In this paper, we investigate a treatment effect model in which individuals interact in a social network and they may not comply with the assigned treatments. We introduce a new concept of exposure mapping, which summarizes spillover effects into a fixed dimensional statistic of instrumental variables, and we call this mapping the instrumental exposure mapping (IEM). We investigate identification conditions for the intention-to-treat effect and the average causal effect for compliers, while explicitly considering the possibility of misspecification of IEM. Based on our identification results, we develop nonparametric estimation procedures for the treatment parameters. Their asymptotic properties, including consistency and asymptotic normality, are investigated using an approximate neighborhood interference framework by Leung (2021). For an empirical illustration of our proposed method, we revisit Paluck et al.'s (2016) experimental data on the anti-conflict intervention school program.
相關內容
Understanding causal relationships is one of the most important goals of modern science. So far, the causal inference literature has focused almost exclusively on outcomes coming from the Euclidean space $\mathbb{R}^p$. However, it is increasingly common that complex datasets collected through electronic sources, such as wearable devices, cannot be represented as data points from $\mathbb{R}^p$. In this paper, we present a novel framework of causal effects for outcomes from the Wasserstein space of cumulative distribution functions, which in contrast to the Euclidean space, is non-linear. We develop doubly robust estimators and associated asymptotic theory for these causal effects. As an illustration, we use our framework to quantify the causal effect of marriage on physical activity patterns using wearable device data collected through the National Health and Nutrition Examination Survey.
This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are linked with the underlying latent confounders through an unknown, possibly nonlinear factor structure. The main building block is a local principal subspace approximation procedure that combines $K$-nearest neighbors matching and principal component analysis. Estimators of many causal parameters, including average treatment effects and counterfactual distributions, are constructed based on doubly-robust score functions. Large-sample properties of these estimators are established, which only require relatively mild conditions on the principal subspace approximation. The results are illustrated with an empirical application studying the effect of political connections on stock returns of financial firms, and a Monte Carlo experiment. The main technical and methodological results regarding the general local principal subspace approximation method may be of independent interest.
Synthetic control methods are commonly used to estimate the treatment effect on a single treated unit in panel data settings. A synthetic control (SC) is a weighted average of control units built to match the treated unit's pre-treatment outcome trajectory, with weights typically estimated by regressing pre-treatment outcomes of the treated unit to those of the control units. However, it has been established that such regression estimators can fail to be consistent. In this paper, we introduce a proximal causal inference framework to formalize identification and inference for both the SC weights and the treatment effect on the treated. We show that control units previously perceived as unusable can be repurposed to consistently estimate the SC weights. We also propose to view the difference in the post-treatment outcomes between the treated unit and the SC as a time series, which opens the door to a rich literature on time-series analysis for treatment effect estimation. We further extend the traditional linear model to accommodate general nonlinear models allowing for binary and count outcomes which are understudied in the SC literature. We illustrate our proposed methods with simulation studies and an application to evaluation of the 1990 German Reunification.
Simultaneous statistical inference problems are at the basis of almost any scientific discovery process. We consider a class of simultaneous inference problems that are invariant under permutations, meaning that all components of the problem are oblivious to the labelling of the multiple instances under consideration. For any such problem we identify the optimal solution which is itself permutation invariant, the most natural condition one could impose on the set of candidate solutions. Interpreted differently, for any possible value of the parameter we find a tight (non-asymptotic) lower bound on the statistical performance of any procedure that obeys the aforementioned condition. By generalizing the standard decision theoretic notions of permutation invariance, we show that the results apply to a myriad of popular problems in simultaneous inference, so that the ultimate benchmark for each of these problems is identified. The connection to the nonparametric empirical Bayes approach of Robbins is discussed in the context of asymptotic attainability of the bound uniformly in the parameter value.
Gaussian Processes (GPs) provide powerful probabilistic frameworks for interpolation, forecasting, and smoothing, but have been hampered by computational scaling issues. Here we investigate data sampled on one dimension (e.g., a scalar or vector time series sampled at arbitrarily-spaced intervals), for which state-space models are popular due to their linearly-scaling computational costs. It has long been conjectured that state-space models are general, able to approximate any one-dimensional GP. We provide the first general proof of this conjecture, showing that any stationary GP on one dimension with vector-valued observations governed by a Lebesgue-integrable continuous kernel can be approximated to any desired precision using a specifically-chosen state-space model: the Latent Exponentially Generated (LEG) family. This new family offers several advantages compared to the general state-space model: it is always stable (no unbounded growth), the covariance can be computed in closed form, and its parameter space is unconstrained (allowing straightforward estimation via gradient descent). The theorem's proof also draws connections to Spectral Mixture Kernels, providing insight about this popular family of kernels. We develop parallelized algorithms for performing inference and learning in the LEG model, test the algorithm on real and synthetic data, and demonstrate scaling to datasets with billions of samples.
Researchers are often interested in learning not only the effect of treatments on outcomes, but also the pathways through which these effects operate. A mediator is a variable that is affected by treatment and subsequently affects outcome. Existing methods for penalized mediation analyses either assume that finite-dimensional linear models are sufficient to remove confounding bias, or perform no confounding control at all. In practice, these assumptions may not hold. We propose a method that considers the confounding functions as nuisance parameters to be estimated using data-adaptive methods. We then use a novel regularization method applied to this objective function to identify a set of important mediators. We derive the asymptotic properties of our estimator and establish the oracle property under certain assumptions. Asymptotic results are also presented in a local setting which contrast the proposal with the standard adaptive lasso. We also propose a perturbation bootstrap technique to provide asymptotically valid post-selection inference for the mediated effects of interest. The performance of these methods will be discussed and demonstrated through simulation studies.
The fundamental problem in treatment effect estimation from observational data is confounder identification and balancing. Most of the previous methods realized confounder balancing by treating all observed pre-treatment variables as confounders, ignoring further identifying confounders and non-confounders. In general, not all the observed pre-treatment variables are confounders that refer to the common causes of the treatment and the outcome, some variables only contribute to the treatment and some only contribute to the outcome. Balancing those non-confounders, including instrumental variables and adjustment variables, would generate additional bias for treatment effect estimation. By modeling the different causal relations among observed pre-treatment variables, treatment and outcome, we propose a synergistic learning framework to 1) identify confounders by learning decomposed representations of both confounders and non-confounders, 2) balance confounder with sample re-weighting technique, and simultaneously 3) estimate the treatment effect in observational studies via counterfactual inference. Empirical results on synthetic and real-world datasets demonstrate that the proposed method can precisely decompose confounders and achieve a more precise estimation of treatment effect than baselines.
Recent years have witnessed remarkable progress towards computational fake news detection. To mitigate its negative impact, we argue that it is critical to understand what user attributes potentially cause users to share fake news. The key to this causal-inference problem is to identify confounders -- variables that cause spurious associations between treatments (e.g., user attributes) and outcome (e.g., user susceptibility). In fake news dissemination, confounders can be characterized by fake news sharing behavior that inherently relates to user attributes and online activities. Learning such user behavior is typically subject to selection bias in users who are susceptible to share news on social media. Drawing on causal inference theories, we first propose a principled approach to alleviating selection bias in fake news dissemination. We then consider the learned unbiased fake news sharing behavior as the surrogate confounder that can fully capture the causal links between user attributes and user susceptibility. We theoretically and empirically characterize the effectiveness of the proposed approach and find that it could be useful in protecting society from the perils of fake news.
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.
Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.
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