Calendar
Causal Identification
- Sept 26
- Lecture Introduction Causal machine learning in practice
- Sept 28
- Lecture Potential Outcomes and DAGs
- Causal identification via the potential outcomes framework, the structural equation framework and its DAG representation. Single world intervention graphs (SWIGs) and identification by adjustment.
- Required Reading Materials
- Estimating causal effects of treatments in randomized and nonrandomized studies
- Causal Diagrams for Empirical Research (with Discussion)
- Further Reading
- Causal identification via the potential outcomes framework, the structural equation framework and its DAG representation. Single world intervention graphs (SWIGs) and identification by adjustment.
- Oct 3
- Lecture DAGs, D-separation and Identification by Conditioning
- Proof of D-separation implies conditional independence.
- Required Reading Materials
- Single World Intervention Graphs [p.1-54]
- Further Reading Materials
- Proof of D-separation implies conditional independence.
- Oct 5
- Lecture Unobserved Confounding beyond DAGs
- Causal identification in the presence of unobserved confounding beyond DAGs. Front-Door, Instrumental variables (IV), Diff-in-Diff (DiD), Regression Discontinuity Design (RDD).
- Required Reading Materials
- Identification of Causal Effects Using Instrumental Variables
- Minimum Wages and Employment: A Case Study of the Fast Food Industry in New Jersey and Pennsylvania
- Regression-discontinuity analysis: An alternative to the ex post facto experiment
- The Economic Costs of Conflict: A Case Study of the Basque Country
- Further Reading Materials
- Causal identification in the presence of unobserved confounding beyond DAGs. Front-Door, Instrumental variables (IV), Diff-in-Diff (DiD), Regression Discontinuity Design (RDD).
- Oct 10
- Lecture Unobserved Confounding beyond DAGs
- Causal identification in the presence of unobserved confounding beyond DAGs. Front-Door, Instrumental variables (IV), Diff-in-Diff (DiD), Regression Discontinuity Design (RDD) (syntheti controls?).
- Required Reading Materials
- Causal identification in the presence of unobserved confounding beyond DAGs. Front-Door, Instrumental variables (IV), Diff-in-Diff (DiD), Regression Discontinuity Design (RDD) (syntheti controls?).
Semi-Parametric Inference and Causal Estimation
- Oct 12
- Lecture Background: Convergence in Probability, Concentration of Measure and Central Limit Theorem
- Oct 15
- Project Proposal Due
- Oct 17
- Lecture Semi-Parametric Inference and Neyman Orthogonality
- Estimation via moment conditions. Neyman orthogonality and Debiased Machine Learning. Proof of asymptotic linearity for Neyman orthogonal moments with sample splitting and without sample splitting. Automatic Debiased Machine Learning and proof. Proof of the Lasso rate. Discuss the multiplier bootstrap for joint inference.
- Required Reading Materials
- Double/debiased machine learning for treatment and structural parameters
- Debiased Machine Learning without Sample-Splitting for Stable Estimators
- Further Reading Materials
- Adjusting for Nonignorable Drop-Out Using Semiparametric Nonresponse Models
- Automatic Debiased Machine Learning via Neural Nets for Generalized Linear Regression
- High-dimensional econometrics and regularized GMM
- Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiency
- Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency
- RieszNet and ForestRiesz
- Estimation via moment conditions. Neyman orthogonality and Debiased Machine Learning. Proof of asymptotic linearity for Neyman orthogonal moments with sample splitting and without sample splitting. Automatic Debiased Machine Learning and proof. Proof of the Lasso rate. Discuss the multiplier bootstrap for joint inference.
- Oct 19
- Lecture Identification and Inference in Dynamic Regimes
- Identification and inference of dynamic counterfactual policies (non-parametric and semi-parametric). Estimation of optimal dynamic regimes and g-estimation. Identification proof. Auto-DML and proof for dynamic regime
- Required Reading Materials
- Double/Debiased Machine Learning for Dynamic Treatment Effects via g-Estimation
- Automatic Debiased Machine Learning for Dynamic Treatment Effects and General Nested Functionals
- Further Reading Materials
- Identification and inference of dynamic counterfactual policies (non-parametric and semi-parametric). Estimation of optimal dynamic regimes and g-estimation. Identification proof. Auto-DML and proof for dynamic regime
- Oct 24
- Lecture Identification and Inference with Proxies and Instruments
- Identification and inference of average treatment effects with unobserved confounding when we have access to either proxy controls or instrumental varialbes
- Required Reading Materials
- Further Reading Materials
- Identification and inference of average treatment effects with unobserved confounding when we have access to either proxy controls or instrumental varialbes
Estimation and Inference on Causal Functions
- Oct 26
- Lecture Background: Concentration Inequalities and Rademacher Complexity
- Oct 31
- Lecture Statistical Learning Theory for Heterogeneous Effects
- Orthogonal statistical learning theory. Localized rademacher complexities and generalization bounds.
- Required Reading Materials
- Orthogonal Statistical Learning
- Machine Learning Estimation of Heterogeneous Treatment Effects with Instruments
- Further Reading Materials
- Orthogonal statistical learning theory. Localized rademacher complexities and generalization bounds.
- Nov 2
- Lecture Background: U-Statistics and Concentration
- Nov 7
- Lecture Non-Parametric Confidence Intervals with Random Forests
- Non-parametric confidence intervals, random forests and nearest neighbors. Proof of asymptotic linearity for kernel based moment estimators. Proof of bias for k-NN and (maybe proof of bias for Trees). Proof of confidence intervals with nuisance parameters and local orthogonality.
- Required Reading Materials
- Orthogonal Random Forest for Causal Inference
- Non-Parametric Inference Adaptive to Intrinsic Dimension
- Further Reading Materials
- Non-parametric confidence intervals, random forests and nearest neighbors. Proof of asymptotic linearity for kernel based moment estimators. Proof of bias for k-NN and (maybe proof of bias for Trees). Proof of confidence intervals with nuisance parameters and local orthogonality.
- Nov 9
- Lecture Non-Parametric Learning and Conditional Moment Restrictions
- Adversarial estimators for conditional moment restrictions. Statistical learning theory for adversarial estimators. Confidence intervals on functionals of endogenous regression functions. Proof of the rate for adversarial estimators based on the localized complexities. Proof of the auto-debiased approach for functionals of endogenous regressions.
- Required Reading Materials
- Minimax Estimation of Conditional Moment Models
- Inference on Strongly Identified Functionals of Weakly Identified Functions
- Further Reasing Materials
- Adversarial estimators for conditional moment restrictions. Statistical learning theory for adversarial estimators. Confidence intervals on functionals of endogenous regression functions. Proof of the rate for adversarial estimators based on the localized complexities. Proof of the auto-debiased approach for functionals of endogenous regressions.
Sensitivity Analysis and Causal ML
- Nov 14
- Lecture Omitted variable bias
- Omitted variable bias in semi-parametric and non-parametric models. Inference on bias bounds
- Required Reading Materials
- Making Sense of Sensitivity: Extending Omitted Variable Bias
- Long Story Short: Omitted Variable Bias in Causal Machine Learning
- Further Reading Materials
- Sensitivity Analysis Without Assumptions
- Sensitivity analysis with the R^2 calculus
- An Omitted Variable Bias Framework for Sensitivity Analysis of Instrumental Variables
- Sensitivity Analysis in Observational Research: Introducing the E-Value
- Partial Identification of Treatment Effects with Implicit Generative Models
- Omitted variable bias in semi-parametric and non-parametric models. Inference on bias bounds
Representation Learning and Causal Inference
- Nov 16
- Lecture Linear and Non-Linear ICA
- Linear and Non-Linear Independent Component Analysis. Impossibilities and possibilities in non-linear causal representation learning.
- Required Reading Materials
- Towards Causal Representation Learning
- Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations
- Further Reading Materials
- Independent component analysis: algorithms and applications
- Independent component analysis: recent advances
- Invariant Risk Minimization
- The Risks of Invariant Risk Minimization
- Learning Counterfactually Invariant Predictors
- Efficient Conditionally Invariant Representation Learning
- Invariant Causal Representation Learning for Out-of-Distribution Generalization
- Linear and Non-Linear Independent Component Analysis. Impossibilities and possibilities in non-linear causal representation learning.
- Nov 17
- Literature Review Due
Causal Discovery
- Nov 28
- Lecture Theoretical Results in Causal Discovery
- Linear ICA and discovery; LinGAM (proof of identification). Causal discovery with unobserved confounding (FCI). Conditional independence testing.
- https://github.com/stanford-msande328/spring23/blob/main/LinGAM.ipynb
- Required Reading Materials
- A Linear Non-Gaussian Acyclic Model for Causal Discovery
- The Hardness of Conditional Independence Testing and the Generalised Covariance Measure
- Further Reading Materials
- Causal Inference in the Presence of Latent Variables and Selection Bias
- Kernel-based Conditional Independence Test and Application in Causal Discovery
- Pairwise Likelihood Ratios for Estimation of Non-Gaussian Structural Equation Models
- Nonlinear causal discovery with additive noise models
- Review of Causal Discovery Methods Based on Graphical Models
- LinGAM Survey
- The Weighted Generalised Covariance Measure
- Estimation of causal effects using linear non-Gaussian causal models with hidden variables and Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables
- Scalable Causal Discovery with Score Matching and Score-based Causal Representation Learning with Interventions
- Valid Inference after Causal Discovery
- Linear ICA and discovery; LinGAM (proof of identification). Causal discovery with unobserved confounding (FCI). Conditional independence testing.
Student Presentations
- Nov 30, Dec 5, 7
- Student Presentations
- Dec 15
- Final Project Due