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This study explores the problem solving capabilities of ChatGPT and its prospective applications in standardized test preparation, focusing on the GRE quantitative exam. Prior research has shown great potential for the utilization of ChatGPT for academic purposes in revolutionizing the approach to studying across various disciplines. We investigate how ChatGPT performs across various question types in the GRE quantitative domain, and how modifying question prompts impacts its accuracy. More specifically this study addressed two research questions: 1. How does ChatGPT perform in answering GRE-based quantitative questions across various content areas? 2. How does the accuracy of ChatGPT vary with modifying the question prompts? The dataset consisting of 100 randomly selected GRE quantitative questions was collected from the ETS official guide to GRE test preparation. We used quantitative evaluation to answer our first research question, and t-test to examine the statistical association between prompt modification and ChatGPT's accuracy. Results show a statistical improvement in the ChatGPT's accuracy after applying instruction priming and contextual prompts to the original questions. ChatGPT showed 84% accuracy with the modified prompts compared to 69% with the original data. The study discusses the areas where ChatGPT struggled with certain questions and how modifications can be helpful for preparing for standardized tests like GRE and provides future directions for prompt modifications.

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Due to the frequent variability of object orientation, accurate prediction of orientation information remains a challenge in oriented object detection. To better extract orientation-related information, current methods primarily focus on the design of reasonable representations of oriented bounding box (OBB) and rotation-sensitive feature extraction. However, existing OBB representations often suffer from boundary discontinuity and representation ambiguity problems. Methods of designing continuous and unambiguous regression losses do not essentially solve such problems. Gaussian bounding box (GBB) avoids these OBB representation problems, but directly regressing GBB is susceptible to numerical instability. In this paper, we propose linear GBB (LGBB), a novel OBB representation. By linearly transforming the elements of GBB, LGBB does not have the boundary discontinuity and representation ambiguity problems, and have high numerical stability. On the other hand, current rotation-sensitive feature extraction methods based on convolutions can only extract features under a local receptive field, which is slow in aggregating rotation-sensitive features. To address this issue, we propose ring-shaped rotated convolution (RRC). By adaptively rotating feature maps to arbitrary orientations, RRC extracts rotation-sensitive features under a ring-shaped receptive field, rapidly aggregating rotation-sensitive features and contextual information. RRC can be applied to various models in a plug-and-play manner. Experimental results demonstrate that the proposed LGBB and RRC are effective and achieve state-of-the-art (SOTA) performance. By integrating LGBB and RRC into various models, the detection accuracy is effectively improved on DOTA and HRSC2016 datasets.

The problem of selecting a handful of truly relevant variables in supervised machine learning algorithms is a challenging problem in terms of untestable assumptions that must hold and unavailability of theoretical assurances that selection errors are under control. We propose a distribution-free feature selection method, referred to as Data Splitting Selection (DSS) which controls False Discovery Rate (FDR) of feature selection while obtaining a high power. Another version of DSS is proposed with a higher power which "almost" controls FDR. No assumptions are made on the distribution of the response or on the joint distribution of the features. Extensive simulation is performed to compare the performance of the proposed methods with the existing ones.

We propose a new approach to formally describing the requirement for statistical inference and checking whether a program uses the statistical method appropriately. Specifically, we define belief Hoare logic (BHL) for formalizing and reasoning about the statistical beliefs acquired via hypothesis testing. This program logic is sound and relatively complete with respect to a Kripke model for hypothesis tests. We demonstrate by examples that BHL is useful for reasoning about practical issues in hypothesis testing. In our framework, we clarify the importance of prior beliefs in acquiring statistical beliefs through hypothesis testing, and discuss the whole picture of the justification of statistical inference inside and outside the program logic.

Multi-object tracking (MOT) or global data association problem is commonly approached as a minimum-cost-flow or minimum-cost-circulation problem on a graph. While there have been numerous studies aimed at enhancing algorithm efficiency, most of them focus on the batch problem, where all the data must be available simultaneously to construct a static graph. However, with the growing number of applications that generate streaming data, an efficient online algorithm is required to handle the streaming nature of the input. In this paper, we present an online extension of the well-known negative cycle canceling algorithm for solving the multi-object tracking problem with streaming fragmented data. We provide a proof of correctness for the proposed algorithm and demonstrate its efficiency through numerical experiments.

This study focuses on the optimization of the Big-means algorithm for clustering large-scale datasets, exploring four distinct parallelization strategies. We conducted extensive experiments to assess the computational efficiency, scalability, and clustering performance of each approach, revealing their benefits and limitations. The paper also delves into the trade-offs between computational efficiency and clustering quality, examining the impacts of various factors. Our insights provide practical guidance on selecting the best parallelization strategy based on available resources and dataset characteristics, contributing to a deeper understanding of parallelization techniques for the Big-means algorithm.

The densest subgraph problem has received significant attention, both in theory and in practice, due to its applications in problems such as community detection, social network analysis, and spam detection. Due to the high cost of obtaining exact solutions, much attention has focused on designing approximate densest subgraph algorithms. However, existing approaches are not able to scale to massive graphs with billions of edges. In this paper, we introduce a new framework that combines approximate densest subgraph algorithms with a pruning optimization. We design new parallel variants of the state-of-the-art sequential Greedy++ algorithm, and plug it into our framework in conjunction with a parallel pruning technique based on $k$-core decomposition to obtain parallel $(1+\varepsilon)$-approximate densest subgraph algorithms. On a single thread, our algorithms achieve $2.6$--$34\times$ speedup over Greedy++, and obtain up to $22.37\times$ self relative parallel speedup on a 30-core machine with two-way hyper-threading. Compared with the state-of-the-art parallel algorithm by Harb et al. [NeurIPS'22], we achieve up to a $114\times$ speedup on the same machine. Finally, against the recent sequential algorithm of Xu et al. [PACMMOD'23], we achieve up to a $25.9\times$ speedup. The scalability of our algorithms enables us to obtain near-optimal density statistics on the hyperlink2012 (with roughly 113 billion edges) and clueweb (with roughly 37 billion edges) graphs for the first time in the literature.

We consider the problem of testing whether a single coefficient is equal to zero in fixed-design linear models under a moderately high-dimensional regime, where the dimension of covariates $p$ is allowed to be in the same order of magnitude as sample size $n$. In this regime, to achieve finite-population validity, existing methods usually require strong distributional assumptions on the noise vector (such as Gaussian or rotationally invariant), which limits their applications in practice. In this paper, we propose a new method, called residual permutation test (RPT), which is constructed by projecting the regression residuals onto the space orthogonal to the union of the column spaces of the original and permuted design matrices. RPT can be proved to achieve finite-population size validity under fixed design with just exchangeable noises, whenever $p < n / 2$. Moreover, RPT is shown to be asymptotically powerful for heavy tailed noises with bounded $(1+t)$-th order moment when the true coefficient is at least of order $n^{-t/(1+t)}$ for $t \in [0,1]$. We further proved that this signal size requirement is essentially rate-optimal in the minimax sense. Numerical studies confirm that RPT performs well in a wide range of simulation settings with normal and heavy-tailed noise distributions.

Functional quantile regression (FQR) is a useful alternative to mean regression for functional data as it provides a comprehensive understanding of how scalar predictors influence the conditional distribution of functional responses. In this article, we study the FQR model for densely sampled, high-dimensional functional data without relying on parametric error or independent stochastic process assumptions, with the focus on statistical inference under this challenging regime along with scalable implementation. This is achieved by a simple but powerful distributed strategy, in which we first perform separate quantile regression to compute $M$-estimators at each sampling location, and then carry out estimation and inference for the entire coefficient functions by properly exploiting the uncertainty quantification and dependence structure of $M$-estimators. We derive a uniform Bahadur representation and a strong Gaussian approximation result for the $M$-estimators on the discrete sampling grid, leading to dimension reduction and serving as the basis for inference. An interpolation-based estimator with minimax optimality is proposed, and large sample properties for point and simultaneous interval estimators are established. The obtained minimax optimal rate under the FQR model shows an interesting phase transition phenomenon that has been previously observed in functional mean regression. The proposed methods are illustrated via simulations and an application to a mass spectrometry proteomics dataset.

This paper implements and analyzes multiple networks with the goal of understanding their suitability for edge device applications such as X-ray threat detection. In this study, we use the state-of-the-art YOLO object detection model to solve this task of detecting threats in security baggage screening images. We designed and studied three models - Tiny YOLO, QCFS Tiny YOLO, and SNN Tiny YOLO. We utilize an alternative activation function calculated to have zero expected conversion error with the activation of a spiking activation function in our Tiny YOLOv7 model. This \textit{QCFS} version of the Tiny YOLO replicates the activation function from ultra-low latency and high-efficiency SNN architecture. It achieves state-of-the-art performance on CLCXray, an open-source X-ray threat Detection dataset. In addition, we also study the behavior of a Spiking Tiny YOLO on the same X-ray threat Detection dataset.

Named entity recognition (NER) is the task to identify text spans that mention named entities, and to classify them into predefined categories such as person, location, organization etc. NER serves as the basis for a variety of natural language applications such as question answering, text summarization, and machine translation. Although early NER systems are successful in producing decent recognition accuracy, they often require much human effort in carefully designing rules or features. In recent years, deep learning, empowered by continuous real-valued vector representations and semantic composition through nonlinear processing, has been employed in NER systems, yielding stat-of-the-art performance. In this paper, we provide a comprehensive review on existing deep learning techniques for NER. We first introduce NER resources, including tagged NER corpora and off-the-shelf NER tools. Then, we systematically categorize existing works based on a taxonomy along three axes: distributed representations for input, context encoder, and tag decoder. Next, we survey the most representative methods for recent applied techniques of deep learning in new NER problem settings and applications. Finally, we present readers with the challenges faced by NER systems and outline future directions in this area.

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