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Jeffrey C. Wong
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We introduce computational causal inference as an interdisciplinary field across causal inference, algorithms design and numerical computing. The field aims to develop software specializing in causal inference that can analyze massive datasets with a variety of causal effects, in a performant, general, and robust way. The focus on software improves research agility, and enables causal inference to be easily integrated into large engineering systems. In particular, we use computational causal inference to deepen the relationship between causal inference, online experimentation, and algorithmic decision making. This paper describes the new field, the demand, opportunities for scalability, open challenges, and begins the discussion for how the community can unite to solve challenges for scaling causal inference and decision making.
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This chapter surveys the most standard Monte Carlo methods available for simulating from a posterior distribution associated with a mixture and conducts some experiments about the robustness of the Gibbs sampler in high dimensional Gaussian settings. This is a chapter prepared for the forthcoming Handbook of Mixture Analysis.
SDRcausal is a package that implements sufficient dimension reduction methods for causal inference as proposed in Ghosh, Ma, and de Luna (2021). The package implements (augmented) inverse probability weighting and outcome regression (imputation) estimators of an average treatment effect (ATE) parameter. Nuisance models, both treatment assignment probability given the covariates (propensity score) and outcome regression models, are fitted by using semiparametric locally efficient dimension reduction estimators, thereby allowing for large sets of confounding covariates. Techniques including linear extrapolation, numerical differentiation, and truncation have been used to obtain a practicable implementation of the methods. Finding the suitable dimension reduction map (central mean subspace) requires solving an optimization problem, and several optimization algorithms are given as choices to the user. The package also provides estimators of the asymptotic variances of the causal effect estimators implemented. Plotting options are provided. The core of the methods are implemented in C language, and parallelization is allowed for. The user-friendly and freeware R language is used as interface. The package can be downloaded from Github repository: https://github.com/stat4reg.
Weighting methods are a common tool to de-bias estimates of causal effects. And though there are an increasing number of seemingly disparate methods, many of them can be folded into one unifying regime: causal optimal transport. This new method directly targets distributional balance by minimizing optimal transport distances between treatment and control groups or, more generally, between a source and target population. Our approach is model-free but can also incorporate moments or any other important functions of covariates that the researcher desires to balance. We find that the causal optimal transport outperforms competitor methods when both the propensity score and outcome models are misspecified, indicating it is a robust alternative to common weighting methods. Finally, we demonstrate the utility of our method in an external control study examining the effect of misoprostol versus oxytocin for treatment of post-partum hemorrhage.
Numerical integration and emulation are fundamental topics across scientific fields. We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate posterior density, combining it with Monte Carlo sampling methods and other quadrature rules. The nodes of the quadrature are sequentially chosen by maximizing a suitable acquisition function, which takes into account the current approximation of the posterior and the positions of the nodes. This maximization does not require additional evaluations of the true posterior. We introduce two specific schemes based on Gaussian and Nearest Neighbors (NN) bases. For the Gaussian case, we also provide a novel procedure for fitting the bandwidth parameter, in order to build a suitable emulator of a density function. With both techniques, we always obtain a positive estimation of the marginal likelihood (a.k.a., Bayesian evidence). An equivalent importance sampling interpretation is also described, which allows the design of extended schemes. Several theoretical results are provided and discussed. Numerical results show the advantage of the proposed approach, including a challenging inference problem in an astronomic dynamical model, with the goal of revealing the number of planets orbiting a star.
We investigate the problem of multiple time series forecasting, with the objective to improve multiple-step-ahead predictions. We propose a multi-task Gaussian process framework to simultaneously model batches of individuals with a common mean function and a specific covariance structure. This common mean is defined as a Gaussian process for which the hyper-posterior distribution is tractable. Therefore an EM algorithm can be derived for simultaneous hyper-parameters optimisation and hyper-posterior computation. Unlike previous approaches in the literature, we account for uncertainty and handle uncommon grids of observations while maintaining explicit formulations, by modelling the mean process in a non-parametric probabilistic framework. We also provide predictive formulas integrating this common mean process. This approach greatly improves the predictive performance far from observations, where information shared across individuals provides a relevant prior mean. Our overall algorithm is called textsc{Magma} (standing for Multi tAsk Gaussian processes with common MeAn), and publicly available as a R package. The quality of the mean process estimation, predictive performances, and comparisons to alternatives are assessed in various simulated scenarios and on real datasets.
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