Causal Effect Inference with Deep Latent-Variable Models
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This document summarizes a presentation on causal effect inference with deep latent-variable models. It introduces the Causal Effect Variational Autoencoder (CEVAE) model, which uses neural networks to parameterize a causal graph as a latent variable model. The CEVAE aims to identify individual treatment effects by learning a latent representation of confounding variables from data. The document describes the CEVAE methodology and objectives, and reports on experiments applying it to benchmark datasets where it achieved improved performance over baselines at estimating average treatment effects and counterfactual outcomes.
![Introduction
y
t
Z
X
# of deaths
Medicine
Socio-economic status
Average income
Q] Is this reasonable?](https://image.slidesharecdn.com/cs59220causaleffectinferencewithdeeplatent-variablemodels-190528054918/85/Causal-Effect-Inference-with-Deep-Latent-Variable-Models-5-320.jpg)
![Introduction
y
t
Z
X
# of deaths
MedicineAverage income
Q] Isn’t this more general?
Socio-economic status](https://image.slidesharecdn.com/cs59220causaleffectinferencewithdeeplatent-variablemodels-190528054918/85/Causal-Effect-Inference-with-Deep-Latent-Variable-Models-6-320.jpg)
![Introduction
y
t
Z
X
# of deaths
MedicineAverage income
Q] Isn’t this more general?
Could be, but X is just a noisy
view on Z. → We can say “only
Z can cause y and t”.
Socio-economic status](https://image.slidesharecdn.com/cs59220causaleffectinferencewithdeeplatent-variablemodels-190528054918/85/Causal-Effect-Inference-with-Deep-Latent-Variable-Models-7-320.jpg)
![Introduction
y
t
Z
X
# of deaths
Medicine
Q] How about this case?
Socio-economic status
Average income](https://image.slidesharecdn.com/cs59220causaleffectinferencewithdeeplatent-variablemodels-190528054918/85/Causal-Effect-Inference-with-Deep-Latent-Variable-Models-8-320.jpg)
![Introduction
y
t
Z
X
# of deaths
MedicineAverage consumption
Q] How about this case?
Socio-economic status](https://image.slidesharecdn.com/cs59220causaleffectinferencewithdeeplatent-variablemodels-190528054918/85/Causal-Effect-Inference-with-Deep-Latent-Variable-Models-9-320.jpg)
![Experiment 3 - Binary treatment outcome on Twins
● inferring the mortality of the unobserved twin (counterfactual)
● nh = number of hidden
layers
● in CEVAE cases,
larger nh, better AUC
Q: “TARnet (nh=0) == LR2“, but
Why are [CEVAE nh=0] and
[LR2] performing differently
when more proxy noisy level?](https://image.slidesharecdn.com/cs59220causaleffectinferencewithdeeplatent-variablemodels-190528054918/85/Causal-Effect-Inference-with-Deep-Latent-Variable-Models-38-320.jpg)
![Experiment 3 - Binary treatment outcome on Twins
● inferring the mortality of the unobserved twin (counterfactual)
● nh = number of hidden
layers
● in CEVAE cases,
larger nh, better AUC
Q: “TARnet (nh=0) == LR2“, but
Why are [CEVAE nh=0] and
[LR2] performing differently
when more proxy noisy level?
● LR2 rely directly on the
noisy proxies instead of
the inferred latent state.](https://image.slidesharecdn.com/cs59220causaleffectinferencewithdeeplatent-variablemodels-190528054918/85/Causal-Effect-Inference-with-Deep-Latent-Variable-Models-39-320.jpg)
Causal Effect Inference with Deep Latent-Variable Models
- 1. CS592 Presentation #20 Causal Effect Inference with Deep Latent-Variable Models 20173586 Jeongmin Cha 20193168 Hyunsu Kim 20183239 Jongjin Park C. Louizos, U. Shalit, J. Mooij, D. Sontag, R. Zemel and M. Welling
- 2. Contents 1. Introduction 2. Identification of causal effect 3. Causal effect variational autoencoder 4. Experiments 5. Group Discussion Point
- 4. Introduction y t Z X # of deaths MedicineAverage income Socio-economic status
- 5. Introduction y t Z X # of deaths Medicine Socio-economic status Average income Q] Is this reasonable?
- 6. Introduction y t Z X # of deaths MedicineAverage income Q] Isn’t this more general? Socio-economic status
- 7. Introduction y t Z X # of deaths MedicineAverage income Q] Isn’t this more general? Could be, but X is just a noisy view on Z. → We can say “only Z can cause y and t”. Socio-economic status
- 8. Introduction y t Z X # of deaths Medicine Q] How about this case? Socio-economic status Average income
- 9. Introduction y t Z X # of deaths MedicineAverage consumption Q] How about this case? Socio-economic status
- 10. Introduction y t Z X # of deaths MedicineAverage income Socio-economic status
- 11. Identification of Causal Effect ● Individual Treatment Effect (ITE) ● Example) “How will the number of deaths(y) vary if we do(t=1) or do not(t=0) treat the poor(Z), whose annual salary(X) is about 10,000 dollars?”
- 12. Do-Calculus ● What if we set X to x ? ● Interventional probability is generally not the same with conditional probability. ● Example) X Y X Y
- 13. Problem Setup y t=1 Z X ( The case for t=0 is identical ) Bayes’ rule Do-calculus
- 14. When ‘t’ causes ‘X’ y t=1 Z X Bayes’ rule Do-calculus ( The case for t=0 is identical )
- 15. Causal effect variational autoencoder Parametrize the causal graph as a latent variable model with neural networks Encoder : model q(z|x,t,y) Decoder : model p(x|z) Inference Network Model Network
- 16. Causal effect variational autoencoder ● Assume the observations factorize conditioned on the latent variables Model Network
- 17. Causal effect variational autoencoder ● First, compute the distribution p(t|z) and sample t ● Next, compute p(y|t,z) and sample y ○ For a continuous outcome: Gaussian distribution ○ For a discrete outcome: Bernoulli distribution. ● Then compute p(x|z) for reconstruction Model Network
- 18. Causal effect variational autoencoder Neural networks outputs the parameters of a posterior approximation over the latent variables z, e.g. a Gaussian x y t Inference Network q(z|x,t=0,y) q(z|x,t=1,y) For the mean parameters For the variance parameters
- 19. Causal effect variational autoencoder The objective from original VAE - ELBO x y t Inference NetworkModel Network q(z|x,t=0,y) q(z|x,t=1,y)
- 20. ○ For a continuous outcome: Gaussian distribution ○ For a discrete outcome: Bernoulli distribution. Causal effect variational autoencoder ● We need two auxiliary distributions that predict t, y for new samples. Inference Network
- 21. ● ELBO term ● The Objective of the Causal Effect Variational Autoencoder (CEVAE) Causal effect variational autoencoder Q: Why this two extra terms are needed?
- 22. ● The Objective of the Causal Effect Variational Autoencoder (CEVAE) Causal effect variational autoencoder Q: Why this two extra terms are needed? ● For unseen data x, we require to know the treatment assignment t and outcome y before inferring the distribution over z. ● So we need two auxiliary distributions that predict t, y for new samples, and two extra terms are for estimating the parameters of these distributions.
- 23. Experiment - Dataset Three main experiment in the present paper 1. Two existing benchmark datasets ● IHDP (Infant Health and Development Program), Jobs 2. a synthetic toy dataset 3. Introduce a new benchmark ● based on twin births and deaths in the USA
- 24. Experiment - Implementation ● neural network architecture ○ 3 hidden layers NN with ELU nonlinearities ■ approximate posterior over the latent variables q(Z|X,t,y) ■ generative model p(X|Z) ■ outcome models p(y|t, Z), q(y|t, X). ○ a single hidden layer NN with ELU nonlinearities ■ Treatment models p(t|Z), q(t|X) ● latent variable ○ 20 dimensional latent variable z ○ weight decay term for all of the parameters
- 25. Experiment - Baseline models ● LR1 = logistic regression ● LR2 = two separate logistic regressions fit ○ to treated (t=1) ○ to control (t=0) ● TARnet ○ FFNN for causal inference
- 26. Experiment 1 - Benchmark datasets ● IHDP (Infant Health and Development Program) ● effect of home visits by specialists on future cognitive test scores ● Metrics ○ PEHE (Precision in Estimation of Heterogeneous Effect) ○ absolute error on ATE (Average Treatment Effect)
- 27. Experiment 1 - Benchmark datasets
- 28. Experiment 1 - Benchmark datasets ● the effect of job training (treatment) on employment after training (outcome) ● Metrics ○ absolute error on Average Treatment effect on the Treated (ATT) ○ Policy risk ■ acts as a proxy to the individual treatment effect.
- 29. Experiment 1 - Benchmark datasets
- 30. Experiment 2 - Synthetic experiment on toy data ● the marginal distribution of X is a mixture of Gaussians ● the hidden variable Z is determining the mixture component ● latent variable z => binary variable ● How models can imitate the true latent variable well
- 31. Experiment 2 - Synthetic experiment on toy data ● CEVAE bin: 5-dim binary latent z ○ latent model is correctly specified ○ better with all sample size
- 32. Experiment 2 - Synthetic experiment on toy data ● CEVAE cont: 5-dim continuous latent z ○ latent model is not correctly specified ● We require more samples for the latent space to imitate more closely the true latent variable
- 33. Experiment 3 - Binary treatment outcome on Twins ● Introduce a new benchmark dataset about twin births in the USA ● t = 1 ○ being born the heavier than the other. ● Y (outcome) ○ mortality of each of the twins in their first year of life ● Z (latent variable) ○ the number of gestation weeks (20 weeks, 20-27, 27-34, …) 10 categories ● X (proxy variables) ○ noisy view of Z ○ encoded vector (Z) flipped with a probability of 0.05-0.5 ○ 0.5 flip means no direct information from Z
- 34. Experiment 3 - Binary treatment outcome on Twins ● inferring the mortality of the unobserved twin (counterfactual)
- 35. Experiment 3 - Binary treatment outcome on Twins ● inferring the mortality of the unobserved twin (counterfactual) Q: Why does all methods perform similarly when the proxy noise is small?
- 36. Experiment 3 - Binary treatment outcome on Twins ● inferring the mortality of the unobserved twin (counterfactual) Q: Why does all methods perform similarly when the proxy noise is small? ● X ≃ Z ● Only CEVAE uses Z ● The others use only X ● Z (the gestation length feature) is very informative
- 37. Experiment 3 - Binary treatment outcome on Twins ● inferring the mortality of the unobserved twin (counterfactual) ● nh = number of hidden layers ● in CEVAE cases, larger nh, better AUC
- 38. Experiment 3 - Binary treatment outcome on Twins ● inferring the mortality of the unobserved twin (counterfactual) ● nh = number of hidden layers ● in CEVAE cases, larger nh, better AUC Q: “TARnet (nh=0) == LR2“, but Why are [CEVAE nh=0] and [LR2] performing differently when more proxy noisy level?
- 39. Experiment 3 - Binary treatment outcome on Twins ● inferring the mortality of the unobserved twin (counterfactual) ● nh = number of hidden layers ● in CEVAE cases, larger nh, better AUC Q: “TARnet (nh=0) == LR2“, but Why are [CEVAE nh=0] and [LR2] performing differently when more proxy noisy level? ● LR2 rely directly on the noisy proxies instead of the inferred latent state.
- 40. Experiment 3 - Binary treatment outcome on Twins ● inferring the average treatment effect ● CEVAE nh=0: not so good ● CEVAE is robust with increasing proxy noise
- 41. Group Discussion Point Balancing Neural Network (BNN) vs. CEVAE
- 42. Group Discussion Point Balancing Neural Network (BNN) vs. CEVAE - Model choice - Discriminative model vs. Generative model - CEVAE learns latent variable z (i.e. unobserved confounder), which BNN does not learn - Architecture - CEVAE split outputs for each treatment group in t after a shared representation BNN CEVAE (~ TARnet architecture) It can learn the difference of t more explicitly
- 43. Thank you