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Treatment effect estimation with disentangled latent factors

Weijia Zhang, Lin Liu, Jiuyong Li

arXiv:2001.10652v3cs.LGstat.ML

TL;DR

Observational treatment-effect estimation is complicated by hidden confounders, noisy proxies, and observed variables that are not confounders. TEDVAE infers latent factors and separates instrumental, confounding, and risk factors; experiments report better performance than compared baselines across synthetic, benchmark, and real-world datasets.

  • Problem

    Observed variables may include hidden confounders inferred through noisy proxies as well as unnecessary covariates, creating a dilemma between omitting confounders and inefficiently including variables that are not confounders.

    Source: Introduction · p. 1

  • Method

    TEDVAE uses a variational approach to infer latent factors from proxy variables and disentangle them into instrumental, confounding, and risk factors for treatment-effect estimation.

    Source: Introduction · pp. 1–2

  • Results

    Experiments on synthetic, benchmark, and real-world datasets report that TEDVAE significantly outperforms compared baselines.

    Source: Conclusion · p. 7

  • Takeaways & Limitations

    The framework includes the all-confounder case, in which its diagram becomes identical to a widely used treatment-effect diagram.

    Source: Treatment Effect Estimation from… · p. 3

    Evaluation focuses on binary treatments because the authors lack datasets with continuous treatment variables, leaving that case for future work.

    Source: Treatment Effect Estimation from… · p. 3

Abstract

from arXiv · show

Much research has been devoted to the problem of estimating treatment effects from observational data; however, most methods assume that the observed variables only contain confounders, i.e., variables that affect both the treatment and the outcome. Unfortunately, this assumption is frequently violated in real-world applications, since some variables only affect the treatment but not the outcome, and vice versa. Moreover, in many cases only the proxy variables of the underlying confounding factors can be observed. In this work, we first show the importance of differentiating confounding factors from instrumental and risk factors for both average and conditional average treatment effect estimation, and then we propose a variational inference approach to simultaneously infer latent factors from the observed variables, disentangle the factors into three disjoint sets corresponding to the instrumental, confounding, and risk factors, and use the disentangled factors for treatment effect estimation. Experimental results demonstrate the effectiveness of the proposed method on a wide range of synthetic, benchmark, and real-world datasets.

Introduction

Treatment-effect estimation from observational data depends on accounting for confounders, which may be hidden and inferred only through noisy proxies. TEDVAE addresses the resulting adjustment dilemma by inferring latent factors and separating confounding factors from treatment-only and outcome-only factors.

Introduction

  • Including unnecessary covariates can reduce estimation efficiency, while excluding confounders or their proxies can increase bias.The dilemma becomes especially pressing in high-dimensional settings, where many observed variables may not be confounders.Source: Introduction · p. 1
  • TEDVAE infers latent factors from proxy variables and separates them into instrumental, confounding, and risk factors.Instrumental factors affect treatment only, risk factors affect outcome only, and confounding factors affect both.Source: Introduction · p. 1, Figure 1 · p. 2
  • The approach targets settings where observed variables include confounders, noisy proxies of confounders, and variables that do not confound treatment and outcome.Source: Introduction · p. 2
  • The paper reports validating TEDVAE on synthetic datasets, treatment-effect benchmarks, and real-world datasets.Source: Introduction · p. 2

Related Work

Prior work includes tree-based, ensemble, meta-algorithm, and representation-learning approaches to treatment-effect estimation. The paper distinguishes TEDVAE from these approaches by its treatment of non-confounders and proxy-inferred latent factors.

Related Work

  • Treatment-effect methods surveyed include tree-based splitting criteria, ensembles, and meta-algorithms such as Causal Forest and X-Learner (Su et al. 2009; Athey and Imbens 2016; Zhang et al. 2017, 2018; K¨unzel et al. 2019; Wager and Athey 2018).Source: Related Work · p. 2
  • Representation-learning methods bring treated and untreated samples closer, but do not separate treatment-only from outcome-only covariates or infer latent covariates from proxies.The cited examples include Counterfactual Regression Net and related methods (Shalit, Johansson, and Sontag 2017; Yao et al. 2018; Hassanpour and Greiner 2018).Source: Related Work · p. 2
  • Variable-decomposition methods for average treatment effects model linear proxy relationships, whereas the authors say their method also estimates individual heterogeneous effects and models nonlinear relationships (Kun et al. 2017; H¨aggstr¨om 2017).Source: Related Work · p. 2
  • CEVAE learns confounders from observed variables but does not account for non-confounders or learn separate instrumental and risk factors.The paper states that disentangling factors significantly improves performance.Source: Related Work · p. 2

Method

TEDVAE separates instrumental, confounding, and risk factors so treatment effects can be estimated using the relevant latent factors. It infers these factors from observed covariates with a variational autoencoder and auxiliary classifiers.

Preliminaries

  • The framework assumes SUTVA, unconfoundedness, and overlap, and distinguishes observed covariates from the two potential outcomes, only one of which is observed per individual.It defines ATE as the population mean difference between potential outcomes and CATE as the expected individual effect conditional on covariates.Source: Preliminaries · pp. 2–3

Treatment Effect Estimation from Latent Factors

  • ATE is identifiable if the confounding factors zc are recovered, while CATE additionally requires recovering the risk factors zy.The treatment-effect calculation uses the back-door criterion; variables unrelated to the outcome can increase estimation bias and variance.Source: Treatment Effect Estimation from… · p. 3
  • The framework allows continuous treatments in principle, but the authors evaluate binary treatment because datasets with continuous treatments are lacking.They leave evaluation of continuous treatment for future work.Source: Treatment Effect Estimation from… · p. 3

Learning of the Disentangled Latent Factors

  • TEDVAE infers three latent factor sets from x using separate variational encoders and a shared decoder that reconstructs x.The model also represents treatment and outcome generation; two auxiliary classifiers predict treatment from (zt, zc) and outcome from (zy, zc) to encourage disentanglement.Source: Learning of the Disentangled Latent… · pp. 3–4, Figure 2 · p. 4
  • Unlike CEVAE, TEDVAE infers latent factors from x alone, and estimates new-subject CATEs by sampling confounding and risk factors and averaging predicted outcomes.For continuous outcomes, separate networks represent the treated and control outcome distributions, allowing for highly imbalanced treatment.Source: Learning of the Disentangled Latent… · pp. 4–5

Experiments

Across synthetic, benchmark, and real-world evaluations, TEDVAE performs better than compared methods and is less sensitive to parameter choice. The experiments assess latent-factor recovery and treatment-effect estimation under varied synthetic settings and benchmark datasets.

Evaluation Criteria

Synthetic Datasets

  • With instrumental and risk factors present, TEDVAE’s PEHE remains stable under treatment imbalance and is significantly lower than CEVAE’s as treatment proportions, outcome scale, and CATE size vary.Figure 3’s first row corresponds to this setting; its columns vary treated-sample proportion, outcome size, and CATE size.Source: Synthetic Datasets · p. 5, Figure 3 · p. 5
  • When instrumental and risk factors are absent, TEDVAE performs better than or as well as CEVAE across a wide range of parameters and is robust to latent-dimensionality choice.The authors suggest differences in prediction for unseen samples may explain this pattern.Source: Synthetic Datasets · pp. 5–6
  • TEDVAE performs significantly better when latent dimensions are nonzero than when any one factor set is ignored, supporting its ability to recover the generating factors.Figure 4 compares TEDVAE with nonzero dimensions against versions with one dimension set to zero.Source: Synthetic Datasets · p. 6, Figure 4 · p. 6

Benchmark I: 2016 Atlantic Causal Inference Challenge

  • On ACIC2016, TEDVAE significantly outperforms compared methods and achieves state-of-the-art performance across 77 settings without tuning parameters separately for each setting.Table 1 reports training- and test-set PEHE means and standard deviations across the 77 benchmark datasets.Source: Benchmark I: 2016 Atlantic Causal… · p. 6, Table 1 · p. 6

Benchmark II: Infant Health Development Program

  • On both IHDP settings, TEDVAE has the lowest PEHE among compared methods, with Wilcoxon signed-rank tests indicating significant superiority.TEDVAE uses the same parameters as on ACIC2016; Table 2 reports PEHE means and standard deviations.Source: Benchmark II: Infant Health… · p. 7, Table 2 · p. 7

Real-world Dataset: Twins

  • On the Twins dataset, TEDVAE achieves the best ATE-estimation performance, with the smallest ϵATE among compared algorithms.The evaluation uses 4,813 samples after exclusions and selection-bias induction, averaging results over 100 replications.Source: Real-world Dataset: Twins · p. 7, Table 3 · p. 7

Experiments

  • TEDVAE significantly outperforms compared methods across synthetic, benchmark, and real-world datasets, with lower sensitivity to parameter choice among deep-learning methods.The authors identify this as making TEDVAE attractive for real-world application scenarios.Source: Real-world Dataset: Twins · p. 7

Conclusion

TEDVAE disentangles instrumental, confounding, and risk factors from observed variables, and significantly outperforms compared baselines across synthetic, benchmark, and real-world datasets. Its generative model motivates future work on continuous-treatment estimation.

  • TEDVAE infers and disentangles instrumental, confounding, and risk factors from observed variables for treatment-effect estimation.Source: Conclusion · p. 7
  • Experiments across synthetic, benchmark, and real-world datasets show that TEDVAE significantly outperforms compared baselines.Source: Conclusion · p. 7
  • The authors identify extending TEDVAE to continuous treatments as future work, citing its generative model as a promising basis.Source: Conclusion · p. 7

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