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Causal inference is a critical research area with multi-disciplinary origins and applications, ranging from statistics, computer science, economics, psychology to public health. In many scientific research, randomized experiments provide a golden standard for estimation of causal effects for decades. However, in many situations, randomized experiments are not feasible in practice so that practitioners need to rely on empirical investigation for causal reasoning. Causal inference via observational data is a challenging task since the knowledge of the treatment assignment mechanism is missing, which typically requires non-testable assumptions to make the inference possible. For several years, great effort has been devoted to the research of causal inference for binary treatments. In practice, it is also common to use observational data on multiple treatment comparisons. Within the potential outcomes framework, we propose a generalized cross-fitting estimator (GCF), which generalizes the doubly robust estimator with cross-fitting for binary treatment to multiple treatment comparisons and provides rigorous proofs on its statistical properties. This estimator permits the use of more flexible machine learning methods to model the nuisance parts, and based on relatively weak assumptions, while there is still a theoretical guarantee for valid statistical inference. We show the asymptotic properties of the GCF estimators, and provide the asymptotic simultaneous confidence intervals that achieve the semiparametric efficiency bound for average treatment effect. The performance of the estimator is accessed through simulation study based on the common evaluation metrics generally considered in the causal inference literature.

We consider a causal inference model in which individuals interact in a social network and they may not comply with the assigned treatments. Estimating causal parameters is challenging in the presence of network interference of unknown form, as each individual may be influenced by both close individuals and distant ones in complex ways. Noncompliance with treatment assignment further complicates this problem, and prior methods dealing with network spillovers but disregarding the noncompliance issue may underestimate the effect of the treatment receipt on the outcome. To estimate meaningful causal parameters, we introduce a new concept of exposure mapping, which summarizes potentially complicated spillover effects into a fixed dimensional statistic of instrumental variables. We investigate identification conditions for the intention-to-treat effect and the average causal effect for compliers, while explicitly considering the possibility of misspecification of exposure mapping. Based on our identification results, we develop nonparametric estimation procedures via inverse probability weighting. Their asymptotic properties, including consistency and asymptotic normality, are investigated using an approximate neighborhood interference framework, which is convenient for dealing with unknown forms of spillovers between individuals. For an empirical illustration, we apply our method to experimental data on the anti-conflict intervention school program.

Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time setting. We show that entropy regularization provides the necessary regularity conditions, that are lacking in the standard finite mean field games. Such regularity conditions enable us to design fixed-point iteration algorithms to find the unique mean-field equilibrium (MFE). Furthermore, the reference policy used in the regularization provides an extra parameter, through which one can control the behavior of the population. We first consider a stochastic game with a large population of $N$ homogeneous agents. We establish conditions for the existence of a Nash equilibrium in the limiting case as $N$ tends to infinity, and we demonstrate that the Nash equilibrium for the infinite population case is also an $\epsilon$-Nash equilibrium for the $N$-agent system, where the sub-optimality $\epsilon$ is of order $\mathcal{O}\big(1/\sqrt{N}\big)$. Finally, we verify the theoretical guarantees through a resource allocation example and demonstrate the efficacy of using a reference policy to control the behavior of a large population.

Causal effect estimation from observational data is a challenging problem, especially with high dimensional data and in the presence of unobserved variables. The available data-driven methods for tackling the problem either provide an estimation of the bounds of a causal effect (i.e. nonunique estimation) or have low efficiency. The major hurdle for achieving high efficiency while trying to obtain unique and unbiased causal effect estimation is how to find a proper adjustment set for confounding control in a fast way, given the huge covariate space and considering unobserved variables. In this paper, we approach the problem as a local search task for finding valid adjustment sets in data. We establish the theorems to support the local search for adjustment sets, and we show that unique and unbiased estimation can be achieved from observational data even when there exist unobserved variables. We then propose a data-driven algorithm that is fast and consistent under mild assumptions. We also make use of a frequent pattern mining method to further speed up the search of minimal adjustment sets for causal effect estimation. Experiments conducted on extensive synthetic and real-world datasets demonstrate that the proposed algorithm outperforms the state-of-the-art criteria/estimators in both accuracy and time-efficiency.

Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general diffeomorphic time warpings, in this work we focus on the hitherto unconsidered setting where phase variation of the component functions are spatially correlated. We propose an algorithm to optimize a metric-based objective function for registration with a novel penalty term that incorporates the spatial correlation between the component phase variations through a kriging estimate of an appropriate phase random field. The penalty term encourages the overall phase at a particular location to be similar to the spatially weighted average phase in its neighbourhood, and thus engenders a regularization that prevents over-alignment. Utility of the registration method, and its superior performance compared to methods that fail to account for the spatial correlation, is demonstrated through performance on simulated examples and two multivariate functional datasets pertaining to EEG signals and ozone concentrations. The generality of the framework opens up the possibility for extension to settings involving different forms of correlation between the component functions and their phases.

Analyses of biomedical studies often necessitate modeling longitudinal causal effects. The current focus on personalized medicine and effect heterogeneity makes this task even more challenging. Towards this end, structural nested mean models (SNMMs) are fundamental tools for studying heterogeneous treatment effects in longitudinal studies. However, when outcomes are binary, current methods for estimating multiplicative and additive SNMM parameters suffer from variation dependence between the causal parameters and the non-causal nuisance parameters. This leads to a series of difficulties in interpretation, estimation and computation. These difficulties have hindered the uptake of SNMMs in biomedical practice, where binary outcomes are very common. We solve the variation dependence problem for the binary multiplicative SNMM via a reparametrization of the non-causal nuisance parameters. Our novel nuisance parameters are variation independent of the causal parameters, and hence allow for coherent modeling of heterogeneous effects from longitudinal studies with binary outcomes. Our parametrization also provides a key building block for flexible doubly robust estimation of the causal parameters. Along the way, we prove that an additive SNMM with binary outcomes does not admit a variation independent parametrization, thereby justifying the restriction to multiplicative SNMMs.

Causal inference for extreme events has many potential applications in fields such as climate science, medicine and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome. Existing methods are limited to the case where the quantile of interest is within the range of the observations. For applications in risk assessment, however, the most relevant cases relate to extremal quantiles that go beyond the data range. We introduce an estimator of the extremal quantile treatment effect that relies on asymptotic tail approximation, and use a new causal Hill estimator for the extreme value indices of potential outcome distributions. We establish asymptotic normality of the estimators and propose a consistent variance estimator to achieve valid statistical inference. We illustrate the performance of our method in simulation studies, and apply it to a real data set to estimate the extremal quantile treatment effect of college education on wage.

Federated learning (FL) provides an effective paradigm to train machine learning models over distributed data with privacy protection. However, recent studies show that FL is subject to various security, privacy, and fairness threats due to the potentially malicious and heterogeneous local agents. For instance, it is vulnerable to local adversarial agents who only contribute low-quality data, with the goal of harming the performance of those with high-quality data. This kind of attack hence breaks existing definitions of fairness in FL that mainly focus on a certain notion of performance parity. In this work, we aim to address this limitation and propose a formal definition of fairness via agent-awareness for FL (FAA), which takes the heterogeneous data contributions of local agents into account. In addition, we propose a fair FL training algorithm based on agent clustering (FOCUS) to achieve FAA. Theoretically, we prove the convergence and optimality of FOCUS under mild conditions for linear models and general convex loss functions with bounded smoothness. We also prove that FOCUS always achieves higher fairness measured by FAA compared with standard FedAvg protocol under both linear models and general convex loss functions. Empirically, we evaluate FOCUS on four datasets, including synthetic data, images, and texts under different settings, and we show that FOCUS achieves significantly higher fairness based on FAA while maintaining similar or even higher prediction accuracy compared with FedAvg.

Encouraged by decision makers' appetite for future information on topics ranging from elections to pandemics, and enabled by the explosion of data and computational methods, model based forecasts have garnered increasing influence on a breadth of decisions in modern society. Using several classic examples from fisheries management, I demonstrate that selecting the model or models that produce the most accurate and precise forecast (measured by statistical scores) can sometimes lead to worse outcomes (measured by real-world objectives). This can create a forecast trap, in which the outcomes such as fish biomass or economic yield decline while the manager becomes increasingly convinced that these actions are consistent with the best models and data available. The forecast trap is not unique to this example, but a fundamental consequence of non-uniqueness of models. Existing practices promoting a broader set of models are the best way to avoid the trap.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.