1. Introduction
This article covers two advanced topics: (1) using deep learning for instrumental variable estimation when treatment is endogenous and nonlinear, and (2) learning causal graph structures from observational data.
2. DeepIV: Deep Instrumental Variables
DeepIV extends IV regression to handle nonlinear, high-dimensional settings using neural networks. The method uses a two-stage approach similar to 2SLS but with flexible neural network approximations.
Stage 1: Model Treatment Distribution
Learn p(W | Z, X) using a mixture density network, where Z is the instrument.
Stage 2: Estimate Treatment Effect
Sample treatments from stage 1 and train outcome model Y ~ f(W, X).
3. Causal Discovery from Data
Causal discovery algorithms learn DAG structures from observational data. Main approaches include:
- Constraint-based: PC algorithm, FCI (use conditional independence tests)
- Score-based: GES, NOTEARS (optimize a score function over DAGs)
- Functional causal models: ANM, LiNGAM (exploit asymmetry in noise)
4. DAG Learning with Neural Networks
NOTEARS (Zheng et al., 2018) formulates DAG learning as a continuous optimization problem by characterizing acyclicity as a smooth constraint.
subject to: tr((I + ฮฑW โ W)แต) - d = 0
Where W is the adjacency matrix and the constraint ensures no cycles.
5. Key Takeaways
- โDeepIV handles nonlinear endogeneity with flexible neural approximations
- โCausal discovery algorithms can learn graph structures from data
- โNOTEARS enables continuous optimization for DAG learning
6. Next Week Preview
Module 5, Week 1: Time Series & Panel Data
We'll cover synthetic control methods, time-varying treatments, and marginal structural models for longitudinal causal inference.