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Quantiles are a fundamental concept in probability and theoretical statistics and a daily tool in their applications. While the univariate concept of quantiles is quite clear and well understood, its multivariate extension is more problematic. After half a century of continued efforts and many proposals, two concepts, essentially, are emerging: the so-called (relabeled) geometric quantiles, extending the characterization of univariate quantiles as minimizers of an L1 loss function involving the check functions, and the more recent center-outward quantiles based on measure transportation ideas. These two concepts yield distinct families of quantile regions and quantile contours. Our objective here is to present a comparison of their main theoretical properties and a numerical investigation of their differences.

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iOS 8 提供的應用間和應用跟系統的功能交互特性。
  • Today (iOS and OS X): widgets for the Today view of Notification Center
  • Share (iOS and OS X): post content to web services or share content with others
  • Actions (iOS and OS X): app extensions to view or manipulate inside another app
  • Photo Editing (iOS): edit a photo or video in Apple's Photos app with extensions from a third-party apps
  • Finder Sync (OS X): remote file storage in the Finder with support for Finder content annotation
  • Storage Provider (iOS): an interface between files inside an app and other apps on a user's device
  • Custom Keyboard (iOS): system-wide alternative keyboards

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We study the fundamental problem of designing contracts in principal-agent problems under uncertainty. Previous works mostly addressed Bayesian settings in which principal's uncertainty is modeled as a probability distribution over agent's types. In this paper, we study a setting in which the principal has no distributional information about agent's type. In particular, in our setting, the principal only knows some uncertainty set defining possible agent's action costs. Thus, the principal takes a robust (adversarial) approach by trying to design contracts which minimize the (additive) regret: the maximum difference between what the principal could have obtained had them known agent's costs and what they actually get under the selected contract.

Localizing the bronchoscope in real time is essential for ensuring intervention quality. However, most existing methods struggle to balance between speed and generalization. To address these challenges, we present BronchoTrack, an innovative real-time framework for accurate branch-level localization, encompassing lumen detection, tracking, and airway association.To achieve real-time performance, we employ a benchmark lightweight detector for efficient lumen detection. We are the first to introduce multi-object tracking to bronchoscopic localization, mitigating temporal confusion in lumen identification caused by rapid bronchoscope movement and complex airway structures. To ensure generalization across patient cases, we propose a training-free detection-airway association method based on a semantic airway graph that encodes the hierarchy of bronchial tree structures.Experiments on nine patient datasets demonstrate BronchoTrack's localization accuracy of 85.64 \%, while accessing up to the 4th generation of airways.Furthermore, we tested BronchoTrack in an in-vivo animal study using a porcine model, where it successfully localized the bronchoscope into the 8th generation airway.Experimental evaluation underscores BronchoTrack's real-time performance in both satisfying accuracy and generalization, demonstrating its potential for clinical applications.

We consider the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a well-known ill-posed inverse problem. We propose a new formulation of the functional partial least-squares (PLS) estimator related to the conjugate gradient method. We shall show that the estimator achieves the (nearly) optimal convergence rate on a class of ellipsoids and we introduce an early stopping rule which adapts to the unknown degree of ill-posedness. Some theoretical and simulation comparison between the estimator and the principal component regression estimator is provided.

In a membership inference attack (MIA), an attacker exploits the overconfidence exhibited by typical machine learning models to determine whether a specific data point was used to train a target model. In this paper, we analyze the performance of the state-of-the-art likelihood ratio attack (LiRA) within an information-theoretical framework that allows the investigation of the impact of the aleatoric uncertainty in the true data generation process, of the epistemic uncertainty caused by a limited training data set, and of the calibration level of the target model. We compare three different settings, in which the attacker receives decreasingly informative feedback from the target model: confidence vector (CV) disclosure, in which the output probability vector is released; true label confidence (TLC) disclosure, in which only the probability assigned to the true label is made available by the model; and decision set (DS) disclosure, in which an adaptive prediction set is produced as in conformal prediction. We derive bounds on the advantage of an MIA adversary with the aim of offering insights into the impact of uncertainty and calibration on the effectiveness of MIAs. Simulation results demonstrate that the derived analytical bounds predict well the effectiveness of MIAs.

In this paper, by treating in-context learning (ICL) as a meta-optimization process, we explain why LLMs are sensitive to the order of ICL examples. This understanding leads us to the development of Batch-ICL, an effective, efficient, and order-agnostic inference algorithm for ICL. Differing from the standard N-shot learning approach, Batch-ICL employs $N$ separate 1-shot forward computations and aggregates the resulting meta-gradients. These aggregated meta-gradients are then applied to the forward computation of a zero-shot query to generate the final prediction. This batch processing approach renders the LLM agnostic to the order of ICL examples. Through extensive experiments and analysis, we demonstrate that Batch-ICL consistently outperforms most permutations of ICL examples. In some cases, it even exceeds the performance of the best order for standard ICL, all while reducing the computational resources required. Furthermore, we develop a novel variant of Batch-ICL featuring multiple "epochs" of meta-optimization. This variant implicitly explores permutations of ICL examples, further enhancing ICL performance.

Understanding treatment heterogeneity is crucial for reliable decision-making in treatment evaluation and selection. While the conditional average treatment effect (CATE) is commonly used to capture treatment heterogeneity induced by covariates and design individualized treatment policies, it remains an averaging metric within subpopulations. This limitation prevents it from unveiling individual-level risks, potentially leading to misleading results. This article addresses this gap by examining individual risk for binary outcomes, specifically focusing on the fraction negatively affected (FNA) conditional on covariates -- a metric assessing the percentage of individuals experiencing worse outcomes with treatment compared to control. Under the strong ignorability assumption, FNA is unidentifiable, and we find that previous bounds are wide and practically unattainable except in certain degenerate cases. By introducing a plausible positive correlation assumption for the potential outcomes, we obtain significantly improved bounds compared to previous studies. We show that even with a positive and statistically significant CATE, the lower bound on FNA can be positive, i.e., in the best-case scenario many units will be harmed if receiving treatment. We establish a nonparametric sensitivity analysis framework for FNA using the Pearson correlation coefficient as the sensitivity parameter, thereby exploring the relationships among the correlation coefficient, FNA, and CATE. We also present a practical and tractable method for selecting the range of correlation coefficients. Furthermore, we propose flexible estimators for refined FNA bounds and prove their consistency and asymptotic normality.

Classic machine learning methods are built on the $i.i.d.$ assumption that training and testing data are independent and identically distributed. However, in real scenarios, the $i.i.d.$ assumption can hardly be satisfied, rendering the sharp drop of classic machine learning algorithms' performances under distributional shifts, which indicates the significance of investigating the Out-of-Distribution generalization problem. Out-of-Distribution (OOD) generalization problem addresses the challenging setting where the testing distribution is unknown and different from the training. This paper serves as the first effort to systematically and comprehensively discuss the OOD generalization problem, from the definition, methodology, evaluation to the implications and future directions. Firstly, we provide the formal definition of the OOD generalization problem. Secondly, existing methods are categorized into three parts based on their positions in the whole learning pipeline, namely unsupervised representation learning, supervised model learning and optimization, and typical methods for each category are discussed in detail. We then demonstrate the theoretical connections of different categories, and introduce the commonly used datasets and evaluation metrics. Finally, we summarize the whole literature and raise some future directions for OOD generalization problem. The summary of OOD generalization methods reviewed in this survey can be found at //out-of-distribution-generalization.com.

With the advances of data-driven machine learning research, a wide variety of prediction problems have been tackled. It has become critical to explore how machine learning and specifically deep learning methods can be exploited to analyse healthcare data. A major limitation of existing methods has been the focus on grid-like data; however, the structure of physiological recordings are often irregular and unordered which makes it difficult to conceptualise them as a matrix. As such, graph neural networks have attracted significant attention by exploiting implicit information that resides in a biological system, with interactive nodes connected by edges whose weights can be either temporal associations or anatomical junctions. In this survey, we thoroughly review the different types of graph architectures and their applications in healthcare. We provide an overview of these methods in a systematic manner, organized by their domain of application including functional connectivity, anatomical structure and electrical-based analysis. We also outline the limitations of existing techniques and discuss potential directions for future research.

With the rise and development of deep learning, computer vision has been tremendously transformed and reshaped. As an important research area in computer vision, scene text detection and recognition has been inescapably influenced by this wave of revolution, consequentially entering the era of deep learning. In recent years, the community has witnessed substantial advancements in mindset, approach and performance. This survey is aimed at summarizing and analyzing the major changes and significant progresses of scene text detection and recognition in the deep learning era. Through this article, we devote to: (1) introduce new insights and ideas; (2) highlight recent techniques and benchmarks; (3) look ahead into future trends. Specifically, we will emphasize the dramatic differences brought by deep learning and the grand challenges still remained. We expect that this review paper would serve as a reference book for researchers in this field. Related resources are also collected and compiled in our Github repository: //github.com/Jyouhou/SceneTextPapers.

Transformers have a potential of learning longer-term dependency, but are limited by a fixed-length context in the setting of language modeling. We propose a novel neural architecture Transformer-XL that enables learning dependency beyond a fixed length without disrupting temporal coherence. It consists of a segment-level recurrence mechanism and a novel positional encoding scheme. Our method not only enables capturing longer-term dependency, but also resolves the context fragmentation problem. As a result, Transformer-XL learns dependency that is 80% longer than RNNs and 450% longer than vanilla Transformers, achieves better performance on both short and long sequences, and is up to 1,800+ times faster than vanilla Transformers during evaluation. Notably, we improve the state-of-the-art results of bpc/perplexity to 0.99 on enwiki8, 1.08 on text8, 18.3 on WikiText-103, 21.8 on One Billion Word, and 54.5 on Penn Treebank (without finetuning). When trained only on WikiText-103, Transformer-XL manages to generate reasonably coherent, novel text articles with thousands of tokens. Our code, pretrained models, and hyperparameters are available in both Tensorflow and PyTorch.

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