Normalizing Flows for Interventional Density Estimation

Existing machine learning methods for causal inference usually estimate quantities expressed via the mean of potential outcomes (e.g., average treatment effect). However, such quantities do not capture the full information about the distribution of potential outcomes. In this work, we estimate the density of potential outcomes after Interventional Normalizing Flows. Specifically, we combine two normalizing flows, namely (i) a teacher flow for estimating nuisance parameters and (ii) a student flow for a parametric estimation of the density of potential outcomes. We further develop a tractable optimization objective via a one-step bias correction for an efficient and doubly robust estimation of the student flow parameters. As a result our Interventional Normalizing Flows offer a properly normalized density estimator. Across various experiments, we demonstrate that our Interventional Normalizing Flows are expressive and highly effective, and scale well with both sample size and high-dimensional confounding. To the best of our knowledge, our Interventional Normalizing Flows are the first fully-parametric, deep learning method for density estimation of potential outcomes

Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model

Counterfactual inference aims to answer retrospective ''what if'' questions and thus belongs to the most fine-grained type of inference in Pearl's causality ladder. Existing methods for counterfactual inference with continuous outcomes aim at point identification and thus make strong and unnatural assumptions about the underlying structural causal model. In this paper, we relax these assumptions and aim at partial counterfactual identification of continuous outcomes, i.e., when the counterfactual query resides in an ignorance interval with informative bounds. We prove that, in general, the ignorance interval of the counterfactual queries has non-informative bounds, already when functions of structural causal models are continuously differentiable. As a remedy, we propose a novel sensitivity model called Curvature Sensitivity Model. This allows us to obtain informative bounds by bounding the curvature of level sets of the functions. We further show that existing point counterfactual identification methods are special cases of our Curvature Sensitivity Model when the bound of the curvature is set to zero. We then propose an implementation of our Curvature Sensitivity Model in the form of a novel deep generative model, which we call Augmented Pseudo-Invertible Decoder. Our implementation employs (i) residual normalizing flows with (ii) variational augmentations. We empirically demonstrate the effectiveness of our Augmented Pseudo-Invertible Decoder. To the best of our knowledge, ours is the first partial identification model for Markovian structural causal models with continuous outcomes

Fair Off-Policy Learning from Observational Data

Algorithmic decision-making in practice must be fair for legal, ethical, and societal reasons. To achieve this, prior research has contributed various approaches that ensure fairness in machine learning predictions, while comparatively little effort has focused on fairness in decision-making, specifically off-policy learning. In this paper, we propose a novel framework for fair off-policy learning: we learn decision rules from observational data under different notions of fairness, where we explicitly assume that observational data were collected under a different potentially discriminatory behavioral policy. For this, we first formalize different fairness notions for off-policy learning. We then propose a neural network-based framework to learn optimal policies under different fairness notions. We further provide theoretical guarantees in the form of generalization bounds for the finite-sample version of our framework. We demonstrate the effectiveness of our framework through extensive numerical experiments using both simulated and real-world data. Altogether, our work enables algorithmic decision-making in a wide array of practical applications where fairness must be ensured.Comment: Revised versio

Sharp Bounds for Generalized Causal Sensitivity Analysis

Causal inference from observational data is crucial for many disciplines such as medicine and economics. However, sharp bounds for causal effects under relaxations of the unconfoundedness assumption (causal sensitivity analysis) are subject to ongoing research. So far, works with sharp bounds are restricted to fairly simple settings (e.g., a single binary treatment). In this paper, we propose a unified framework for causal sensitivity analysis under unobserved confounding in various settings. For this, we propose a flexible generalization of the marginal sensitivity model (MSM) and then derive sharp bounds for a large class of causal effects. This includes (conditional) average treatment effects, effects for mediation analysis and path analysis, and distributional effects. Furthermore, our sensitivity model is applicable to discrete, continuous, and time-varying treatments. It allows us to interpret the partial identification problem under unobserved confounding as a distribution shift in the latent confounders while evaluating the causal effect of interest. In the special case of a single binary treatment, our bounds for (conditional) average treatment effects coincide with recent optimality results for causal sensitivity analysis. Finally, we propose a scalable algorithm to estimate our sharp bounds from observational data.Comment: Accepted at NeurIPS 202

Reliable Off-Policy Learning for Dosage Combinations

Decision-making in personalized medicine such as cancer therapy or critical care must often make choices for dosage combinations, i.e., multiple continuous treatments. Existing work for this task has modeled the effect of multiple treatments independently, while estimating the joint effect has received little attention but comes with non-trivial challenges. In this paper, we propose a novel method for reliable off-policy learning for dosage combinations. Our method proceeds along three steps: (1) We develop a tailored neural network that estimates the individualized dose-response function while accounting for the joint effect of multiple dependent dosages. (2) We estimate the generalized propensity score using conditional normalizing flows in order to detect regions with limited overlap in the shared covariate-treatment space. (3) We present a gradient-based learning algorithm to find the optimal, individualized dosage combinations. Here, we ensure reliable estimation of the policy value by avoiding regions with limited overlap. We finally perform an extensive evaluation of our method to show its effectiveness. To the best of our knowledge, ours is the first work to provide a method for reliable off-policy learning for optimal dosage combinations.Comment: Accepted at NeurIPS 202

Counterfactual Fairness for Predictions using Generative Adversarial Networks

Fairness in predictions is of direct importance in practice due to legal, ethical, and societal reasons. It is often achieved through counterfactual fairness, which ensures that the prediction for an individual is the same as that in a counterfactual world under a different sensitive attribute. However, achieving counterfactual fairness is challenging as counterfactuals are unobservable. In this paper, we develop a novel deep neural network called Generative Counterfactual Fairness Network (GCFN) for making predictions under counterfactual fairness. Specifically, we leverage a tailored generative adversarial network to directly learn the counterfactual distribution of the descendants of the sensitive attribute, which we then use to enforce fair predictions through a novel counterfactual mediator regularization. If the counterfactual distribution is learned sufficiently well, our method is mathematically guaranteed to ensure the notion of counterfactual fairness. Thereby, our GCFN addresses key shortcomings of existing baselines that are based on inferring latent variables, yet which (a) are potentially correlated with the sensitive attributes and thus lead to bias, and (b) have weak capability in constructing latent representations and thus low prediction performance. Across various experiments, our method achieves state-of-the-art performance. Using a real-world case study from recidivism prediction, we further demonstrate that our method makes meaningful predictions in practice

Estimating average causal effects from patient trajectories

In medical practice, treatments are selected based on the expected causal effects on patient outcomes. Here, the gold standard for estimating causal effects are randomized controlled trials; however, such trials are costly and sometimes even unethical. Instead, medical practice is increasingly interested in estimating causal effects among patient (sub)groups from electronic health records, that is, observational data. In this paper, we aim at estimating the average causal effect (ACE) from observational data (patient trajectories) that are collected over time. For this, we propose DeepACE: an end-to-end deep learning model. DeepACE leverages the iterative G-computation formula to adjust for the bias induced by time-varying confounders. Moreover, we develop a novel sequential targeting procedure which ensures that DeepACE has favorable theoretical properties, i.e., is doubly robust and asymptotically efficient. To the best of our knowledge, this is the first work that proposes an end-to-end deep learning model tailored for estimating time-varying ACEs. We compare DeepACE in an extensive number of experiments, confirming that it achieves state-of-the-art performance. We further provide a case study for patients suffering from low back pain to demonstrate that DeepACE generates important and meaningful findings for clinical practice. Our work enables practitioners to develop effective treatment recommendations based on population effects.Comment: Accepted at AAAI 202

Bayesian Neural Controlled Differential Equations for Treatment Effect Estimation

Treatment effect estimation in continuous time is crucial for personalized medicine. However, existing methods for this task are limited to point estimates of the potential outcomes, whereas uncertainty estimates have been ignored. Needless to say, uncertainty quantification is crucial for reliable decision-making in medical applications. To fill this gap, we propose a novel Bayesian neural controlled differential equation (BNCDE) for treatment effect estimation in continuous time. In our BNCDE, the time dimension is modeled through a coupled system of neural controlled differential equations and neural stochastic differential equations, where the neural stochastic differential equations allow for tractable variational Bayesian inference. Thereby, for an assigned sequence of treatments, our BNCDE provides meaningful posterior predictive distributions of the potential outcomes. To the best of our knowledge, ours is the first tailored neural method to provide uncertainty estimates of treatment effects in continuous time. As such, our method is of direct practical value for promoting reliable decision-making in medicine