arXiv subjects

Zhi Geng

Publications and source records attributed to Zhi Geng.

At least 37 records · Page 2Linked to original sources

arXiv2024

Identification and Estimation of the Bi-Directional MR with Some Invalid Instruments

We consider the challenging problem of estimating causal effects from purely observational data in the bi-directional Mendelian randomization (MR), where some invalid instruments, as well as unmeasured confounding, usually exist. To address this problem, most existing methods attempt to find proper valid instrumental variables (IVs) for the target causal effect by expert knowledge or by assuming that the causal model is a one-directional MR model. As such, in this paper, we first theoretically investigate the identification of the bi-directional MR from observational data. In particular, we provide necessary and sufficient conditions under which valid IV sets are correctly identified such that the bi-directional MR model is identifiable, including the causal directions of a pair of phenotypes (i.e., the treatment and outcome). Moreover, based on the identification theory, we develop a cluster fusion-like method to discover valid IV sets and estimate the causal effects of interest. We theoretically demonstrate the correctness of the proposed algorithm. Experimental results show the effectiveness of our method for estimating causal effects in bi-directional MR.

stat.ME↗

arXiv2024

Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables

We investigate the task of learning causal structure in the presence of latent variables, including locating latent variables and determining their quantity, and identifying causal relationships among both latent and observed variables. To this end, we propose a Generalized Independent Noise (GIN) condition for linear non-Gaussian acyclic causal models that incorporate latent variables, which establishes the independence between a linear combination of certain measured variables and some other measured variables. Specifically, for two observed random vectors $\bf{Y}$ and $\bf{Z}$, GIN holds if and only if $ω^{\intercal}\mathbf{Y}$ and $\mathbf{Z}$ are independent, where $ω$ is a non-zero parameter vector determined by the cross-covariance between $\mathbf{Y}$ and $\mathbf{Z}$. We then give necessary and sufficient graphical criteria of the GIN condition in linear non-Gaussian acyclic models. Roughly speaking, GIN implies the existence of a set $\mathcal{S}$ such that $\mathcal{S}$ is causally earlier (w.r.t. the causal ordering) than $\mathbf{Y}$, and that every active (collider-free) path between $\mathbf{Y}$ and $\mathbf{Z}$ must contain a node from $\mathcal{S}$. Interestingly, we find that the independent noise condition (i.e., if there is no confounder, causes are independent of the residual derived from regressing the effect on the causes) can be seen as a special case of GIN. With such a connection between GIN and latent causal structures, we further leverage the proposed GIN condition, together with a well-designed search procedure, to efficiently estimate Linear, Non-Gaussian Latent Hierarchical Models (LiNGLaHs), where latent confounders may also be causally related and may even follow a hierarchical structure. We show that the causal structure of a LiNGLaH is identifiable in light of GIN conditions. Experimental results show the effectiveness of the proposed method.

cs.LG↗

arXiv2024

Local Causal Structure Learning in the Presence of Latent Variables

Discovering causal relationships from observational data, particularly in the presence of latent variables, poses a challenging problem. While current local structure learning methods have proven effective and efficient when the focus lies solely on the local relationships of a target variable, they operate under the assumption of causal sufficiency. This assumption implies that all the common causes of the measured variables are observed, leaving no room for latent variables. Such a premise can be easily violated in various real-world applications, resulting in inaccurate structures that may adversely impact downstream tasks. In light of this, our paper delves into the primary investigation of locally identifying potential parents and children of a target from observational data that may include latent variables. Specifically, we harness the causal information from m-separation and V-structures to derive theoretical consistency results, effectively bridging the gap between global and local structure learning. Together with the newly developed stop rules, we present a principled method for determining whether a variable is a direct cause or effect of a target. Further, we theoretically demonstrate the correctness of our approach under the standard causal Markov and faithfulness conditions, with infinite samples. Experimental results on both synthetic and real-world data validate the effectiveness and efficiency of our approach.

cs.LG↗

arXiv2024

Automating the Selection of Proxy Variables of Unmeasured Confounders

Recently, interest has grown in the use of proxy variables of unobserved confounding for inferring the causal effect in the presence of unmeasured confounders from observational data. One difficulty inhibiting the practical use is finding valid proxy variables of unobserved confounding to a target causal effect of interest. These proxy variables are typically justified by background knowledge. In this paper, we investigate the estimation of causal effects among multiple treatments and a single outcome, all of which are affected by unmeasured confounders, within a linear causal model, without prior knowledge of the validity of proxy variables. To be more specific, we first extend the existing proxy variable estimator, originally addressing a single unmeasured confounder, to accommodate scenarios where multiple unmeasured confounders exist between the treatments and the outcome. Subsequently, we present two different sets of precise identifiability conditions for selecting valid proxy variables of unmeasured confounders, based on the second-order statistics and higher-order statistics of the data, respectively. Moreover, we propose two data-driven methods for the selection of proxy variables and for the unbiased estimation of causal effects. Theoretical analysis demonstrates the correctness of our proposed algorithms. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach.

cs.LG↗

arXiv2024

Debiased Collaborative Filtering with Kernel-Based Causal Balancing

Debiased collaborative filtering aims to learn an unbiased prediction model by removing different biases in observational datasets. To solve this problem, one of the simple and effective methods is based on the propensity score, which adjusts the observational sample distribution to the target one by reweighting observed instances. Ideally, propensity scores should be learned with causal balancing constraints. However, existing methods usually ignore such constraints or implement them with unreasonable approximations, which may affect the accuracy of the learned propensity scores. To bridge this gap, in this paper, we first analyze the gaps between the causal balancing requirements and existing methods such as learning the propensity with cross-entropy loss or manually selecting functions to balance. Inspired by these gaps, we propose to approximate the balancing functions in reproducing kernel Hilbert space and demonstrate that, based on the universal property and representer theorem of kernel functions, the causal balancing constraints can be better satisfied. Meanwhile, we propose an algorithm that adaptively balances the kernel function and theoretically analyze the generalization error bound of our methods. We conduct extensive experiments to demonstrate the effectiveness of our methods, and to promote this research direction, we have released our project at https://github.com/haoxuanli-pku/ICLR24-Kernel-Balancing.

cs.IR↗

arXiv2024

Be Aware of the Neighborhood Effect: Modeling Selection Bias under Interference

Selection bias in recommender system arises from the recommendation process of system filtering and the interactive process of user selection. Many previous studies have focused on addressing selection bias to achieve unbiased learning of the prediction model, but ignore the fact that potential outcomes for a given user-item pair may vary with the treatments assigned to other user-item pairs, named neighborhood effect. To fill the gap, this paper formally formulates the neighborhood effect as an interference problem from the perspective of causal inference and introduces a treatment representation to capture the neighborhood effect. On this basis, we propose a novel ideal loss that can be used to deal with selection bias in the presence of neighborhood effect. We further develop two new estimators for estimating the proposed ideal loss. We theoretically establish the connection between the proposed and previous debiasing methods ignoring the neighborhood effect, showing that the proposed methods can achieve unbiased learning when both selection bias and neighborhood effect are present, while the existing methods are biased. Extensive semi-synthetic and real-world experiments are conducted to demonstrate the effectiveness of the proposed methods.

cs.LG↗

arXiv2024

Assessing the causes of continuous effects by posterior effects of causes

To evaluate a single cause of a binary effect, Dawid et al. (2014) defined the probability of causation, while Pearl (2015) defined the probabilities of necessity and sufficiency. For assessing the multiple correlated causes of a binary effect, Lu et al. (2023) defined the posterior causal effects based on post-treatment variables. In many scenarios, outcomes are continuous, simply binarizing them and applying previous methods may result in information loss or biased conclusions. To address this limitation, we propose a series of posterior causal estimands for retrospectively evaluating multiple correlated causes from a continuous effect, including posterior intervention effects, posterior total causal effects, and posterior natural direct effects. Under the assumptions of sequential ignorability, monotonicity, and perfect positive rank, we show that the posterior causal estimands of interest are identifiable and present the corresponding identification equations. We also provide a simple but effective estimation procedure and establish the asymptotic properties of the proposed estimators. An artificial hypertension example and a real developmental toxicity dataset are employed to illustrate our method.

stat.ME↗

arXiv2024

Efficiency-improved doubly robust estimation with non-confounding predictive covariates

In observational studies, covariates with substantial missing data are often omitted, despite their strong predictive capabilities. These excluded covariates are generally believed not to simultaneously affect both treatment and outcome, indicating that they are not genuine confounders and do not impact the identification of the average treatment effect (ATE). In this paper, we introduce an alternative doubly robust (DR) estimator that fully leverages non-confounding predictive covariates to enhance efficiency, while also allowing missing values in such covariates. Beyond the double robustness property, our proposed estimator is designed to be more efficient than the standard DR estimator. Specifically, when the propensity score model is correctly specified, it achieves the smallest asymptotic variance among the class of DR estimators, and brings additional efficiency gains by further integrating predictive covariates. Simulation studies demonstrate the notable performance of the proposed estimator over current popular methods. An illustrative example is provided to assess the effectiveness of right heart catheterization (RHC) for critically ill patients.

stat.ME↗

arXiv2023

Study on Virtual Gear Hobbing Simulation and Gear Tooth Surface Accuracy

This paper presents a digital simulation method for the hobbing process of cylindrical gears. Based on the gear generation principle, taking the professional software as the tool, the problem of virtual hobbing simulation on involute helical gears was studied, and the virtual hobbing simulation of hobbing on the whole gear was completed by using macros of CATIA V5. The validity of this method was validated by analyzing the tooth surface accuracy error of the model which was below 0.001 mm between the virtual tooth surface and the theoretical tooth surface and the possible factors that affected the tooth surface accuracy during manufacturing were also carried on the discussion. It offers a fictitious three-D platform for studying the principle of manufacture errors of a gear-cutting machine as well as the finite element analysis between the ideal tooth surface and the erroneous tooth surface.

cs.GR↗

arXiv2022

A Local Method for Identifying Causal Relations under Markov Equivalence

Causality is important for designing interpretable and robust methods in artificial intelligence research. We propose a local approach to identify whether a variable is a cause of a given target under the framework of causal graphical models of directed acyclic graphs (DAGs). In general, the causal relation between two variables may not be identifiable from observational data as many causal DAGs encoding different causal relations are Markov equivalent. In this paper, we first introduce a sufficient and necessary graphical condition to check the existence of a causal path from a variable to a target in every Markov equivalent DAG. Next, we provide local criteria for identifying whether a variable is a cause/non-cause of a target based only on the local structure instead of the entire graph. Finally, we propose a local learning algorithm for this causal query via learning the local structure of the variable and some additional statistical independence tests related to the target. Simulation studies show that our local algorithm is efficient and effective, compared with other state-of-art methods.

stat.ML↗

arXiv2022

Modeling High-Dimensional Data with Unknown Cut Points: A Fusion Penalized Logistic Threshold Regression

In traditional logistic regression models, the link function is often assumed to be linear and continuous in predictors. Here, we consider a threshold model that all continuous features are discretized into ordinal levels, which further determine the binary responses. Both the threshold points and regression coefficients are unknown and to be estimated. For high dimensional data, we propose a fusion penalized logistic threshold regression (FILTER) model, where a fused lasso penalty is employed to control the total variation and shrink the coefficients to zero as a method of variable selection. Under mild conditions on the estimate of unknown threshold points, we establish the non-asymptotic error bound for coefficient estimation and the model selection consistency. With a careful characterization of the error propagation, we have also shown that the tree-based method, such as CART, fulfill the threshold estimation conditions. We find the FILTER model is well suited in the problem of early detection and prediction for chronic disease like diabetes, using physical examination data. The finite sample behavior of our proposed method are also explored and compared with extensive Monte Carlo studies, which supports our theoretical discoveries.

stat.ME↗

arXiv2020

Causal Mediation Analysis with Multiple Treatments and Latent Confounders

Causal mediation analysis is used to evaluate direct and indirect causal effects of a treatment on an outcome of interest through an intermediate variable or a mediator.It is difficult to identify the direct and indirect causal effects because the mediator cannot be randomly assigned in many real applications. In this article, we consider a causal model including latent confounders between the mediator and the outcome. We present sufficient conditions for identifying the direct and indirect effects and propose an approach for estimating them. The performance of the proposed approach is evaluated by simulation studies. Finally, we apply the approach to a data set of the customer loyalty survey by a telecom company.

stat.AP↗

arXiv2019

Identification, Doubly Robust Estimation, and Semiparametric Efficiency Theory of Nonignorable Missing Data With a Shadow Variable

We consider identification and estimation with an outcome missing not at random (MNAR). We study an identification strategy based on a so-called shadow variable. A shadow variable is assumed to be correlated with the outcome, but independent of the missingness process conditional on the outcome and fully observed covariates. We describe a general condition for nonparametric identification of the full data law under MNAR using a valid shadow variable. Our condition is satisfied by many commonly-used models; moreover, it is imposed on the complete cases, and therefore has testable implications with observed data only. We describe semiparametric estimation methods and evaluate their performance on both simulation data and a real data example. We characterize the semiparametric efficiency bound for the class of regular and asymptotically linear estimators, and derive a closed form for the efficient influence function.

stat.ME↗

arXiv2018

Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder

We consider a causal effect that is confounded by an unobserved variable, but with observed proxy variables of the confounder. We show that, with at least two independent proxy variables satisfying a certain rank condition, the causal effect is nonparametrically identified, even if the measurement error mechanism, i.e., the conditional distribution of the proxies given the con- founder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl (2014) that rests on identification of the measurement error mechanism. When only one proxy for the confounder is available, or the required rank condition is not met, we develop a strategy to test the null hypothesis of no causal effect.

stat.ME↗

arXiv2017

On the Individual Surrogate Paradox

When the primary outcome is difficult to collect, surrogate endpoint is typically used as a substitute. It is possible that for every individual, treatment has a positive effect on surrogate, and surrogate has a positive effect on primary outcome, but for some individuals, treatment has a negative effect on primary outcome. For example, a treatment may be substantially effective in preventing the stroke for everyone, and lowering the risk of stroke is universally beneficial for a longer survival time, however, the treatment may still cause death for some individuals. We define such paradoxical phenomenon as individual surrogate paradox. The individual surrogate paradox is preposed to capture the treatment effect heterogeneity, which is unable to be described by either the surrogate paradox based on average causal effect (ACE) (Chen et al., 2007) or that based on distributional causal effect (DCE) (Ju and Geng, 2010). We investigate existing surrogate criteria in terms of whether the individual surrogate paradox could manifest. We find that only the strong binary surrogate can avoid such paradox without additional assumptions. Utilizing the sharp bounds, we propose novel criteria to exclude the individual surrogate paradox. Our methods are illustrated in an application to determine the effect of the intensive glycemia on the risk of development or progression of diabetic retinopathy.

stat.ME↗

arXiv2016

Causal Network Learning from Multiple Interventions of Unknown Manipulated Targets

In this paper, we discuss structure learning of causal networks from multiple data sets obtained by external intervention experiments where we do not know what variables are manipulated. For example, the conditions in these experiments are changed by changing temperature or using drugs, but we do not know what target variables are manipulated by the external interventions. From such data sets, the structure learning becomes more difficult. For this case, we first discuss the identifiability of causal structures. Next we present a graph-merging method for learning causal networks for the case that the sample sizes are large for these interventions. Then for the case that the sample sizes of these interventions are relatively small, we propose a data-pooling method for learning causal networks in which we pool all data sets of these interventions together for the learning. Further we propose a re-sampling approach to evaluate the edges of the causal network learned by the data-pooling method. Finally we illustrate the proposed learning methods by simulations.

stat.ML↗

arXiv2016

Novel Criteria to Exclude the Surrogate Paradox and Their Optimalities

When the primary outcome is hard to collect, surrogate endpoint is typically used as a substitute. However, even when the treatment has a positive average causal effect (ACE) on the surrogate endpoint, which also has a positive ACE on the primary outcome, it is still possible that the treatment has a negative ACE on the primary outcome. Such a phenomenon is called the surrogate paradox and greatly challenges the use of surrogate. In this paper, we provide novel criteria to exclude the surrogate paradox. Unlike other conditions previously proposed, our conditions are testable since they only involve observed data. Furthermore, our criteria are optimal in the sense that they are sufficient and "almost necessary" to exclude the paradox: if the conditions are satisfied, the surrogate paradox is guaranteed to be absent while if the conditions fail, there exists a data generating process with surrogate paradox that can generate the same observed data. That is, our criteria capture all the information in the observed data to exclude the surrogate paradox rather than relying on unverifiable distributional assumptions.

math.ST↗

arXiv2016

Assessing the Treatment Effect Heterogeneity with a Latent Variable

The average treatment effect (ATE) is popularly used to assess the treatment effect. However, the ATE implicitly assumes a homogenous treatment effect even amongst individuals with different characteristics. In this paper, we mainly focus on assessing the treatment effect heterogeneity, which has important implications in designing the optimal individual treatment regimens and in policy making. The treatment benefit rate (TBR) and treatment harm rate (THR) have been defined to characterize the magnitude of heterogeneity for binary outcomes. When the outcomes are continuous, we extend the definitions of the TBR and THR to compare the difference between potential outcomes with a pre-specified level c. Unlike the ATE, these rates involve the joint distribution of the potential outcomes and can not be identified without further assumptions even in randomized clinical trials. In this article, we assume the potential outcomes are independent conditional on the observed covariates and an unmeasured latent variable. Under this assumption, we prove the identification of the TBR and THR in non-separable (generalized) linear models for both continuous and binary outcomes. We then propose estimators and derive their asymptotic distributions. In the simulation studies, we implement our proposed methods to assess the performance of our estimators and carry out a sensitive analysis for different underlying distribution for the latent variable. Finally, we illustrate the proposed methods in two randomized controlled trials.

stat.ME↗