influence, cycles as feedback
2. Translate causal graphs to matrices — adjacency and weighted matrices
3. Perform topological ordering — order nodes to expose causality
4. Prove lower-triangular structure — how DAGs guarantee non-collapsibility
5. Analyze eigenvalues and stability — behavior from structure
6. Identify cycles and their effects — positive vs. negative feedback
7. Understand multi-scale causality — causality at different hierarchical levels
8. Test causal hypotheses empirically — intervention calculus basics

Core Concepts

causality, causal-graph, DAG, adjacency-matrix, topological-order, lower-triangular, feedback, cycle, eigenvalue, stability, multi-scale-causality

Course Structure (14 weeks)

← Back to Stage II