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Factorial analyses offer a powerful nonparametric means to detect main or interaction effects among multiple treatments. For survival outcomes, e.g. from clinical trials, such techniques can be adopted for comparing reasonable quantifications of treatment effects. The key difficulty to solve in survival analysis concerns the proper handling of censoring. So far, all existing factorial analyses for survival data were developed under the independent censoring assumption, which is too strong for many applications. As a solution, the central aim of this article is to develop new methods in factorial survival analyses under quite general dependent censoring regimes. This will be accomplished by combining existing results for factorial survival analyses with techniques developed for survival copula models. As a result, we will present an appealing F-test that exhibits sound performance in our simulation study. The new methods are illustrated in real data analysis. We implement the proposed method in an R function surv.factorial(.) in the R package compound.Cox.

With continuous outcomes, the average causal effect is typically defined using a contrast of expected potential outcomes. However, in the presence of skewed outcome data, the expectation may no longer be meaningful. In practice the typical approach is to either "ignore or transform" - ignore the skewness altogether or transform the outcome to obtain a more symmetric distribution, although neither approach is entirely satisfactory. Alternatively the causal effect can be redefined as a contrast of median potential outcomes, yet discussion of confounding-adjustment methods to estimate this parameter is limited. In this study we described and compared confounding-adjustment methods to address this gap. The methods considered were multivariable quantile regression, an inverse probability weighted (IPW) estimator, weighted quantile regression and two little-known implementations of g-computation for this problem. Motivated by a cohort investigation in the Longitudinal Study of Australian Children, we conducted a simulation study that found the IPW estimator, weighted quantile regression and g-computation implementations minimised bias when the relevant models were correctly specified, with g-computation additionally minimising the variance. These methods provide appealing alternatives to the common "ignore or transform" approach and multivariable quantile regression, enhancing our capability to obtain meaningful causal effect estimates with skewed outcome data.

Causal inference on populations embedded in social networks poses technical challenges, since the typical no interference assumption may no longer hold. For instance, in the context of social research, the outcome of a study unit will likely be affected by an intervention or treatment received by close neighbors. While inverse probability-of-treatment weighted (IPW) estimators have been developed for this setting, they are often highly inefficient. In this work, we assume that the network is a union of disjoint components and propose doubly robust (DR) estimators combining models for treatment and outcome that are consistent and asymptotically normal if either model is correctly specified. We present empirical results that illustrate the DR property and the efficiency gain of DR over IPW estimators when both the outcome and treatment models are correctly specified. Simulations are conducted for networks with equal and unequal component sizes and outcome data with and without a multilevel structure. We apply these methods in an illustrative analysis using the Add Health network, examining the impact of maternal college education on adolescent school performance, both direct and indirect.

We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds in two steps. We first specify the maximal degree to which the distribution of unobserved potential outcomes may deviate from that of observed outcomes. We then derive sharp bounds on the average treatment effects under this assumption. Our framework encompasses the popular marginal sensitivity model as a special case, and we demonstrate how the proposed methodology can address a primary challenge of the marginal sensitivity model that it produces uninformative results when unobserved confounders substantially affect treatment and outcome. Specifically, we develop an alternative sensitivity model, called the distributional sensitivity model, under the assumption that heterogeneity of treatment effect due to unobserved variables is relatively small. Unlike the marginal sensitivity model, the distributional sensitivity model allows for potential lack of overlap and often produces informative bounds even when unobserved variables substantially affect both treatment and outcome. Finally, we show how to extend the distributional sensitivity model to difference-in-differences designs and settings with instrumental variables. Through simulation and empirical studies, we demonstrate the applicability of the proposed methodology.

Gradient Balancing (GraB) is a recently proposed technique that finds provably better data permutations when training models with multiple epochs over a finite dataset. It converges at a faster rate than the widely adopted Random Reshuffling, by minimizing the discrepancy of the gradients on adjacently selected examples. However, GraB only operates under critical assumptions such as small batch sizes and centralized data, leaving open the question of how to order examples at large scale -- i.e. distributed learning with decentralized data. To alleviate the limitation, in this paper we propose D-GraB that involves two novel designs: (1) $\textsf{PairBalance}$ that eliminates the requirement to use stale gradient mean in GraB which critically relies on small learning rates; (2) an ordering protocol that runs $\textsf{PairBalance}$ in a distributed environment with negligible overhead, which benefits from both data ordering and parallelism. We prove D-GraB enjoys linear speed up at rate $\tilde{O}((mnT)^{-2/3})$ on smooth non-convex objectives and $\tilde{O}((mnT)^{-2})$ under PL condition, where $n$ denotes the number of parallel workers, $m$ denotes the number of examples per worker and $T$ denotes the number of epochs. Empirically, we show on various applications including GLUE, CIFAR10 and WikiText-2 that D-GraB outperforms naive parallel GraB and Distributed Random Reshuffling in terms of both training and validation performance.

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.

The problem of generalization and transportation of treatment effect estimates from a study sample to a target population is central to empirical research and statistical methodology. In both randomized experiments and observational studies, weighting methods are often used with this objective. Traditional methods construct the weights by separately modeling the treatment assignment and study selection probabilities and then multiplying functions (e.g., inverses) of their estimates. In this work, we provide a justification and an implementation for weighting in a single step. We show a formal connection between this one-step method and inverse probability and inverse odds weighting. We demonstrate that the resulting estimator for the target average treatment effect is consistent, asymptotically Normal, multiply robust, and semiparametrically efficient. We evaluate the performance of the one-step estimator in a simulation study. We illustrate its use in a case study on the effects of physician racial diversity on preventive healthcare utilization among Black men in California. We provide R code implementing the methodology.

The ability to accurately predict the opponent's behavior is central to the safety and efficiency of robotic systems in interactive settings, such as human-robot interaction and multi-robot teaming tasks. Unfortunately, robots often lack access to key information on which these predictions may hinge, such as opponent's goals, attention, and willingness to cooperate. Dual control theory addresses this challenge by treating unknown parameters of a predictive model as hidden states and inferring their values at runtime using information gathered during system operation. While able to optimally and automatically trade off exploration and exploitation, dual control is computationally intractable for general interactive motion planning. In this paper, we present a novel algorithmic approach to enable active uncertainty reduction for interactive motion planning based on the implicit dual control paradigm. Our approach relies on sampling-based approximation of stochastic dynamic programming, leading to a model predictive control problem. The resulting policy is shown to preserve the dual control effect for a broad class of predictive models with both continuous and categorical uncertainty. To ensure the safe operation of the interacting agents, we leverage a supervisory control scheme, oftentimes referred to as ``shielding'', which overrides the ego agent's dual control policy with a safety fallback strategy when a safety-critical event is imminent. We then augment the dual control framework with an improved variant of the recently proposed shielding-aware robust planning scheme, which proactively balances the nominal planning performance with the risk of high-cost emergency maneuvers triggered by low-probability opponent's behaviors. We demonstrate the efficacy of our approach with both simulated driving examples and hardware experiments using 1/10 scale autonomous vehicles.

Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian nonparametric regression. This problem becomes tremendously more difficult when considering other families such as logistic regression, Poisson and negative-binomial. For the first time, we present a method aiming to correct for measurement error when estimating regression functions flexibly covering virtually all distributions and link functions regularly considered in generalized linear models. This approach depends on approximating the first and the second moment of the response after integrating out the true unobserved predictors in a semiparametric generalized linear model. Unlike previous methods, this method is not restricted to truncated splines and can utilize various basis functions. Through extensive simulation studies, we study the performance of our method under many scenarios.

Small data challenges have emerged in many learning problems, since the success of deep neural networks often relies on the availability of a huge amount of labeled data that is expensive to collect. To address it, many efforts have been made on training complex models with small data in an unsupervised and semi-supervised fashion. In this paper, we will review the recent progresses on these two major categories of methods. A wide spectrum of small data models will be categorized in a big picture, where we will show how they interplay with each other to motivate explorations of new ideas. We will review the criteria of learning the transformation equivariant, disentangled, self-supervised and semi-supervised representations, which underpin the foundations of recent developments. Many instantiations of unsupervised and semi-supervised generative models have been developed on the basis of these criteria, greatly expanding the territory of existing autoencoders, generative adversarial nets (GANs) and other deep networks by exploring the distribution of unlabeled data for more powerful representations. While we focus on the unsupervised and semi-supervised methods, we will also provide a broader review of other emerging topics, from unsupervised and semi-supervised domain adaptation to the fundamental roles of transformation equivariance and invariance in training a wide spectrum of deep networks. It is impossible for us to write an exclusive encyclopedia to include all related works. Instead, we aim at exploring the main ideas, principles and methods in this area to reveal where we are heading on the journey towards addressing the small data challenges in this big data era.