Marginal structural models are a popular method for estimating causal effects in the presence of time-varying exposures. In spite of their popularity, no scalable non-parametric estimator exist for marginal structural models with multi-valued and time-varying treatments. In this paper, we use machine learning together with recent developments in semiparametric efficiency theory for longitudinal studies to propose such an estimator. The proposed estimator is based on a study of the non-parametric identifying functional, including first order von-Mises expansions as well as the efficient influence function and the efficiency bound. We show conditions under which the proposed estimator is efficient, asymptotically normal, and sequentially doubly robust in the sense that it is consistent if, for each time point, either the outcome or the treatment mechanism is consistently estimated. We perform a simulation study to illustrate the properties of the estimators, and present the results of our motivating study on a COVID-19 dataset studying the impact of mobility on the cumulative number of observed cases.

Recent advances in deep learning have mainly relied on Transformers due to their data dependency and ability to learn at scale. The attention module in these architectures, however, exhibits quadratic time and space in input size, limiting their scalability for long-sequence modeling. State Space Models (SSMs), and more specifically Selective SSMs (S6), with efficient hardware-aware implementation, have shown promising potential for long causal sequence modeling. They, however, use separate blocks for each channel and fail to filter irrelevant channels and capture inter-channel dependencies. Natural attempt to mix information across channels using MLP, attention, or SSMs results in further instability in the training of SSMs for large networks and/or nearly double the number of parameters. We present the MambaMixer block, a new SSM-based architecture with data-dependent weights that uses a dual selection mechanism across tokens and channels-called Selective Token and Channel Mixer. To mitigate doubling the number of parameters, we present a new non-causal heuristic of the S6 block with a hardware-friendly implementation. We further present an efficient variant of MambaMixer, called QSMixer, that mixes information along both sequence and embedding dimensions. As a proof of concept, we design Vision MambaMixer (ViM2) and Vision QSMixer (ViQS) architectures. To enhance their ability to capture spatial information in images, we present Switch of Scans (SoS) that dynamically uses a set of useful image scans to traverse image patches. We evaluate the performance of our methods in image classification, segmentation, and object detection. Our results underline the importance of selectively mixing across both tokens and channels and show the competitive (resp. superior) performance of our methods with well-established vision models (resp. SSM-based models).

We study the problem of estimating survival causal effects, where the aim is to characterize the impact of an intervention on survival times, i.e., how long it takes for an event to occur. Applications include determining if a drug reduces the time to ICU discharge or if an advertising campaign increases customer dwell time. Historically, the most popular estimates have been based on parametric or semiparametric (e.g. proportional hazards) models; however, these methods suffer from problematic levels of bias. Recently debiased machine learning approaches are becoming increasingly popular, especially in applications to large datasets. However, despite their appealing theoretical properties, these estimators tend to be unstable because the debiasing step involves the use of the inverses of small estimated probabilities -- small errors in the estimated probabilities can result in huge changes in their inverses and therefore the resulting estimator. This problem is exacerbated in survival settings where probabilities are a product of treatment assignment and censoring probabilities. We propose a covariate balancing approach to estimating these inverses directly, sidestepping this problem. The result is an estimator that is stable in practice and enjoys many of the same theoretical properties. In particular, under overlap and asymptotic equicontinuity conditions, our estimator is asymptotically normal with negligible bias and optimal variance. Our experiments on synthetic and semi-synthetic data demonstrate that our method has competitive bias and smaller variance than debiased machine learning approaches.

Estimating causal effects from large experimental and observational data has become increasingly prevalent in both industry and research. The bootstrap is an intuitive and powerful technique used to construct standard errors and confidence intervals of estimators. Its application however can be prohibitively demanding in settings involving large data. In addition, modern causal inference estimators based on machine learning and optimization techniques exacerbate the computational burden of the bootstrap. The bag of little bootstraps has been proposed in non-causal settings for large data but has not yet been applied to evaluate the properties of estimators of causal effects. In this paper, we introduce a new bootstrap algorithm called causal bag of little bootstraps for causal inference with large data. The new algorithm significantly improves the computational efficiency of the traditional bootstrap while providing consistent estimates and desirable confidence interval coverage. We describe its properties, provide practical considerations, and evaluate the performance of the proposed algorithm in terms of bias, coverage of the true 95% confidence intervals, and computational time in a simulation study. We apply it in the evaluation of the effect of hormone therapy on the average time to coronary heart disease using a large observational data set from the Women's Health Initiative.

Many scientific questions require estimating the effects of continuous treatments. Outcome modeling and weighted regression based on the generalized propensity score are the most commonly used methods to evaluate continuous effects. However, these techniques may be sensitive to model misspecification, extreme weights or both. In this paper, we propose Kernel Optimal Orthogonality Weighting (KOOW), a convex optimization-based method, for estimating the effects of continuous treatments. KOOW finds weights that minimize the worst-case penalized functional covariance between the continuous treatment and the confounders. By minimizing this quantity, KOOW successfully provides weights that orthogonalize confounders and the continuous treatment, thus providing optimal covariate balance, while controlling for extreme weights. We valuate its comparative performance in a simulation study. Using data from the Women's Health Initiative observational study, we apply KOOW to evaluate the effect of red meat consumption on blood pressure.

In causal inference, a variety of causal effect estimands have been studied, including the sample, uncensored, target, conditional, optimal subpopulation, and optimal weighted average treatment effects. Ad-hoc methods have been developed for each estimand based on inverse probability weighting (IPW) and on outcome regression modeling, but these may be sensitive to model misspecification, practical violations of positivity, or both. The contribution of this paper is twofold. First, we formulate the generalized average treatment effect (GATE) to unify these causal estimands as well as their IPW estimates. Second, we develop a method based on Kernel Optimal Matching (KOM) to optimally estimate GATE and to find the GATE most easily estimable by KOM, which we term the Kernel Optimal Weighted Average Treatment Effect. KOM provides uniform control on the conditional mean squared error of a weighted estimator over a class of models while simultaneously controlling for precision. We study its theoretical properties and evaluate its comparative performance in a simulation study. We illustrate the use of KOM for GATE estimation in two case studies: comparing spine surgical interventions and studying the effect of peer support on people living with HIV.

The ability to perform offline A/B-testing and off-policy learning using logged contextual bandit feedback is highly desirable in a broad range of applications, including recommender systems, search engines, ad placement, and personalized health care. Both offline A/B-testing and off-policy learning require a counterfactual estimator that evaluates how some new policy would have performed, if it had been used instead of the logging policy. This paper proposes a new counterfactual estimator - called Continuous Adaptive Blending (CAB) - for this policy evaluation problem that combines regression and weighting approaches for an effective bias/variance trade-off. It can be substantially less biased than clipped Inverse Propensity Score weighting and the Direct Method, and it can have less variance compared with Doubly Robust and IPS estimators. Experimental results show that CAB provides excellent and reliable estimation accuracy compared to other blended estimators, and - unlike the SWITCH estimator - is sub-differentiable such that it can be used for learning.

Marginal structural models (MSMs) estimate the causal effect of a time-varying treatment in the presence of time-dependent confounding via weighted regression. The standard approach of using inverse probability of treatment weighting (IPTW) can lead to high-variance estimates due to extreme weights and be sensitive to model misspecification. Various methods have been proposed to partially address this, including truncation and stabilized-IPTW to temper extreme weights and covariate balancing propensity score (CBPS) to address treatment model misspecification. In this paper, we present Kernel Optimal Weighting (KOW), a convex-optimization-based approach that finds weights for fitting the MSM that optimally balance time-dependent confounders while simultaneously controlling for precision, directly addressing the above limitations. KOW directly minimizes the error in estimation due to time-dependent confounding via a new decomposition as a functional. We further extend KOW to control for informative censoring. We evaluate the performance of KOW in a simulation study, comparing it with IPTW, stabilized-IPTW, and CBPS. We demonstrate the use of KOW in studying the effect of treatment initiation on time-to-death among people living with HIV and the effect of negative advertising on elections in the United States.