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Dropout often threatens the validity of causal inference in longitudinal studies. While existing studies have focused on the problem of missing outcomes caused by treatment, we study an important but overlooked source of dropout, selective eligibility. For example, patients may become ineligible for subsequent treatments due to severe side effects or complete recovery. Selective eligibility differs from the problem of ``truncation by death'' because dropout occurs after observing the outcome but before receiving the subsequent treatment. This difference makes the standard approach to dropout inapplicable. We propose a general methodological framework for longitudinal causal inference with selective eligibility. By focusing on subgroups of units who would become eligible for treatment given a specific treatment history, we define the time-specific eligible treatment effect (ETE) and expected number of outcome events (EOE) under a treatment sequence of interest. Assuming a generalized version of sequential ignorability, we derive two nonparametric identification formulae, each leveraging different parts of the observed data distribution. We then derive the efficient influence function of each causal estimand, yielding the corresponding doubly robust estimator. Finally, we apply the proposed methodology to an impact evaluation of a pre-trial risk assessment instrument in the criminal justice system, in which selective eligibility arises due to recidivism.

3D face alignment is a very challenging and fundamental problem in computer vision. Existing deep learning-based methods manually design different networks to regress either parameters of a 3D face model or 3D positions of face vertices. However, designing such networks relies on expert knowledge, and these methods often struggle to produce consistent results across various face poses. To address this limitation, we employ Neural Architecture Search (NAS) to automatically discover the optimal architecture for 3D face alignment. We propose a novel Multi-path One-shot Neural Architecture Search (MONAS) framework that leverages multi-scale features and contextual information to enhance face alignment across various poses. The MONAS comprises two key algorithms: Multi-path Networks Unbiased Sampling Based Training and Simulated Annealing based Multi-path One-shot Search. Experimental results on three popular benchmarks demonstrate the superior performance of the MONAS for both sparse alignment and dense alignment.

The use of Artificial Intelligence (AI), or more generally data-driven algorithms, has become ubiquitous in today's society. Yet, in many cases and especially when stakes are high, humans still make final decisions. The critical question, therefore, is whether AI helps humans make better decisions compared to a human-alone or AI-alone system. We introduce a new methodological framework to empirically answer this question with a minimal set of assumptions. We measure a decision maker's ability to make correct decisions using standard classification metrics based on the baseline potential outcome. We consider a single-blinded and unconfounded treatment assignment, where the provision of AI-generated recommendations is assumed to be randomized across cases with humans making final decisions. Under this study design, we show how to compare the performance of three alternative decision-making systems--human-alone, human-with-AI, and AI-alone. Importantly, the AI-alone system includes any individualized treatment assignment, including those that are not used in the original study. We also show when AI recommendations should be provided to a human-decision maker, and when one should follow such recommendations. We apply the proposed methodology to our own randomized controlled trial evaluating a pretrial risk assessment instrument. We find that the risk assessment recommendations do not improve the classification accuracy of a judge's decision to impose cash bail. Furthermore, we find that replacing a human judge with algorithms--the risk assessment score and a large language model in particular--leads to a worse classification performance.

Post-treatment variables often complicate causal inference. They appear in many scientific problems, including noncompliance, truncation by death, mediation, and surrogate endpoint evaluation. Principal stratification is a strategy to address these challenges by adjusting for the potential values of the post-treatment variables, defined as the principal strata. It allows for characterizing treatment effect heterogeneity across principal strata and unveiling the mechanism of the treatment's impact on the outcome related to post-treatment variables. However, the existing literature has primarily focused on binary post-treatment variables, leaving the case with continuous post-treatment variables largely unexplored. This gap persists due to the complexity of infinitely many principal strata, which present challenges to both the identification and estimation of causal effects. We fill this gap by providing nonparametric identification and semiparametric estimation theory for principal stratification with continuous post-treatment variables. We propose to use working models to approximate the underlying causal effect surfaces and derive the efficient influence functions of the corresponding model parameters. Based on the theory, we construct doubly robust estimators and implement them in an R package.

Point processes are probabilistic tools for modeling event data. While there exists a fast-growing literature studying the relationships between point processes, it remains unexplored how such relationships connect to causal effects. In the presence of unmeasured confounders, parameters from point process models do not necessarily have causal interpretations. We propose an instrumental variable method for causal inference with point process treatment and outcome. We define causal quantities based on potential outcomes and establish nonparametric identification results with a binary instrumental variable. We extend the traditional Wald estimation to deal with point process treatment and outcome, showing that it should be performed after a Fourier transform of the intention-to-treat effects on the treatment and outcome and thus takes the form of deconvolution. We term this as the generalised Wald estimation and propose an estimation strategy based on well-established deconvolution methods.

Data-driven decision making plays an important role even in high stakes settings like medicine and public policy. Learning optimal policies from observed data requires a careful formulation of the utility function whose expected value is maximized across a population. Although researchers typically use utilities that depend on observed outcomes alone, in many settings the decision maker's utility function is more properly characterized by the joint set of potential outcomes under all actions. For example, the Hippocratic principle to ``do no harm'' implies that the cost of causing death to a patient who would otherwise survive without treatment is greater than the cost of forgoing life-saving treatment. We consider optimal policy learning with asymmetric utility functions of this form. We show that asymmetric utilities lead to an unidentifiable social welfare function, and so we first partially identify it. Drawing on statistical decision theory, we then derive minimax decision rules by minimizing the maximum regret relative to alternative policies. We show that one can learn minimax decision rules from observed data by solving intermediate classification problems. We also establish that the finite sample regret of this procedure is bounded by the mis-classification rate of these intermediate classifiers. We apply this conceptual framework and methodology to the decision about whether or not to use right heart catheterization for patients with possible pulmonary hypertension.

Algorithmic recommendations and decisions have become ubiquitous in today's society. Many of these and other data-driven policies, especially in the realm of public policy, are based on known, deterministic rules to ensure their transparency and interpretability. For example, algorithmic pre-trial risk assessments, which serve as our motivating application, provide relatively simple, deterministic classification scores and recommendations to help judges make release decisions. How can we use the data based on existing deterministic policies to learn new and better policies? Unfortunately, prior methods for policy learning are not applicable because they require existing policies to be stochastic rather than deterministic. We develop a robust optimization approach that partially identifies the expected utility of a policy, and then finds an optimal policy by minimizing the worst-case regret. The resulting policy is conservative but has a statistical safety guarantee, allowing the policy-maker to limit the probability of producing a worse outcome than the existing policy. We extend this approach to common and important settings where humans make decisions with the aid of algorithmic recommendations. Lastly, we apply the proposed methodology to a unique field experiment on pre-trial risk assessment instruments. We derive new classification and recommendation rules that retain the transparency and interpretability of the existing instrument while potentially leading to better overall outcomes at a lower cost.

Classical recommender system methods typically face the filter bubble problem when users only receive recommendations of their familiar items, making them bored and dissatisfied. To address the filter bubble problem, unexpected recommendations have been proposed to recommend items significantly deviating from user's prior expectations and thus surprising them by presenting "fresh" and previously unexplored items to the users. In this paper, we describe a novel Personalized Unexpected Recommender System (PURS) model that incorporates unexpectedness into the recommendation process by providing multi-cluster modeling of user interests in the latent space and personalized unexpectedness via the self-attention mechanism and via selection of an appropriate unexpected activation function. Extensive offline experiments on three real-world datasets illustrate that the proposed PURS model significantly outperforms the state-of-the-art baseline approaches in terms of both accuracy and unexpectedness measures. In addition, we conduct an online A/B test at a major video platform Alibaba-Youku, where our model achieves over 3\% increase in the average video view per user metric. The proposed model is in the process of being deployed by the company., Comment: Accepted to RecSys20

Cross domain recommender system constitutes a powerful method to tackle the cold-start and sparsity problem by aggregating and transferring user preferences across multiple category domains. Therefore, it has great potential to improve click-through-rate prediction performance in online commerce platforms having many domains of products. While several cross domain sequential recommendation models have been proposed to leverage information from a source domain to improve CTR predictions in a target domain, they did not take into account bidirectional latent relations of user preferences across source-target domain pairs. As such, they cannot provide enhanced cross-domain CTR predictions for both domains simultaneously. In this paper, we propose a novel approach to cross-domain sequential recommendations based on the dual learning mechanism that simultaneously transfers information between two related domains in an iterative manner until the learning process stabilizes. In particular, the proposed Dual Attentive Sequential Learning (DASL) model consists of two novel components Dual Embedding and Dual Attention, which jointly establish the two-stage learning process: we first construct dual latent embeddings that extract user preferences in both domains simultaneously, and subsequently provide cross-domain recommendations by matching the extracted latent embeddings with candidate items through dual-attention learning mechanism. We conduct extensive offline experiments on three real-world datasets to demonstrate the superiority of our proposed model, which significantly and consistently outperforms several state-of-the-art baselines across all experimental settings. We also conduct an online A/B test at a major video streaming platform Alibaba-Youku, where our proposed model significantly improves business performance over the latest production system in the company., Comment: Accepted to KDD21

Despite an increasing reliance on fully-automated algorithmic decision-making in our day-to-day lives, human beings still make highly consequential decisions. As frequently seen in business, healthcare, and public policy, recommendations produced by algorithms are provided to human decision-makers to guide their decisions. While there exists a fast-growing literature evaluating the bias and fairness of such algorithmic recommendations, an overlooked question is whether they help humans make better decisions. We develop a statistical methodology for experimentally evaluating the causal impacts of algorithmic recommendations on human decisions. We also show how to examine whether algorithmic recommendations improve the fairness of human decisions and derive the optimal decision rules under various settings. We apply the proposed methodology to preliminary data from the first-ever randomized controlled trial that evaluates the pretrial Public Safety Assessment (PSA) in the criminal justice system. A goal of the PSA is to help judges decide which arrested individuals should be released. On the basis of the preliminary data available, we find that providing the PSA to the judge has little overall impact on the judge's decisions and subsequent arrestee behavior. However, our analysis yields some potentially suggestive evidence that the PSA may help avoid unnecessarily harsh decisions for female arrestees regardless of their risk levels while it encourages the judge to make stricter decisions for male arrestees who are deemed to be risky. In terms of fairness, the PSA appears to increase the gender bias against males while having little effect on any existing racial differences in judges' decision. Finally, we find that the PSA's recommendations might be unnecessarily severe unless the cost of a new crime is sufficiently high.

Causal inference concerns not only the average effect of the treatment on the outcome but also the underlying mechanism through an intermediate variable of interest. Principal stratification characterizes such a mechanism by targeting subgroup causal effects within principal strata, which are defined by the joint potential values of an intermediate variable. Due to the fundamental problem of causal inference, principal strata are inherently latent, rendering it challenging to identify and estimate subgroup effects within them. A line of research leverages the principal ignorability assumption that the latent principal strata are mean independent of the potential outcomes conditioning on the observed covariates. Under principal ignorability, we derive various nonparametric identification formulas for causal effects within principal strata in observational studies, which motivate estimators relying on the correct specifications of different parts of the observed-data distribution. Appropriately combining these estimators yields triply robust estimators for the causal effects within principal strata. These triply robust estimators are consistent if two of the treatment, intermediate variable, and outcome models are correctly specified, and moreover, they are locally efficient if all three models are correctly specified. We show that these estimators arise naturally from either the efficient influence functions in the semiparametric theory or the model-assisted estimators in the survey sampling theory. We evaluate different estimators based on their finite-sample performance through simulation and apply them to two observational studies., Comment: to appear in JRSSB

Two-stage randomized experiments are becoming an increasingly popular experimental design for causal inference when the outcome of one unit may be affected by the treatment assignments of other units in the same cluster. In this paper, we provide a methodological framework for general tools of statistical inference and power analysis for two-stage randomized experiments. Under the randomization-based framework, we consider the estimation of a new direct effect of interest as well as the average direct and spillover effects studied in the literature. We provide unbiased estimators of these causal quantities and their conservative variance estimators in a general setting. Using these results, we then develop hypothesis testing procedures and derive sample size formulas. We theoretically compare the two-stage randomized design with the completely randomized and cluster randomized designs, which represent two limiting designs. Finally, we conduct simulation studies to evaluate the empirical performance of our sample size formulas. For empirical illustration, the proposed methodology is applied to the randomized evaluation of the Indian national health insurance program. An open-source software package is available for implementing the proposed methodology.

In causal inference, principal stratification is a framework for dealing with a posttreatment intermediate variable between a treatment and an outcome, in which the principal strata are defined by the joint potential values of the intermediate variable. Because the principal strata are not fully observable, the causal effects within them, also known as the principal causal effects, are not identifiable without additional assumptions. Several previous empirical studies leveraged auxiliary variables to improve the inference of principal causal effects. We establish a general theory for identification and estimation of the principal causal effects with auxiliary variables, which provides a solid foundation for statistical inference and more insights for model building in empirical research. In particular, we consider two commonly-used strategies for principal stratification problems: principal ignorability, and the conditional independence between the auxiliary variable and the outcome given principal strata and covariates. For these two strategies, we give non-parametric and semi-parametric identification results without modeling assumptions on the outcome. When the assumptions for neither strategies are plausible, we propose a large class of flexible parametric and semi-parametric models for identifying principal causal effects. Our theory not only establishes formal identification results of several models that have been used in previous empirical studies but also generalizes them to allow for different types of outcomes and intermediate variables.

Using the concept of principal stratification from the causal inference literature, we introduce a new notion of fairness, called principal fairness, for human and algorithmic decision-making. The key idea is that one should not discriminate among individuals who would be similarly affected by the decision. Unlike the existing statistical definitions of fairness, principal fairness explicitly accounts for the fact that individuals can be impacted by the decision. Furthermore, we explain how principal fairness differs from the existing causality-based fairness criteria. In contrast to the counterfactual fairness criteria, for example, principal fairness considers the effects of decision in question rather than those of protected attributes of interest. We briefly discuss how to approach empirical evaluation and policy learning problems under the proposed principal fairness criterion.

This commentary has two goals. We first critically review the deconfounder method and point out its advantages and limitations. We then briefly consider three possible ways to address some of the limitations of the deconfounder method.

Instrumental variable methods can identify causal effects even when the treatment and outcome are confounded. We study the problem of imperfect measurements of the binary instrumental variable, treatment or outcome. We first consider non-differential measurement errors, that is, the mis-measured variable does not depend on other variables given its true value. We show that the measurement error of the instrumental variable does not bias the estimate, the measurement error of the treatment biases the estimate away from zero, and the measurement error of the outcome biases the estimate toward zero. Moreover, we derive sharp bounds on the causal effects without additional assumptions. These bounds are informative because they exclude zero. We then consider differential measurement errors, and focus on sensitivity analyses in those settings.

Frequently, empirical studies are plagued with missing data. When the data are missing not at random, the parameter of interest is not identifiable in general. Without additional assumptions, we can derive bounds of the parameters of interest, which, unfortunately, are often too wide to be informative. Therefore, it is of great importance to sharpen these worst-case bounds by exploiting additional information. Traditional missing data analysis uses only the information of the binary missing data indicator, that is, a certain data point is either missing or not. Nevertheless, real data often provide more information than a binary missing data indicator, and they often record different types of missingness. In a motivating HIV status survey, missing data may be due to the units' unwillingness to respond to the survey items or their hospitalization during the visit, and may also be due to the units' temporarily absence or relocation. It is apparent that some missing types are more likely to be missing not at random, but other missing types are more likely to be missing at random. We show that making full use of the missing types results in narrower bounds of the parameters of interest. In a real-life example, we demonstrate substantial improvement of more than 50% reduction in bound widths for estimating the prevalence of HIV in rural Malawi. As we illustrate using the HIV study, our strategy is also useful for conducting sensitivity analysis by gradually increasing or decreasing the set of types that are missing at random. In addition, we propose an easy-to-implement method to construct confidence intervals for partially identified parameters with bounds expressed as the minimums and maximums of finite parameters, which is useful for not only our problem but also many other problems involving bounds.

We show that if the exposure and the outcome affect the selection indicator in the same direction and have non-positive interaction on the risk difference, risk ratio or odds ratio scale, the exposure-outcome odds ratio in the selected population is a lower bound for true odds ratio.

Models based on multivariate t distributions are widely applied to analyze data with heavy tails. However, all the marginal distributions of the multivariate t distributions are restricted to have the same degrees of freedom, making these models unable to describe different marginal heavy-tailedness. We generalize the traditional multivariate t distributions to non-elliptically contoured multivariate t distributions, allowing for different marginal degrees of freedom. We apply the non-elliptically contoured multivariate t distributions to three widely-used models: the Heckman selection model with different degrees of freedom for selection and outcome equations, the multivariate Robit model with different degrees of freedom for marginal responses, and the linear mixed-effects model with different degrees of freedom for random effects and within-subject errors. Based on the Normal mixture representation of our t distribution, we propose efficient Bayesian inferential procedures for the model parameters based on data augmentation and parameter expansion. We show via simulation studies and real examples that the conclusions are sensitive to the existence of different marginal heavy-tailedness.