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In the present paper, we study a Crouzeix-Raviart approximation of the obstacle problem, which imposes the obstacle constraint in the midpoints (i.e., barycenters) of the elements of a triangulation. We establish a priori error estimates imposing natural regularity assumptions, which are optimal, and the reliability and efficiency of a primal-dual type a posteriori error estimator for general obstacles and involving data oscillation terms stemming only from the right-hand side. Numerical experiments are carried out to support the theoretical findings.

Algorithm aversion occurs when humans are reluctant to use algorithms despite their superior performance. Studies show that giving users outcome control by providing agency over how models' predictions are incorporated into decision-making mitigates algorithm aversion. We study whether algorithm aversion is mitigated by process control, wherein users can decide what input factors and algorithms to use in model training. We conduct a replication study of outcome control, and test novel process control study conditions on Amazon Mechanical Turk (MTurk) and Prolific. Our results partly confirm prior findings on the mitigating effects of outcome control, while also forefronting reproducibility challenges. We find that process control in the form of choosing the training algorithm mitigates algorithm aversion, but changing inputs does not. Furthermore, giving users both outcome and process control does not reduce algorithm aversion more than outcome or process control alone. This study contributes to design considerations around mitigating algorithm aversion.

Correlated outcomes are common in many practical problems. In some settings, one outcome is of particular interest, and others are auxiliary. To leverage information shared by all the outcomes, traditional multi-task learning (MTL) minimizes an averaged loss function over all the outcomes, which may lead to biased estimation for the target outcome, especially when the MTL model is mis-specified. In this work, based on a decomposition of estimation bias into two types, within-subspace and against-subspace, we develop a robust transfer learning approach to estimating a high-dimensional linear decision rule for the outcome of interest with the presence of auxiliary outcomes. The proposed method includes an MTL step using all outcomes to gain efficiency, and a subsequent calibration step using only the outcome of interest to correct both types of biases. We show that the final estimator can achieve a lower estimation error than the one using only the single outcome of interest. Simulations and real data analysis are conducted to justify the superiority of the proposed method.

Drought events are the second most expensive type of natural disaster within the French legal framework known as the natural disasters compensation scheme. In recent years, drought events have been remarkable in their geographical scale and intensity. We develop and apply a new methodology to forecast the cost of a drought event in France. The methodology hinges on Super Learning (van der Laan et al., 2007; Benkeser et al., 2018), a general aggregation strategy to learn a feature of the law of the data identified through an ad hoc risk function by relying on a library of algorithms. The algorithms either compete (discrete Super Learning) or collaborate (continuous Super Learning), with a cross-validation scheme determining the best performing algorithm or combination of algorithms, respectively. Our Super Learner takes into account the complex dependence structure induced in the data by the spatial and temporal nature of drought events.

With the proliferation of devices that display augmented reality (AR), now is the time for scholars and practitioners to evaluate and engage critically with emerging applications of the medium. AR mediates the way users see their bodies, hear their environment and engage with places. Applied in various forms, including social media, e-commerce, gaming, enterprise and art, the medium facilitates a hybrid experience of physical and digital spaces. This article employs a model of real-and-imagined space from geographer Edward Soja to examine how the user of an AR app navigates the two intertwined spaces of physical and digital, experiencing what Soja calls a 'Third-space'. The article illustrates the potential for headset-based AR to engender such a Thirdspace through the author's practice-led research project, the installation Through the Wardrobe. This installation demonstrates how AR has the potential to shift the way that users view and interact with their world with artistic applications providing an opportunity to question assumptions of social norms, identity and uses of physical space.

We study the computational complexity of multi-stage robust optimization problems. Such problems are formulated with alternating min/max quantifiers and therefore naturally fall into a higher stage of the polynomial hierarchy. Despite this, almost no hardness results with respect to the polynomial hierarchy are known. In this work, we examine the hardness of robust two-stage adjustable and robust recoverable optimization with budgeted uncertainty sets. Our main technical contribution is the introduction of a technique tailored to prove $\Sigma^p_3$-hardness of such problems. We highlight a difference between continuous and discrete budgeted uncertainty: In the discrete case, indeed a wide range of problems becomes complete for the third stage of the polynomial hierarchy; in particular, this applies to the TSP, independent set, and vertex cover problems. However, in the continuous case this does not happen and problems remain in the first stage of the hierarchy. Finally, if we allow the uncertainty to not only affect the objective, but also multiple constraints, then this distinction disappears and even in the continuous case we encounter hardness for the third stage of the hierarchy. This shows that even robust problems which are already NP-complete can still exhibit a significant computational difference between column-wise and row-wise uncertainty.

Along with the massive growth of the Internet from the 1990s until now, various innovative technologies have been created to bring users breathtaking experiences with more virtual interactions in cyberspace. Many virtual environments with thousands of services and applications, from social networks to virtual gaming worlds, have been developed with immersive experience and digital transformation, but most are incoherent instead of being integrated into a platform. In this context, metaverse, a term formed by combining meta and universe, has been introduced as a shared virtual world that is fueled by many emerging technologies, such as fifth-generation networks and beyond, virtual reality, and artificial intelligence (AI). Among such technologies, AI has shown the great importance of processing big data to enhance immersive experience and enable human-like intelligence of virtual agents. In this survey, we make a beneficial effort to explore the role of AI in the foundation and development of the metaverse. We first deliver a preliminary of AI, including machine learning algorithms and deep learning architectures, and its role in the metaverse. We then convey a comprehensive investigation of AI-based methods concerning six technical aspects that have potentials for the metaverse: natural language processing, machine vision, blockchain, networking, digital twin, and neural interface, and being potential for the metaverse. Subsequently, several AI-aided applications, such as healthcare, manufacturing, smart cities, and gaming, are studied to be deployed in the virtual worlds. Finally, we conclude the key contribution of this survey and open some future research directions in AI for the metaverse.

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.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.