Estimating conditional average treatment effects (CATE) is challenging, especially when treatment information is missing. Although this is a widespread problem in practice, CATE estimation with missing treatments has received little attention. In this paper, we analyze CATE estimation in the setting with missing treatments where unique challenges arise in the form of covariate shifts. We identify two covariate shifts in our setting: (i) a covariate shift between the treated and control population; and (ii) a covariate shift between the observed and missing treatment population. We first theoretically show the effect of these covariate shifts by deriving a generalization bound for estimating CATE in our setting with missing treatments. Then, motivated by our bound, we develop the missing treatment representation network (MTRNet), a novel CATE estimation algorithm that learns a balanced representation of covariates using domain adaptation. By using balanced representations, MTRNet provides more reliable CATE estimates in the covariate domains where the data are not fully observed. In various experiments with semi-synthetic and real-world data, we show that our algorithm improves over the state-of-the-art by a substantial margin.
The problem of missingness in observational data is ubiquitous. When the confounders are missing at random, multiple imputation is commonly used; however, the method requires congeniality conditions for valid inferences, which may not be satisfied when estimating average causal treatment effects. Alternatively, fractional imputation, proposed by Kim 2011, has been implemented to handling missing values in regression context. In this article, we develop fractional imputation methods for estimating the average treatment effects with confounders missing at random. We show that the fractional impu…
Design and analysis of cluster randomized trials must take into account correlation among outcomes from the same clusters. When applying standard generalized estimating equations (GEE), the first-order (e.g. treatment) effects can be estimated consistently even with a misspecified correlation structure. In settings for which the correlation is of interest, one could estimate this quantity via second-order generalized estimating equations (GEE2). We build upon GEE2 in the setting of missing data, for which we incorporate a "second-order" inverse-probability weighting (IPW) scheme and "second-or…
The Australian National University（澳大利亚国立大学）；Data61；Inria（法国国家信息与自动化研究所）；University College London（伦敦大学学院）
Conditional Value at Risk (CVaR) is a family of "coherent risk measures" which generalize the traditional mathematical expectation. Widely used in mathematical finance, it is garnering increasing interest in machine learning, e.g., as an alternate approach to regularization, and as a means for ensuring fairness. This paper presents a generalization bound for learning algorithms that minimize the CVaR of the empirical loss. The bound is of PAC-Bayesian type and is guaranteed to be small when the empirical CVaR is small. We achieve this by reducing the problem of estimating CVaR to that of merel…
KTH Royal Institute of Technology（瑞典皇家理工学院）；Carnegie Mellon University（卡内基梅隆大学）；Karolinska Institute（卡罗林斯卡学院）；Microsoft Research（微软研究院）
Missing data are ubiquitous in many domains including healthcare. When these data entries are not missing completely at random, the (conditional) independence relations in the observed data may be different from those in the complete data generated by the underlying causal process. Consequently, simply applying existing causal discovery methods to the observed data may lead to wrong conclusions. In this paper, we aim at developing a causal discovery method to recover the underlying causal structure from observed data that follow different missingness mechanisms, including missing completely at…
Columbia University（哥伦比亚大学）；Imperial College London（帝国理工学院）；Babylon Health（巴比伦健康）
We investigate the task of estimating the conditional average causal effect of treatment-dosage pairs from a combination of observational data and assumptions on the causal relationships in the underlying system. This has been a longstanding challenge for fields of study such as epidemiology or economics that require a treatment-dosage pair to make decisions but may not be able to run randomized trials to precisely quantify their effect and heterogeneity across individuals. In this paper, we extend (Shalit et al, 2017) to give new bounds on the counterfactual generalization error in the contex…
A Guide to Estimating Conditional Average Treatment Effects in Competing Risks Settings
Department of Statistics, TU Dortmund University（图恩-多特蒙德大学统计学系）；Research Center Trustworthy Data Science and Security, University Alliance Ruhr (UA Ruhr)（鲁尔大学联盟可信数据科学与安全研究中心）；Institute for Mathematics, University of Augsburg（艾希施泰特大学数学研究所）
Complete randomization allows for consistent estimation of the average treatment effect based on the difference in means of the outcomes without strong modeling assumptions on the outcome-generating process. Appropriate use of the pretreatment covariates can further improve the estimation efficiency. However, missingness in covariates is common in experiments and raises an important question: should we adjust for covariates subject to missingness, and if so, how? The unadjusted difference in means is always unbiased. The complete-covariate analysis adjusts for all completely observed covariate…
Semi-parametric methods are often used for the estimation of intervention effects on correlated outcomes in cluster-randomized trials (CRTs). When outcomes are missing at random (MAR), Inverse Probability Weighted (IPW) methods incorporating baseline covariates can be used to deal with informative missingness. Also, augmented generalized estimating equations (AUG) correct for imbalance in baseline covariates but need to be extended for MAR outcomes. However, in the presence of interactions between treatment and baseline covariates, neither method alone produces consistent estimates for the mar…
Though they may offer valuable patient and disease information that is impossible to study in a randomized trial, clinical disease registries also require special care and attention in causal inference. Registry data may be incomplete, inconsistent, and subject to confounding. In this paper we aim to address several analytical issues in estimating treatment effects that plague clinical registries such as the Emory amyotrophic lateral sclerosis (ALS) Clinic Registry. When attempting to assess the effect of a surgical insertion of a percutaneous endoscopic gastrostomy (PEG) tube on body mass ind…
Estimating conditional mutual information (CMI) is an essential yet challenging step in many machine learning and data mining tasks. Estimating CMI from data that contains both discrete and continuous variables, or even discrete-continuous mixture variables, is a particularly hard problem. In this paper, we show that CMI for such mixture variables, defined based on the Radon-Nikodym derivate, can be written as a sum of entropies, just like CMI for purely discrete or continuous data. Further, we show that CMI can be consistently estimated for discrete-continuous mixture variables by learning an…
This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used to aid in estimation of causal relationships between the primary variables. We give causal semantics for this model class and prove that, under certain assumptions, the direction of causal influence is identifiable from the joint observational distribution of the primary and secondary variables. A score-based approach is developed for estimation of causal st…
This research was motivated by studying anti-drug antibody (ADA) formation and its potential impact on long-term benefit of a biologic treatment in a randomized controlled trial, in which ADA status was not only unobserved in the control arm but also in a subset of patients from the experimental treatment arm. Recent literature considers the principal stratum estimand strategy to estimate treatment effect in groups of patients defined by an intercurrent status, i.e. in groups defined by a post-randomization variable only observed in one arm and potentially associated with the outcome. However,…
Inferring the heterogeneous treatment effect is a fundamental problem in the sciences and commercial applications. In this paper, we focus on estimating Conditional Average Treatment Effect (CATE), that is, the difference in the conditional mean outcome between treatments given covariates. Traditionally, Q-Learning based approaches rely on the estimation of conditional mean outcome given treatment and covariates. However, they are subject to misspecification of the main effect model. Recently, simple and flexible one-step methods to directly learn (D-Learning) the CATE without model specificat…
Rank-based methods for estimating landmark win probability in longitudinal randomized controlled trials with missing data
Western University（韦仕敦大学）；Alimentiv Inc（Alimentiv公司）；Chongqing University of Technology（重庆理工大学）；University of Waterloo（滑铁卢大学）；Harvard T H Chan School of Public Health（哈佛陈曾熙公共卫生学院）
Statistical independence and conditional independence are two fundamental concepts in statistics and machine learning. Copula Entropy is a mathematical concept defined by Ma and Sun for multivariate statistical independence measuring and testing, and also proved to be closely related to conditional independence (or transfer entropy). As the unified framework for measuring both independence and causality, CE has been applied to solve several related statistical or machine learning problems, including association discovery, structure learning, variable selection, and causal discovery. The nonpar…
Clinical trials with longitudinal outcomes typically include missing data due to missed assessments or structural missingness of outcomes after intercurrent events handled with a hypothetical strategy. Approaches based on Bayesian random multiple imputation and Rubin's rule for pooling results across multiple imputed datasets are increasingly used in order to align the analysis of these trials with the targeted estimand. We propose and justify deterministic conditional mean imputation combined with the jackknife for inference as an alternative approach. The method is applicable to imputations …
In the context of missing data, the identifiability or "recoverability" of the average causal effect (ACE) depends on causal and missingness assumptions. The latter can be depicted by adding variable-specific missingness indicators to causal diagrams, creating "missingness-directed acyclic graphs" (m-DAGs). Previous research described ten canonical m-DAGs, representing typical multivariable missingness mechanisms in epidemiological studies, and determined the recoverability of the ACE in the absence of effect modification. We extend the research by determining the recoverability of the ACE in …
Aalto University（阿尔托大学）；University of Helsinki（赫尔辛基大学）；Bayer Pharmaceuticals（拜耳制药）
Conditional variational autoencoders (CVAEs) are versatile deep generative models that extend the standard VAE framework by conditioning the generative model with auxiliary covariates. The original CVAE model assumes that the data samples are independent, whereas more recent conditional VAE models, such as the Gaussian process (GP) prior VAEs, can account for complex correlation structures across all data samples. While several methods have been proposed to learn standard VAEs from partially observed datasets, these methods fall short for conditional VAEs. In this work, we propose a method to …
BMW Group（宝马集团）；Technical University of Dortmund（多特蒙德工业大学）
In this work we present a rigorous application of the Expectation Maximization algorithm to determine the marginal distributions and the dependence structure in a Gaussian copula model with missing data. We further show how to circumvent a priori assumptions on the marginals with semiparametric modelling. The joint distribution learned through this algorithm is considerably closer to the underlying distribution than existing methods.
Matrix completion is often applied to data with entries missing not at random (MNAR). For example, consider a recommendation system where users tend to only reveal ratings for items they like. In this case, a matrix completion method that relies on entries being revealed at uniformly sampled row and column indices can yield overly optimistic predictions of unseen user ratings. Recently, various papers have shown that we can reduce this bias in MNAR matrix completion if we know the probabilities of different matrix entries being missing. These probabilities are typically modeled using logistic …
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Washington, Seattle（西雅图华盛顿大学）；Amazon（亚马逊）
Matching the performance of conditional Generative Adversarial Networks with little supervision is an important task, especially in venturing into new domains. We design a new training algorithm, which is robust to missing or ambiguous labels. The main idea is to intentionally corrupt the labels of generated examples to match the statistics of the real data, and have a discriminator process the real and generated examples with corrupted labels. We showcase the robustness of this proposed approach both theoretically and empirically. We show that minimizing the proposed loss is equivalent to min…
Semi-supervised learning is a powerful technique for leveraging unlabeled data to improve machine learning models, but it can be affected by the presence of ``informative'' labels, which occur when some classes are more likely to be labeled than others. In the missing data literature, such labels are called missing not at random. In this paper, we propose a novel approach to address this issue by estimating the missing-data mechanism and using inverse propensity weighting to debias any SSL algorithm, including those using data augmentation. We also propose a likelihood ratio test to assess whe…
In data streams, the data distribution of arriving observations at different time points may change - a phenomenon called concept drift. While detecting concept drift is a relatively mature area of study, solutions to the uncertainty introduced by observations with missing values have only been studied in isolation. No one has yet explored whether or how these solutions might impact drift detection performance. We, however, believe that data imputation methods may actually increase uncertainty in the data rather than reducing it. We also conjecture that imputation can introduce bias into the p…
Icahn School of Medicine at Mt Sinai（西奈山伊坎医学院）；Child Mind Institute（儿童心理研究所）；Duke University（杜克大学）
Nonparametric estimation of the conditional distribution of a response given high-dimensional features is a challenging problem. It is important to allow not only the mean but also the variance and shape of the response density to change flexibly with features, which are massive-dimensional. We propose a multiscale dictionary learning model, which expresses the conditional response density as a convex combination of dictionary densities, with the densities used and their weights dependent on the path through a tree decomposition of the feature space. A fast graph partitioning algorithm is appl…
Aggregate network properties such as cluster cohesion and the number of bridge nodes can be used to glean insights about a network's community structure, spread of influence and the resilience of the network to faults. Efficiently computing network properties when the network is fully observed has received significant attention (Wasserman and Faust 1994; Cook and Holder 2006), however the problem of computing aggregate network properties when there is missing data attributes has received little attention. Computing these properties for networks with missing attributes involves performing infer…
Conditional expectation with regularization for missing data imputation
University of Science, Ho Chi Minh City（胡志明市科学大学）；Simula Metropolitan（Simula大都会）；University of Notre Dame（圣母大学）；Vietnam National University, Ho Chi Minh City（胡志明市越南国家大学）
Yantai University（烟台大学）；East China Normal University（华东师范大学）
Datasets with missing values are very common in real world applications. GAIN, a recently proposed deep generative model for missing data imputation, has been proved to outperform many state-of-the-art methods. But GAIN only uses a reconstruction loss in the generator to minimize the imputation error of the non-missing part, ignoring the potential category information which can reflect the relationship between samples. In this paper, we propose a novel unsupervised missing data imputation method named PC-GAIN, which utilizes potential category information to further enhance the imputation powe…
BI Norwegian Business School（BI挪威商学院）；UiT The Arctic University of Norway（挪威北极大学）；Norwegian Computing Center（挪威计算中心）
Deep generative models with latent variables have been used lately to learn joint representations and generative processes from multi-modal data. These two learning mechanisms can, however, conflict with each other and representations can fail to embed information on the data modalities. This research studies the realistic scenario in which all modalities and class labels are available for model training, but where some modalities and labels required for downstream tasks are missing. We show, in this scenario, that the variational lower bound limits mutual information between joint representat…
Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional density itself is preferable, but conditional density estimation (CDE) is challenging in high-dimensional space. A naive approach to coping with high-dimensionality is to first perform dimensionality reduction (DR) and then execute CDE. However, such a two-step process does not perform well in practice because the error incurred in the first DR step can be mag…
This paper formulates dynamic density functions, based upon skewed-t and similar representations, to model and forecast electricity price spreads between different hours of the day. This supports an optimal day ahead storage and discharge schedule, and thereby facilitates a bidding strategy for a merchant arbitrage facility into the day-ahead auctions for wholesale electricity. The four latent moments of the density functions are dynamic and conditional upon exogenous drivers, thereby permitting the mean, variance, skewness and kurtosis of the densities to respond hourly to such factors as wea…
We revisit the problem of \emph{missing mass concentration}, developing a new method of estimating concentration of heterogenic sums, in spirit of celebrated Rosenthal's inequality. As a result we slightly improve the state-of-art bounds due to Ben-Hamou at al., and simplify the proofs.
Doubly robust target inference for generalized linear regression with completely missing covariates
School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院）；Department of Statistics and Data Science, Tsinghua University（清华大学统计与数据科学系）
