To comprehensively evaluate a public policy intervention, researchers must consider the effects of the policy not just on the implementing region, but also nearby, indirectly-affected regions. For example, an excise tax on sweetened beverages in Philadelphia was shown to not only be associated with a decrease in volume sales of taxed beverages in Philadelphia, but also an increase in sales in bordering counties not subject to the tax. The latter association may be explained by cross-border shopping behaviors of Philadelphia residents and indicate a causal effect of the tax on nearby regions, which may offset the total effect of the intervention. To estimate causal effects in this setting, we extend difference-in-differences methodology to account for such interference between regions and adjust for potential confounding present in quasi-experimental evaluations. Our doubly robust estimators for the average treatment effect on the treated and neighboring control relax standard assumptions on interference and model specification. We apply these methods to evaluate the change in volume sales of taxed beverages in 231 Philadelphia and bordering county stores due to the Philadelphia beverage tax. We also use our methods to explore the heterogeneity of effects across geographic features.
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In the past decade, the technology industry has adopted online randomized controlled experiments (a.k.a. A/B testing) to guide product development and make business decisions. In practice, A/B tests are often implemented with increasing treatment allocation: the new treatment is gradually released to an increasing number of units through a sequence of randomized experiments. In scenarios such as experimenting in a social network setting or in a bipartite online marketplace, interference among units may exist, which can harm the validity of simple inference procedures. In this work, we introduce a widely applicable procedure to test for interference in A/B testing with increasing allocation. Our procedure can be implemented on top of an existing A/B testing platform with a separate flow and does not require a priori a specific interference mechanism. In particular, we introduce two permutation tests that are valid under different assumptions. Firstly, we introduce a general statistical test for interference requiring no additional assumption. Secondly, we introduce a testing procedure that is valid under a time fixed effect assumption. The testing procedure is of very low computational complexity, it is powerful, and it formalizes a heuristic algorithm implemented already in industry. We demonstrate the performance of the proposed testing procedure through simulations on synthetic data. Finally, we discuss one application at LinkedIn, where a screening step is implemented to detect potential interference in all their marketplace experiments with the proposed methods in the paper.
Synthetic control is a causal inference tool used to estimate the treatment effects of an intervention by creating synthetic counterfactual data. This approach combines measurements from other similar observations (i.e., donor pool ) to predict a counterfactual time series of interest (i.e., target unit) by analyzing the relationship between the target and the donor pool before the intervention. As synthetic control tools are increasingly applied to sensitive or proprietary data, formal privacy protections are often required. In this work, we provide the first algorithms for differentially private synthetic control with explicit error bounds. Our approach builds upon tools from non-private synthetic control and differentially private empirical risk minimization. We provide upper and lower bounds on the sensitivity of the synthetic control query and provide explicit error bounds on the accuracy of our private synthetic control algorithms. We show that our algorithms produce accurate predictions for the target unit, and that the cost of privacy is small. Finally, we empirically evaluate the performance of our algorithm, and show favorable performance in a variety of parameter regimes, as well as providing guidance to practitioners for hyperparameter tuning.
In the task of predicting spatio-temporal fields in environmental science using statistical methods, introducing statistical models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest. Large space-time datasets call for new numerical methods to efficiently process them. The Stochastic Partial Differential Equation (SPDE) approach has proven to be effective for the estimation and the prediction in a spatial context. We present here the advection-diffusion SPDE with first order derivative in time which defines a large class of nonseparable spatio-temporal models. A Gaussian Markov random field approximation of the solution to the SPDE is built by discretizing the temporal derivative with a finite difference method (implicit Euler) and by solving the spatial SPDE with a finite element method (continuous Galerkin) at each time step. The ''Streamline Diffusion'' stabilization technique is introduced when the advection term dominates the diffusion. Computationally efficient methods are proposed to estimate the parameters of the SPDE and to predict the spatio-temporal field by kriging, as well as to perform conditional simulations. The approach is applied to a solar radiation dataset. Its advantages and limitations are discussed.
sparseDFM is an R package for the implementation of popular estimation methods for dynamic factor models (DFMs) including the novel Sparse DFM approach of Mosley et al. (2023). The Sparse DFM ameliorates interpretability issues of factor structure in classic DFMs by constraining the loading matrices to have few non-zero entries (i.e. are sparse). Mosley et al. (2023) construct an efficient expectation maximisation (EM) algorithm to enable estimation of model parameters using a regularised quasi-maximum likelihood. We provide detail on the estimation strategy in this paper and show how we implement this in a computationally efficient way. We then provide two real-data case studies to act as tutorials on how one may use the sparseDFM package. The first case study focuses on summarising the structure of a small subset of quarterly CPI (consumer price inflation) index data for the UK, while the second applies the package onto a large-scale set of monthly time series for the purpose of nowcasting nine of the main trade commodities the UK exports worldwide.
We consider identification and inference about a counterfactual outcome mean when there is unmeasured confounding using tools from proximal causal inference (Miao et al. [2018], Tchetgen Tchetgen et al. [2020]). Proximal causal inference requires existence of solutions to at least one of two integral equations. We motivate the existence of solutions to the integral equations from proximal causal inference by demonstrating that, assuming the existence of a solution to one of the integral equations, $\sqrt{n}$-estimability of a linear functional (such as its mean) of that solution requires the existence of a solution to the other integral equation. Solutions to the integral equations may not be unique, which complicates estimation and inference. We construct a consistent estimator for the solution set for one of the integral equations and then adapt the theory of extremum estimators to find from the estimated set a consistent estimator for a uniquely defined solution. A debiased estimator for the counterfactual mean is shown to be root-$n$ consistent, regular, and asymptotically semiparametrically locally efficient under additional regularity conditions.
Motivated by applications in personalized medicine and individualized policy making, there is a growing interest in techniques for quantifying treatment effect heterogeneity in terms of the conditional average treatment effect (CATE). Some of the most prominent methods for CATE estimation developed in recent years are T-Learner, DR-Learner and R-Learner. The latter two were designed to improve on the former by being Neyman-orthogonal. However, the relations between them remain unclear, and likewise does the literature remain vague on whether these learners converge to a useful quantity or (functional) estimand when the underlying optimization procedure is restricted to a class of functions that does not include the CATE. In this article, we provide insight into these questions by discussing DR-learner and R-learner as special cases of a general class of Neyman-orthogonal learners for the CATE, for which we moreover derive oracle bounds. Our results shed light on how one may construct Neyman-orthogonal learners with desirable properties, on when DR-learner may be preferred over R-learner (and vice versa), and on novel learners that may sometimes be preferable to either of these. Theoretical findings are confirmed using results from simulation studies on synthetic data, as well as an application in critical care medicine.
Estimating long-term causal effects based on short-term surrogates is a significant but challenging problem in many real-world applications, e.g., marketing and medicine. Despite its success in certain domains, most existing methods estimate causal effects in an idealistic and simplistic way - ignoring the causal structure among short-term outcomes and treating all of them as surrogates. However, such methods cannot be well applied to real-world scenarios, in which the partially observed surrogates are mixed with their proxies among short-term outcomes. To this end, we develop our flexible method, Laser, to estimate long-term causal effects in the more realistic situation that the surrogates are observed or have observed proxies.Given the indistinguishability between the surrogates and proxies, we utilize identifiable variational auto-encoder (iVAE) to recover the whole valid surrogates on all the surrogates candidates without the need of distinguishing the observed surrogates or the proxies of latent surrogates. With the help of the recovered surrogates, we further devise an unbiased estimation of long-term causal effects. Extensive experimental results on the real-world and semi-synthetic datasets demonstrate the effectiveness of our proposed method.
With the proliferation of devices that display augmented reality (AR), now is the time for scholars and practitioners to evaluate and engage critically with emerging applications of the medium. AR mediates the way users see their bodies, hear their environment and engage with places. Applied in various forms, including social media, e-commerce, gaming, enterprise and art, the medium facilitates a hybrid experience of physical and digital spaces. This article employs a model of real-and-imagined space from geographer Edward Soja to examine how the user of an AR app navigates the two intertwined spaces of physical and digital, experiencing what Soja calls a 'Third-space'. The article illustrates the potential for headset-based AR to engender such a Thirdspace through the author's practice-led research project, the installation Through the Wardrobe. This installation demonstrates how AR has the potential to shift the way that users view and interact with their world with artistic applications providing an opportunity to question assumptions of social norms, identity and uses of physical space.
The concept of causality plays an important role in human cognition . In the past few decades, causal inference has been well developed in many fields, such as computer science, medicine, economics, and education. With the advancement of deep learning techniques, it has been increasingly used in causal inference against counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective optimization functions to estimate counterfactual data unbiasedly based on the different optimization methods. This paper focuses on the survey of the deep causal models, and its core contributions are as follows: 1) we provide relevant metrics under multiple treatments and continuous-dose treatment; 2) we incorporate a comprehensive overview of deep causal models from both temporal development and method classification perspectives; 3) we assist a detailed and comprehensive classification and analysis of relevant datasets and source code.
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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