[Paper Review] Causal Effect Inference with Deep Latent-Variable Models

Christos Louizos, Uri Shalit+4 more|arXiv (Cornell University)|May 24, 2017

Advanced Causal Inference Techniques39 references293 citations

TL;DR

CEVAE learns latent confounders via variational autoencoders to estimate individual and population causal effects from observational data, handling proxies for hidden confounders more robustly than prior methods.

ABSTRACT

Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal effects from observational data is the handling of confounders, factors that affect both an intervention and its outcome. A carefully designed observational study attempts to measure all important confounders. However, even if one does not have direct access to all confounders, there may exist noisy and uncertain measurement of proxies for confounders. We build on recent advances in latent variable modeling to simultaneously estimate the unknown latent space summarizing the confounders and the causal effect. Our method is based on Variational Autoencoders (VAE) which follow the causal structure of inference with proxies. We show our method is significantly more robust than existing methods, and matches the state-of-the-art on previous benchmarks focused on individual treatment effects.

Motivation & Objective

• Motivation: infer individual-level causal effects when confounders are unobserved or noisy proxies.
• Goal: estimate ITE/CATE and ATE under a latent confounder model using deep latent-variable methods.
• Aim: improve robustness to noisy proxies and hidden confounding compared with existing benchmarks.
• Develop a scalable approach that can leverage multiple proxies to identify latent confounders.

Proposed method

• Model the data with a latent variable Z representing hidden confounders.
• Use a variational autoencoder to approximate p(Z,X,t,y) from (X,t,y).
• Define p(z)=N(0,I) and p(x|z), p(t|z), p(y|t,z) with neural networks; treat t as binary.
• Infer q(z|x,t,y) via an inference network with a TARnet-like structure split by treatment.
• Optimize the variational lower bound L with an auxiliary predictive objective for t and y on new samples.
• Provide auxiliary distributions q(t|x) and q(y|x,t) to predict t and y for out-of-sample inferences.

Experimental results

Research questions

• RQ1 Can latent-variable VAEs recover the joint distribution p(Z,X,t,y) to identify causal effects from observational data?
• RQ2 Does modeling hidden confounders as latent variables improve ITE/CATE and ATE estimation when proxies are noisy?
• RQ3 How does CEVAE perform relative to state-of-the-art benchmarks on IHDP and Jobs datasets and on synthetic and Twins data?
• RQ4 Is CEVAE robust to increasing proxy noise in estimating counterfactuals and ATE?
• RQ5 Can the approach handle binary and continuous outcomes within a unified VAE framework?

Key findings

• CEVAE is competitive with state-of-the-art methods on IHDP and Jobs benchmarks.
• CEVAE shows robustness to noisy proxies and hidden confounding in synthetic toy data.
• On the Twins dataset, CEVAE with latent space outperforms methods relying directly on proxies under higher proxy noise.
• The model uses a TARnet-inspired generative structure and a block-enabled inference network to capture treatment-specific effects.
• Auxiliary predictive terms enable reliable out-of-sample treatment and outcome predictions for counterfactual estimation.