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Motivated by models of human decision making proposed to explain commonly observed deviations from conventional expected value preferences, we formulate two stochastic multi-armed bandit problems with distorted probabilities on the reward distributions: the classic $K$-armed bandit and the linearly parameterized bandit settings. We consider the aforementioned problems in the regret minimization as well as best arm identification framework for multi-armed bandits. For the regret minimization setting in $K$-armed as well as linear bandit problems, we propose algorithms that are inspired by Upper Confidence Bound (UCB) algorithms, incorporate reward distortions, and exhibit sublinear regret. For the $K$-armed bandit setting, we derive an upper bound on the expected regret for our proposed algorithm, and then we prove a matching lower bound to establish the order-optimality of our algorithm. For the linearly parameterized setting, our algorithm achieves a regret upper bound that is of the same order as that of regular linear bandit algorithm called Optimism in the Face of Uncertainty Linear (OFUL) bandit algorithm, and unlike OFUL, our algorithm handles distortions and an arm-dependent noise model. For the best arm identification problem in the $K$-armed bandit setting, we propose algorithms, derive guarantees on their performance, and also show that these algorithms are order optimal by proving matching fundamental limits on performance. For best arm identification in linear bandits, we propose an algorithm and establish sample complexity guarantees. Finally, we present simulation experiments which demonstrate the advantages resulting from using distortion-aware learning algorithms in a vehicular traffic routing application.

Question answering methods are well-known for leveraging data bias, such as the language prior in visual question answering and the position bias in machine reading comprehension (extractive question answering). Current debiasing methods often come at the cost of significant in-distribution performance to achieve favorable out-of-distribution generalizability, while non-debiasing methods sacrifice a considerable amount of out-of-distribution performance in order to obtain high in-distribution performance. Therefore, it is challenging for them to deal with the complicated changing real-world situations. In this paper, we propose a simple yet effective novel loss function with adaptive loose optimization, which seeks to make the best of both worlds for question answering. Our main technical contribution is to reduce the loss adaptively according to the ratio between the previous and current optimization state on mini-batch training data. This loose optimization can be used to prevent non-debiasing methods from overlearning data bias while enabling debiasing methods to maintain slight bias learning. Experiments on the visual question answering datasets, including VQA v2, VQA-CP v1, VQA-CP v2, GQA-OOD, and the extractive question answering dataset SQuAD demonstrate that our approach enables QA methods to obtain state-of-the-art in- and out-of-distribution performance in most cases. The source code has been released publicly in \url{//github.com/reml-group/ALO}.

In survival contexts, substantial literature exists on estimating optimal treatment regimes, where treatments are assigned based on personal characteristics for the purpose of maximizing the survival probability. These methods assume that a set of covariates is sufficient to deconfound the treatment-outcome relationship. Nevertheless, the assumption can be limited in observational studies or randomized trials in which non-adherence occurs. Thus, we propose a novel approach for estimating the optimal treatment regime when certain confounders are not observable and a binary instrumental variable is available. Specifically, via a binary instrumental variable, we propose two semiparametric estimators for the optimal treatment regime by maximizing Kaplan-Meier-like estimators within a pre-defined class of regimes, one of which possesses the desirable property of double robustness. Because the Kaplan-Meier-like estimators are jagged, we incorporate kernel smoothing methods to enhance their performance. Under appropriate regularity conditions, the asymptotic properties are rigorously established. Furthermore, the finite sample performance is assessed through simulation studies. Finally, we exemplify our method using data from the National Cancer Institute's (NCI) prostate, lung, colorectal, and ovarian cancer screening trial.

The joint analysis of multimodal neuroimaging data is critical in the field of brain research because it reveals complex interactive relationships between neurobiological structures and functions. In this study, we focus on investigating the effects of structural imaging (SI) features, including white matter micro-structure integrity (WMMI) and cortical thickness, on the whole brain functional connectome (FC) network. To achieve this goal, we propose a network-based vector-on-matrix regression model to characterize the FC-SI association patterns. We have developed a novel multi-level dense bipartite and clique subgraph extraction method to identify which subsets of spatially specific SI features intensively influence organized FC sub-networks. The proposed method can simultaneously identify highly correlated structural-connectomic association patterns and suppress false positive findings while handling millions of potential interactions. We apply our method to a multimodal neuroimaging dataset of 4,242 participants from the UK Biobank to evaluate the effects of whole-brain WMMI and cortical thickness on the resting-state FC. The results reveal that the WMMI on corticospinal tracts and inferior cerebellar peduncle significantly affect functional connections of sensorimotor, salience, and executive sub-networks with an average correlation of 0.81 (p<0.001).

This work presents a comparative study to numerically compute impulse approximate controls for parabolic equations with various boundary conditions. Theoretical controllability results have been recently investigated using a logarithmic convexity estimate at a single time based on a Carleman commutator approach. We propose a numerical algorithm for computing the impulse controls with minimal $L^2$-norms by adapting a penalized Hilbert Uniqueness Method (HUM) combined with a Conjugate Gradient (CG) method. We consider static boundary conditions (Dirichlet and Neumann) and dynamic boundary conditions. Some numerical experiments based on our developed algorithm are given to validate and compare the theoretical impulse controllability results.

Threshold selection is a fundamental problem in any threshold-based extreme value analysis. While models are asymptotically motivated, selecting an appropriate threshold for finite samples can be difficult through standard methods. Inference can also be highly sensitive to the choice of threshold. Too low a threshold choice leads to bias in the fit of the extreme value model, while too high a choice leads to unnecessary additional uncertainty in the estimation of model parameters. In this paper, we develop a novel methodology for automated threshold selection that directly tackles this bias-variance trade-off. We also develop a method to account for the uncertainty in this threshold choice and propagate this uncertainty through to high quantile inference. Through a simulation study, we demonstrate the effectiveness of our method for threshold selection and subsequent extreme quantile estimation. We apply our method to the well-known, troublesome example of the River Nidd dataset.

Difference-in-differences (DID) is a popular approach to identify the causal effects of treatments and policies in the presence of unmeasured confounding. DID identifies the sample average treatment effect in the treated (SATT). However, a goal of such research is often to inform decision-making in target populations outside the treated sample. Transportability methods have been developed to extend inferences from study samples to external target populations; these methods have primarily been developed and applied in settings where identification is based on conditional independence between the treatment and potential outcomes, such as in a randomized trial. This paper develops identification and estimators for effects in a target population, based on DID conducted in a study sample that differs from the target population. We present a range of assumptions under which one may identify causal effects in the target population and employ causal diagrams to illustrate these assumptions. In most realistic settings, results depend critically on the assumption that any unmeasured confounders are not effect measure modifiers on the scale of the effect of interest. We develop several estimators of transported effects, including a doubly robust estimator based on the efficient influence function. Simulation results support theoretical properties of the proposed estimators. We discuss the potential application of our approach to a study of the effects of a US federal smoke-free housing policy, where the original study was conducted in New York City alone and the goal is extend inferences to other US cities.

A core component of human intelligence is the ability to identify abstract patterns inherent in complex, high-dimensional perceptual data, as exemplified by visual reasoning tasks such as Raven's Progressive Matrices (RPM). Motivated by the goal of designing AI systems with this capacity, recent work has focused on evaluating whether neural networks can learn to solve RPM-like problems. Previous work has generally found that strong performance on these problems requires the incorporation of inductive biases that are specific to the RPM problem format, raising the question of whether such models might be more broadly useful. Here, we investigated the extent to which a general-purpose mechanism for processing visual scenes in terms of objects might help promote abstract visual reasoning. We found that a simple model, consisting only of an object-centric encoder and a transformer reasoning module, achieved state-of-the-art results on both of two challenging RPM-like benchmarks (PGM and I-RAVEN), as well as a novel benchmark with greater visual complexity (CLEVR-Matrices). These results suggest that an inductive bias for object-centric processing may be a key component of abstract visual reasoning, obviating the need for problem-specific inductive biases.

The processing and analysis of computed tomography (CT) imaging is important for both basic scientific development and clinical applications. In AutoCT, we provide a comprehensive pipeline that integrates an end-to-end automatic preprocessing, registration, segmentation, and quantitative analysis of 3D CT scans. The engineered pipeline enables atlas-based CT segmentation and quantification leveraging diffeomorphic transformations through efficient forward and inverse mappings. The extracted localized features from the deformation field allow for downstream statistical learning that may facilitate medical diagnostics. On a lightweight and portable software platform, AutoCT provides a new toolkit for the CT imaging community to underpin the deployment of artificial intelligence-driven applications.

Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.