In applications where the study data are collected within cluster units (e.g., patients within transplant centers), it is often of interest to estimate and perform inference on the treatment effects of the cluster units. However, it is well-established that cluster-level confounding variables can bias these assessments, and many of these confounding factors may be unobservable. In healthcare settings, data sharing restrictions often make it impossible to directly fit conventional risk-adjustment models on patient-level data, and existing privacy-preserving approaches cannot adequately adjust for both observed and unobserved cluster-level confounding factors. In this paper, we propose a privacy-preserving model for cluster-level confounding that only depends on publicly-available summary statistics, can be fit using a single optimization routine, and is robust to outlying cluster unit effects. In addition, we develop a Pseudo-Bayesian inference procedure that accounts for the estimated cluster-level confounding effects and corrects for the impact of unobservable factors. Simulations show that our estimates are robust and accurate, and the proposed inference approach has better Frequentist properties than existing methods. Motivated by efforts to improve equity in transplant care, we apply these methods to evaluate transplant centers while adjusting for observed geographic disparities in donor organ availability and unobservable confounders.
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Causal inference in spatial settings is met with unique challenges and opportunities. In spatial settings, a unit's outcome might be affected by the exposure at many locations and the confounders might be spatially structured. Using causal diagrams, we investigate the complications that arise when investigating causal relationships from spatial data. We illustrate that spatial confounding and interference can manifest as each other, meaning that investigating the presence of one can lead to wrongful conclusions in the presence of the other. We also show that statistical dependencies in the exposure can render standard analyses invalid, which can have crucial implications for understanding the effect of interventions on dependent units. Based on the conclusions from this investigation, we propose a parametric approach that simultaneously accounts for interference and mitigates bias from local and neighborhood unmeasured spatial confounding. We show that incorporating an exposure model is necessary from a Bayesian perspective. Therefore, the proposed approach is based on modeling the exposure and the outcome simultaneously while accounting for the presence of common spatially-structured unmeasured predictors. We illustrate our approach with a simulation study and with an analysis of the local and interference effects of sulfur dioxide emissions from power plants on cardiovascular mortality.
Eigenspace estimation is fundamental in machine learning and statistics, which has found applications in PCA, dimension reduction, and clustering, among others. The modern machine learning community usually assumes that data come from and belong to different organizations. The low communication power and the possible privacy breaches of data make the computation of eigenspace challenging. To address these challenges, we propose a class of algorithms called \textsf{FedPower} within the federated learning (FL) framework. \textsf{FedPower} leverages the well-known power method by alternating multiple local power iterations and a global aggregation step, thus improving communication efficiency. In the aggregation, we propose to weight each local eigenvector matrix with {\it Orthogonal Procrustes Transformation} (OPT) for better alignment. To ensure strong privacy protection, we add Gaussian noise in each iteration by adopting the notion of \emph{differential privacy} (DP). We provide convergence bounds for \textsf{FedPower} that are composed of different interpretable terms corresponding to the effects of Gaussian noise, parallelization, and random sampling of local machines. Additionally, we conduct experiments to demonstrate the effectiveness of our proposed algorithms.
The federated learning (FL) technique was developed to mitigate data privacy issues in the traditional machine learning paradigm. While FL ensures that a user's data always remain with the user, the gradients are shared with the centralized server to build the global model. This results in privacy leakage, where the server can infer private information from the shared gradients. To mitigate this flaw, the next-generation FL architectures proposed encryption and anonymization techniques to protect the model updates from the server. However, this approach creates other challenges, such as malicious users sharing false gradients. Since the gradients are encrypted, the server is unable to identify rogue users. To mitigate both attacks, this paper proposes a novel FL algorithm based on a fully homomorphic encryption (FHE) scheme. We develop a distributed multi-key additive homomorphic encryption scheme that supports model aggregation in FL. We also develop a novel aggregation scheme within the encrypted domain, utilizing users' non-poisoning rates, to effectively address data poisoning attacks while ensuring privacy is preserved by the proposed encryption scheme. Rigorous security, privacy, convergence, and experimental analyses have been provided to show that FheFL is novel, secure, and private, and achieves comparable accuracy at reasonable computational cost.
Gaussian process regression (GPR) is a non-parametric model that has been used in many real-world applications that involve sensitive personal data (e.g., healthcare, finance, etc.) from multiple data owners. To fully and securely exploit the value of different data sources, this paper proposes a privacy-preserving GPR method based on secret sharing (SS), a secure multi-party computation (SMPC) technique. In contrast to existing studies that protect the data privacy of GPR via homomorphic encryption, differential privacy, or federated learning, our proposed method is more practical and can be used to preserve the data privacy of both the model inputs and outputs for various data-sharing scenarios (e.g., horizontally/vertically-partitioned data). However, it is non-trivial to directly apply SS on the conventional GPR algorithm, as it includes some operations whose accuracy and/or efficiency have not been well-enhanced in the current SMPC protocol. To address this issue, we derive a new SS-based exponentiation operation through the idea of 'confusion-correction' and construct an SS-based matrix inversion algorithm based on Cholesky decomposition. More importantly, we theoretically analyze the communication cost and the security of the proposed SS-based operations. Empirical results show that our proposed method can achieve reasonable accuracy and efficiency under the premise of preserving data privacy.
Although data-driven methods usually have noticeable performance on disease diagnosis and treatment, they are suspected of leakage of privacy due to collecting data for model training. Recently, federated learning provides a secure and trustable alternative to collaboratively train model without any exchange of medical data among multiple institutes. Therefore, it has draw much attention due to its natural merit on privacy protection. However, when heterogenous medical data exists between different hospitals, federated learning usually has to face with degradation of performance. In the paper, we propose a new personalized framework of federated learning to handle the problem. It successfully yields personalized models based on awareness of similarity between local data, and achieves better tradeoff between generalization and personalization than existing methods. After that, we further design a differentially sparse regularizer to improve communication efficiency during procedure of model training. Additionally, we propose an effective method to reduce the computational cost, which improves computation efficiency significantly. Furthermore, we collect 5 real medical datasets, including 2 public medical image datasets and 3 private multi-center clinical diagnosis datasets, and evaluate its performance by conducting nodule classification, tumor segmentation, and clinical risk prediction tasks. Comparing with 13 existing related methods, the proposed method successfully achieves the best model performance, and meanwhile up to 60% improvement of communication efficiency. Source code is public, and can be accessed at: //github.com/ApplicationTechnologyOfMedicalBigData/pFedNet-code.
Knowledge graph embedding (KGE) that maps entities and relations into vector representations is essential for downstream tasks. Conventional KGE methods require relatively high-dimensional entity representations to preserve the structural information of knowledge graph, but lead to oversized model parameters. Recent methods reduce model parameters by adopting low-dimensional entity representations, while developing techniques (e.g., knowledge distillation) to compensate for the reduced dimension. However, such operations produce degraded model accuracy and limited reduction of model parameters. Specifically, we view the concatenation of all entity representations as an embedding layer, and then conventional KGE methods that adopt high-dimensional entity representations equal to enlarging the width of the embedding layer to gain expressiveness. To achieve parameter efficiency without sacrificing accuracy, we instead increase the depth and propose a deeper embedding network for entity representations, i.e., a narrow embedding layer and a multi-layer dimension lifting network (LiftNet). Experiments on three public datasets show that the proposed method (implemented based on TransE and DistMult) with 4-dimensional entity representations achieves more accurate link prediction results than counterpart parameter-efficient KGE methods and strong KGE baselines, including TransE and DistMult with 512-dimensional entity representations.
Many real-world decision-making tasks require learning causal relationships between a set of variables. Traditional causal discovery methods, however, require that all variables are observed, which is often not feasible in practical scenarios. Without additional assumptions about the unobserved variables, it is not possible to recover any causal relationships from observational data. Fortunately, in many applied settings, additional structure among the confounders can be expected. In particular, pervasive confounding is commonly encountered and has been utilized for consistent causal estimation in linear causal models. In this paper, we present a provably consistent method to estimate causal relationships in the non-linear, pervasive confounding setting. The core of our procedure relies on the ability to estimate the confounding variation through a simple spectral decomposition of the observed data matrix. We derive a DAG score function based on this insight, prove its consistency in recovering a correct ordering of the DAG, and empirically compare it to previous approaches. We demonstrate improved performance on both simulated and real datasets by explicitly accounting for both confounders and non-linear effects.
An N-of-1 trial is a multiple crossover trial conducted in a single individual to provide evidence to directly inform personalized treatment decisions. Advancements in wearable devices greatly improved the feasibility of adopting these trials to identify optimal individual treatment plans, particularly when treatments differ among individuals and responses are highly heterogeneous. Our work was motivated by the I-STOP-AFib Study, which examined the impact of different triggers on atrial fibrillation (AF) occurrence. We described a causal framework for 'N-of-1' trial using potential treatment selection paths and potential outcome paths. Two estimands of individual causal effect were defined:(a) the effect of continuous exposure, and (b) the effect of an individual observed behavior. We addressed three challenges: (a) imperfect compliance to the randomized treatment assignment; (b) binary treatments and binary outcomes which led to the 'non-collapsibility' issue of estimating odds ratios; and (c) serial inference in the longitudinal observations. We adopted the Bayesian IV approach where the study randomization was the IV as it impacted the choice of exposure of a subject but not directly the outcome. Estimations were through a system of two parametric Bayesian models to estimate the individual causal effect. Our model got around the non-collapsibility and non-consistency by modeling the confounding mechanism through latent structural models and by inferring with Bayesian posterior of functionals. Autocorrelation present in the repeated measurements was also accounted for. The simulation study showed our method largely reduced bias and greatly improved the coverage of the estimated causal effect, compared to existing methods (ITT, PP, and AT). We applied the method to I-STOP-AFib Study to estimate the individual effect of alcohol on AF occurrence.
To date, various neural methods have been proposed for causal effect estimation based on observational data, where a default assumption is the same distribution and availability of variables at both training and inference (i.e., runtime) stages. However, distribution shift (i.e., domain shift) could happen during runtime, and bigger challenges arise from the impaired accessibility of variables. This is commonly caused by increasing privacy and ethical concerns, which can make arbitrary variables unavailable in the entire runtime data and imputation impractical. We term the co-occurrence of domain shift and inaccessible variables runtime domain corruption, which seriously impairs the generalizability of a trained counterfactual predictor. To counter runtime domain corruption, we subsume counterfactual prediction under the notion of domain adaptation. Specifically, we upper-bound the error w.r.t. the target domain (i.e., runtime covariates) by the sum of source domain error and inter-domain distribution distance. In addition, we build an adversarially unified variational causal effect model, named VEGAN, with a novel two-stage adversarial domain adaptation scheme to reduce the latent distribution disparity between treated and control groups first, and between training and runtime variables afterwards. We demonstrate that VEGAN outperforms other state-of-the-art baselines on individual-level treatment effect estimation in the presence of runtime domain corruption on benchmark datasets.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
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