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Causal inference is difficult in the presence of unobserved confounders. We introduce the instrumented common confounding (ICC) approach to (nonparametrically) identify causal effects with instruments, which are exogenous only conditional on some unobserved common confounders. The ICC approach is most useful in rich observational data with multiple sources of unobserved confounding, where instruments are at most exogenous conditional on some unobserved common confounders. Suitable examples of this setting are various identification problems in the social sciences, nonlinear dynamic panels, and problems with multiple endogenous confounders. The ICC identifying assumptions are closely related to those in mixture models, negative control and IV. Compared to mixture models [Bonhomme et al., 2016], we require less conditionally independent variables and do not need to model the unobserved confounder. Compared to negative control [Cui et al., 2020], we allow for non-common confounders, with respect to which the instruments are exogenous. Compared to IV [Newey and Powell, 2003], we allow instruments to be exogenous conditional on some unobserved common confounders, for which a set of relevant observed variables exists. We prove point identification with outcome model and alternatively first stage restrictions. We provide a practical step-by-step guide to the ICC model assumptions and present the causal effect of education on income as a motivating example.

Algorithmic decision-making in societal contexts, such as retail pricing, loan administration, recommendations on online platforms, etc., often involves experimentation with decisions for the sake of learning, which results in perceptions of unfairness among people impacted by these decisions. It is hence necessary to embed appropriate notions of fairness in such decision-making processes. The goal of this paper is to highlight the rich interface between temporal notions of fairness and online decision-making through a novel meta-objective of ensuring fairness at the time of decision. Given some arbitrary comparative fairness notion for static decision-making (e.g., students should pay at most 90% of the general adult price), a corresponding online decision-making algorithm satisfies fairness at the time of decision if the said notion of fairness is satisfied for any entity receiving a decision in comparison to all the past decisions. We show that this basic requirement introduces new methodological challenges in online decision-making. We illustrate the novel approaches necessary to address these challenges in the context of stochastic convex optimization with bandit feedback under a comparative fairness constraint that imposes lower bounds on the decisions received by entities depending on the decisions received by everyone in the past. The paper showcases novel research opportunities in online decision-making stemming from temporal fairness concerns.

Reaching a consensus in a swarm of robots is one of the fundamental problems in swarm robotics, examining the possibility of reaching an agreement within the swarm members. The recently-introduced contamination problem offers a new perspective of the problem, in which swarm members should reach a consensus in spite of the existence of adversarial members that intentionally act to divert the swarm members towards a different consensus. In this paper, we search for a consensus-reaching algorithm under the contamination problem setting by taking a top-down approach: We transform the problem to a centralized two-player game in which each player controls the behavior of a subset of the swarm, trying to force the entire swarm to converge to an agreement on its own value. We define a performance metric for each players performance, proving a correlation between this metric and the chances of the player to win the game. We then present the globally optimal solution to the game and prove that unfortunately it is unattainable in a distributed setting, due to the challenging characteristics of the swarm members. We therefore examine the problem on a simplified swarm model, and compare the performance of the globally optimal strategy with locally optimal strategies, demonstrating its superiority in rigorous simulation experiments.

Binary stars undergo a variety of interactions and evolutionary phases, critical for predicting and explaining observed properties. Binary population synthesis with full stellar-structure and evolution simulations are computationally expensive requiring a large number of mass-transfer sequences. The recently developed binary population synthesis code POSYDON incorporates grids of MESA binary star simulations which are then interpolated to model large-scale populations of massive binaries. The traditional method of computing a high-density rectilinear grid of simulations is not scalable for higher-dimension grids, accounting for a range of metallicities, rotation, and eccentricity. We present a new active learning algorithm, psy-cris, which uses machine learning in the data-gathering process to adaptively and iteratively select targeted simulations to run, resulting in a custom, high-performance training set. We test psy-cris on a toy problem and find the resulting training sets require fewer simulations for accurate classification and regression than either regular or randomly sampled grids. We further apply psy-cris to the target problem of building a dynamic grid of MESA simulations, and we demonstrate that, even without fine tuning, a simulation set of only $\sim 1/4$ the size of a rectilinear grid is sufficient to achieve the same classification accuracy. We anticipate further gains when algorithmic parameters are optimized for the targeted application. We find that optimizing for classification only may lead to performance losses in regression, and vice versa. Lowering the computational cost of producing grids will enable future versions of POSYDON to cover more input parameters while preserving interpolation accuracies.

The human prioritization of image regions can be modeled in a time invariant fashion with saliency maps or sequentially with scanpath models. However, while both types of models have steadily improved on several benchmarks and datasets, there is still a considerable gap in predicting human gaze. Here, we leverage two recent developments to reduce this gap: theoretical analyses establishing a principled framework for predicting the next gaze target and the empirical measurement of the human cost for gaze switches independently of image content. We introduce an algorithm in the framework of sequential decision making, which converts any static saliency map into a sequence of dynamic history-dependent value maps, which are recomputed after each gaze shift. These maps are based on 1) a saliency map provided by an arbitrary saliency model, 2) the recently measured human cost function quantifying preferences in magnitude and direction of eye movements, and 3) a sequential exploration bonus, which changes with each subsequent gaze shift. The parameters of the spatial extent and temporal decay of this exploration bonus are estimated from human gaze data. The relative contributions of these three components were optimized on the MIT1003 dataset for the NSS score and are sufficient to significantly outperform predictions of the next gaze target on NSS and AUC scores for five state of the art saliency models on three image data sets. Thus, we provide an implementation of human gaze preferences, which can be used to improve arbitrary saliency models' predictions of humans' next gaze targets.

Treatment decisions in cancer care are guided by treatment effect estimates from randomized controlled trials (RCTs). RCTs estimate the average effect of one treatment versus another in a certain population. However, treatments may not be equally effective for every patient in a population. Knowing the effectiveness of treatments tailored to specific patient and tumor characteristics would enable individualized treatment decisions. Getting tailored treatment effects by averaging outcomes in different patient subgroups in RCTs requires an unfeasible number of patients to have sufficient statistical power in all relevant subgroups for all possible treatments. The American Joint Committee on Cancer (AJCC) recommends that researchers develop outcome prediction models (OPMs) in an effort to individualize treatment decisions. OPMs sometimes called risk models or prognosis models, use patient and tumor characteristics to predict a patient outcome such as overall survival. The assumption is that the predictions are useful for treatment decisions using rules such as "prescribe chemotherapy only if the OPM predicts the patient has a high risk of recurrence". Recognizing the importance of reliable predictions, the AJCC published a checklist for OPMs to ensure dependable OPM prediction accuracy in the patient population for which the OPM was designed. However, accurate outcome predictions do not imply that these predictions yield good treatment decisions. In this perspective, we show that OPM rely on a fixed treatment policy which implies that OPM that were found to accurately predict outcomes in validation studies can still lead to patient harm when used to inform treatment decisions. We then give guidance on how to develop models that are useful for individualized treatment decisions and how to evaluate whether a model has value for decision-making.

To estimate causal effects, analysts performing observational studies in health settings utilize several strategies to mitigate bias due to confounding by indication. There are two broad classes of approaches for these purposes: use of confounders and instrumental variables (IVs). Because such approaches are largely characterized by untestable assumptions, analysts must operate under an indefinite paradigm that these methods will work imperfectly. In this tutorial, we formalize a set of general principles and heuristics for estimating causal effects in the two approaches when the assumptions are potentially violated. This crucially requires reframing the process of observational studies as hypothesizing potential scenarios where the estimates from one approach are less inconsistent than the other. While most of our discussion of methodology centers around the linear setting, we touch upon complexities in non-linear settings and flexible procedures such as target minimum loss-based estimation (TMLE) and double machine learning (DML). To demonstrate the application of our principles, we investigate the use of donepezil off-label for mild cognitive impairment (MCI). We compare and contrast results from confounder and IV methods, traditional and flexible, within our analysis and to a similar observational study and clinical trial.

Analyzing observational data from multiple sources can be useful for increasing statistical power to detect a treatment effect; however, practical constraints such as privacy considerations may restrict individual-level information sharing across data sets. This paper develops federated methods that only utilize summary-level information from heterogeneous data sets. Our federated methods provide doubly-robust point estimates of treatment effects as well as variance estimates. We derive the asymptotic distributions of our federated estimators, which are shown to be asymptotically equivalent to the corresponding estimators from the combined, individual-level data. We show that to achieve these properties, federated methods should be adjusted based on conditions such as whether models are correctly specified and stable across heterogeneous data sets.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.