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1. Energy balancing of covariate distributions

   https://doi.org/10.1515/jci-2022-0029  

   Huling, Jared D; Mak, Simon (January 2024, Journal of Causal Inference)

   Abstract Bias in causal comparisons has a correspondence with distributional imbalance of covariates between treatment groups. Weighting strategies such as inverse propensity score weighting attempt to mitigate bias by either modeling the treatment assignment mechanism or balancing specified covariate moments. This article introduces a new weighting method, called energy balancing, which instead aims to balance weighted covariate distributions. By directly targeting distributional imbalance, the proposed weighting strategy can be flexibly utilized in a wide variety of causal analyses without the need for careful model or moment specification. Our energy balancing weights (EBW) approach has several advantages over existing weighting techniques. First, it offers a model-free and robust approach for obtaining covariate balance that does not require tuning parameters, obviating the need for modeling decisions of secondary nature to the scientific question at hand. Second, since this approach is based on a genuine measure of distributional balance, it provides a means for assessing the balance induced by a given set of weights for a given dataset. We demonstrate the effectiveness of this EBW approach in a suite of simulation experiments, and in studies on the safety of right heart catheterization and on three additional studies using electronic health record data. 

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2. Robust data-driven discovery of governing physical laws with error bars

   https://doi.org/10.1098/rspa.2018.0305  

   Zhang, Sheng; Lin, Guang (September 2018, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   Discovering governing physical laws from noisy data is a grand challenge in many science and engineering research areas. We present a new approach to data-driven discovery of ordinary differential equations (ODEs) and partial differential equations (PDEs), in explicit or implicit form. We demonstrate our approach on a wide range of problems, including shallow water equations and Navier–Stokes equations. The key idea is to select candidate terms for the underlying equations using dimensional analysis, and to approximate the weights of the terms with error bars using our threshold sparse Bayesian regression. This new algorithm employs Bayesian inference to tune the hyperparameters automatically. Our approach is effective, robust and able to quantify uncertainties by providing an error bar for each discovered candidate equation. The effectiveness of our algorithm is demonstrated through a collection of classical ODEs and PDEs. Numerical experiments demonstrate the robustness of our algorithm with respect to noisy data and its ability to discover various candidate equations with error bars that represent the quantified uncertainties. Detailed comparisons with the sequential threshold least-squares algorithm and the lasso algorithm are studied from noisy time-series measurements and indicate that the proposed method provides more robust and accurate results. In addition, the data-driven prediction of dynamics with error bars using discovered governing physical laws is more accurate and robust than classical polynomial regressions. 

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3. Propensity Score Weighting for Causal Inference with Clustered Data

   https://doi.org/10.1515/jci-2017-0027  

   Yang, Shu (September 2018, Journal of Causal Inference)

   Abstract Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-level covariates that are related to both the treatment assignment and outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment may be biased. In this article, we propose a calibration technique for propensity score estimation under the latent ignorable treatment assignment mechanism, i. e., the treatment-outcome relationship is unconfounded given the observed covariates and the latent cluster-specific confounders. We impose novel balance constraints which imply exact balance of the observed confounders and the unobserved cluster-level confounders between the treatment groups. We show that the proposed calibrated propensity score weighting estimator is doubly robust in that it is consistent for the average treatment effect if either the propensity score model is correctly specified or the outcome follows a linear mixed effects model. Moreover, the proposed weighting method can be combined with sampling weights for an integrated solution to handle confounding and sampling designs for causal inference with clustered survey data. In simulation studies, we show that the proposed estimator is superior to other competitors. We estimate the effect of School Body Mass Index Screening on prevalence of overweight and obesity for elementary schools in Pennsylvania. 

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4. Multisite causal mediation analysis in the presence of complex sample and survey designs and non-random nonresponse

   Qin, X.; Hong, G.; Deutsch, J.; & Bein, E. (January 2019, Journal of the Royal Statistical Society)

   This study provides a template for multisite causal mediation analysis using a comprehensive weighting-based analytic procedure that enhances external and internal validity. The template incorporates a sample weight to adjust for complex sample and survey designs, adopts an IPTW weight to adjust for differential treatment assignment probabilities, employs an estimated nonresponse weight to account for non-random nonresponse, and utilizes a propensity score-based weighting strategy to flexibly decompose not only the population average but also the between-site heterogeneity of the total program impact. Because the identification assumptions are not always warranted, a weighting-based balance checking procedure assesses the remaining overt bias, while a weighting-based sensitivity analysis further evaluates the potential bias related to omitted confounding or to propensity score model misspecification. We derive the asymptotic variance of the estimators for the causal effects that account for the sampling uncertainty in the estimated weights. The method is applied to a re-analysis of the data from the National Job Corps Study. 

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5. Easy Variational Inference for Categorical Models via an Independent Binary Approximation

   Michael T Wojnowicz, Shuchin Aeron (January 2022, The 39th International Conference on Machine Learning,)

   We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. GLMs have been difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using conjugate auxiliary variable methods. We define a new class of GLMs for categorical data called categorical-from-binary (CB) models. Each CB model has a likelihood that is bounded by the product of binary likelihoods, suggesting a natural posterior approximation. This approximation makes inference straightforward and fast; using well-known auxiliary variables for probit or logistic regression, the product of binary models admits conjugate closed-form variational inference that is embarrassingly parallel across categories and invariant to category ordering. Moreover, an independent binary model simultaneously approximates multiple CB models. Bayesian model averaging over these can improve the quality of the approximation for any given dataset. We show that our approach scales to thousands of categories, outperforming posterior estimation competitors like Automatic Differentiation Variational Inference (ADVI) and No U-Turn Sampling (NUTS) in the time required to achieve fixed prediction quality. 

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