Causal inference using observational text data is becoming increasingly popular in many research areas. This paper presents the Bayesian Topic Regression (BTR) model that uses both text and numerical information to model an outcome variable. It allows estimation of both discrete and continuous treatment effects. Furthermore, it allows for the inclusion of additional numerical confounding factors next to text data. To this end, we combine a supervised Bayesian topic model with a Bayesian regression framework and perform supervised representation learning for the text features jointly with the regression parameter training, respecting the Frisch-Waugh-Lovell theorem. Our paper makes two main contributions. First, we provide a regression framework that allows causal inference in settings when both text and numerical confounders are of relevance. We show with synthetic and semi-synthetic datasets that our joint approach recovers ground truth with lower bias than any benchmark model, when text and numerical features are correlated. Second, experiments on two real-world datasets demonstrate that a joint and supervised learning strategy also yields superior prediction results compared to strategies that estimate regression weights for text and non-text features separately, being even competitive with more complex deep neural networks.
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Estimating personalized treatment effects from high-dimensional observational data is essential in situations where experimental designs are infeasible, unethical, or expensive. Existing approaches rely on fitting deep models on outcomes observed for treated and control populations. However, when measuring individual outcomes is costly, as is the case of a tumor biopsy, a sample-efficient strategy for acquiring each result is required. Deep Bayesian active learning provides a framework for efficient data acquisition by selecting points with high uncertainty. However, existing methods bias training data acquisition towards regions of non-overlapping support between the treated and control populations. These are not sample-efficient because the treatment effect is not identifiable in such regions. We introduce causal, Bayesian acquisition functions grounded in information theory that bias data acquisition towards regions with overlapping support to maximize sample efficiency for learning personalized treatment effects. We demonstrate the performance of the proposed acquisition strategies on synthetic and semi-synthetic datasets IHDP and CMNIST and their extensions, which aim to simulate common dataset biases and pathologies.
This paper studies causal inference in randomized experiments under network interference. Commonly used models of interference posit that treatments assigned to alters beyond a certain network distance from the ego have no effect on the ego's response. However, this assumption is violated in common models of social interactions. We propose a substantially weaker model of "approximate neighborhood interference" (ANI) under which treatments assigned to alters further from the ego have a smaller, but potentially nonzero, effect on the ego's response. We formally verify that ANI holds for well-known models of social interactions. Under ANI, restrictions on the network topology, and asymptotics under which the network size increases, we prove that standard inverse-probability weighting estimators consistently estimate useful exposure effects and are approximately normal. For inference, we consider a network HAC variance estimator. Under a finite population model, we show that the estimator is biased but that the bias can be interpreted as the variance of unit-level exposure effects. This generalizes Neyman's well-known result on conservative variance estimation to settings with interference.
Several problems in neuroimaging and beyond require inference on the parameters of multi-task sparse hierarchical regression models. Examples include M/EEG inverse problems, neural encoding models for task-based fMRI analyses, and temperature monitoring of climate or CPU and GPU. In these domains, both the model parameters to be inferred and the measurement noise may exhibit a complex spatio-temporal structure. Existing work either neglects the temporal structure or leads to computationally demanding inference schemes. Overcoming these limitations, we devise a novel flexible hierarchical Bayesian framework within which the spatio-temporal dynamics of model parameters and noise are modeled to have Kronecker product covariance structure. Inference in our framework is based on majorization-minimization optimization and has guaranteed convergence properties. Our highly efficient algorithms exploit the intrinsic Riemannian geometry of temporal autocovariance matrices. For stationary dynamics described by Toeplitz matrices, the theory of circulant embeddings is employed. We prove convex bounding properties and derive update rules of the resulting algorithms. On both synthetic and real neural data from M/EEG, we demonstrate that our methods lead to improved performance.
Quantile regression is a powerful data analysis tool that accommodates heterogeneous covariate-response relationships. We find that by coupling the asymmetric Laplace working likelihood with appropriate shrinkage priors, we can deliver posterior inference that automatically adapts to possible sparsity in quantile regression analysis. After a suitable adjustment on the posterior variance, the posterior inference provides asymptotically valid inference under heterogeneity. Furthermore, the proposed approach leads to oracle asymptotic efficiency for the active (nonzero) quantile regression coefficients and super-efficiency for the non-active ones. By avoiding the need to pursue dichotomous variable selection, the Bayesian computational framework demonstrates desirable inference stability with respect to tuning parameter selection. Our work helps to uncloak the value of Bayesian computational methods in frequentist inference for quantile regression.
In the era of open data, Poisson and other count regression models are increasingly important. Still, conventional Poisson regression has remaining issues in terms of identifiability and computational efficiency. Especially, due to an identification problem, Poisson regression can be unstable for small samples with many zeros. Provided this, we develop a closed-form inference for an over-dispersed Poisson regression including Poisson additive mixed models. The approach is derived via mode-based log-Gaussian approximation. The resulting method is fast, practical, and free from the identification problem. Monte Carlo experiments demonstrate that the estimation error of the proposed method is a considerably smaller estimation error than the closed-form alternatives and as small as the usual Poisson regressions. For counts with many zeros, our approximation has better estimation accuracy than conventional Poisson regression. We obtained similar results in the case of Poisson additive mixed modeling considering spatial or group effects. The developed method was applied for analyzing COVID-19 data in Japan. This result suggests that influences of pedestrian density, age, and other factors on the number of cases change over periods.
Using bandit algorithms to conduct adaptive randomised experiments can minimise regret, but it poses major challenges for statistical inference (e.g., biased estimators, inflated type-I error and reduced power). Recent attempts to address these challenges typically impose restrictions on the exploitative nature of the bandit algorithm$-$trading off regret$-$and require large sample sizes to ensure asymptotic guarantees. However, large experiments generally follow a successful pilot study, which is tightly constrained in its size or duration. Increasing power in such small pilot experiments, without limiting the adaptive nature of the algorithm, can allow promising interventions to reach a larger experimental phase. In this work we introduce a novel hypothesis test, uniquely based on the allocation probabilities of the bandit algorithm, and without constraining its exploitative nature or requiring a minimum experimental size. We characterise our $Allocation\ Probability\ Test$ when applied to $Thompson\ Sampling$, presenting its asymptotic theoretical properties, and illustrating its finite-sample performances compared to state-of-the-art approaches. We demonstrate the regret and inferential advantages of our approach, particularly in small samples, in both extensive simulations and in a real-world experiment on mental health aspects.
We propose two robust methods for testing hypotheses on unknown parameters of predictive regression models under heterogeneous and persistent volatility as well as endogenous, persistent and/or fat-tailed regressors and errors. The proposed robust testing approaches are applicable both in the case of discrete and continuous time models. Both of the methods use the Cauchy estimator to effectively handle the problems of endogeneity, persistence and/or fat-tailedness in regressors and errors. The difference between our two methods is how the heterogeneous volatility is controlled. The first method relies on robust t-statistic inference using group estimators of a regression parameter of interest proposed in Ibragimov and Muller, 2010. It is simple to implement, but requires the exogenous volatility assumption. To relax the exogenous volatility assumption, we propose another method which relies on the nonparametric correction of volatility. The proposed methods perform well compared with widely used alternative inference procedures in terms of their finite sample properties.
This paper is concerned with data-driven unsupervised domain adaptation, where it is unknown in advance how the joint distribution changes across domains, i.e., what factors or modules of the data distribution remain invariant or change across domains. To develop an automated way of domain adaptation with multiple source domains, we propose to use a graphical model as a compact way to encode the change property of the joint distribution, which can be learned from data, and then view domain adaptation as a problem of Bayesian inference on the graphical models. Such a graphical model distinguishes between constant and varied modules of the distribution and specifies the properties of the changes across domains, which serves as prior knowledge of the changing modules for the purpose of deriving the posterior of the target variable $Y$ in the target domain. This provides an end-to-end framework of domain adaptation, in which additional knowledge about how the joint distribution changes, if available, can be directly incorporated to improve the graphical representation. We discuss how causality-based domain adaptation can be put under this umbrella. Experimental results on both synthetic and real data demonstrate the efficacy of the proposed framework for domain adaptation. The code is available at //github.com/mgong2/DA_Infer .
The inaccessibility of controlled randomized trials due to inherent constraints in many fields of science has been a fundamental issue in causal inference. In this paper, we focus on distinguishing the cause from effect in the bivariate setting under limited observational data. Based on recent developments in meta learning as well as in causal inference, we introduce a novel generative model that allows distinguishing cause and effect in the small data setting. Using a learnt task variable that contains distributional information of each dataset, we propose an end-to-end algorithm that makes use of similar training datasets at test time. We demonstrate our method on various synthetic as well as real-world data and show that it is able to maintain high accuracy in detecting directions across varying dataset sizes.
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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