In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding matrices of a tensor, which may be suboptimal. In order to explore the low-rankness of the underlying tensor effectively, we propose a nonconvex model based on transformed tensor nuclear norm for low-rank tensor learning. Specifically, a family of nonconvex functions are employed onto the singular values of all frontal slices of a tensor in the transformed domain to characterize the low-rankness of the underlying tensor. An error bound between the stationary point of the nonconvex model and the underlying tensor is established under restricted strong convexity on the loss function (such as least squares loss and logistic regression) and suitable regularity conditions on the nonconvex penalty function. By reformulating the nonconvex function into the difference of two convex functions, a proximal majorization-minimization (PMM) algorithm is designed to solve the resulting model. Then the global convergence and convergence rate of PMM are established under very mild conditions. Numerical experiments are conducted on tensor completion and binary classification to demonstrate the effectiveness of the proposed method over other state-of-the-art methods.

Accurately predicting the state of charge of Lithium-ion batteries is essential to the performance of battery management systems of electric vehicles. One of the main reasons for the slow global adoption of electric cars is driving range anxiety. The ability of a battery management system to accurately estimate the state of charge can help alleviate this problem. In this paper, a comparison between data-driven state-of-charge estimation methods is conducted. The paper compares different neural network-based models and common regression models for SOC estimation. These models include several ablated transformer networks, a neural network, a lasso regression model, a linear regression model and a decision tree. Results of various experiments conducted on data obtained from natural driving cycles of the BMW i3 battery show that the decision tree outperformed all other models including the more complex transformer network with self-attention and positional encoding.

In this letter, we address the task of adaptive sampling to model vector fields. When modeling environmental phenomena with a robot, gathering high resolution information can be resource intensive. Actively gathering data and modeling flows with the data is a more efficient alternative. However, in such scenarios, data is often sparse and thus requires flow modeling techniques that are effective at capturing the relevant dynamical features of the flow to ensure high prediction accuracy of the resulting models. To accomplish this effectively, regions with high informative value must be identified. We propose EnKode, an active sampling approach based on Koopman Operator theory and ensemble methods that can build high quality flow models and effectively estimate model uncertainty. For modeling complex flows, EnKode provides comparable or better estimates of unsampled flow regions than Gaussian Process Regression models with hyperparameter optimization. Additionally, our active sensing scheme provides more accurate flow estimates than comparable strategies that rely on uniform sampling. We evaluate EnKode using three common benchmarking systems: the Bickley Jet, Lid-Driven Cavity flow with an obstacle, and real ocean currents from the National Oceanic and Atmospheric Administration (NOAA).

An efficient system of a queue control and regulation in public spaces is very important in order to avoid the traffic jams and to improve the customer satisfaction. This article offers a detailed road map based on a merger of intelligent systems and creating an efficient systems of queues in public places. Through the utilization of different technologies i.e. computer vision, machine learning algorithms, deep learning our system provide accurate information about the place is crowded or not and the necessary efforts to be taken.

Multi-Output Regression (MOR) has been widely used in scientific data analysis for decision-making. Unlike traditional regression models, MOR aims to simultaneously predict multiple real-valued outputs given an input. However, the increasing dimensionality of the outputs poses significant challenges regarding interpretability and computational scalability for modern MOR applications. As a first step to address these challenges, this paper proposes a Sparse \& High-dimensional-Output REgression (SHORE) model by incorporating additional sparsity requirements to resolve the output interpretability, and then designs a computationally efficient two-stage optimization framework capable of solving SHORE with provable accuracy via compression on outputs. Theoretically, we show that the proposed framework is computationally scalable while maintaining the same order of training loss and prediction loss before-and-after compression under arbitrary or relatively weak sample set conditions. Empirically, numerical results further validate the theoretical findings, showcasing the efficiency and accuracy of the proposed framework.

We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as domain adaptation and algorithmic fairness, where comparing two groups is essential while controlling for confounding variables. We begin by establishing a hardness result for conditional two-sample testing, demonstrating that no valid test can have significant power against any single alternative without proper assumptions. We then introduce two general frameworks that implicitly or explicitly target specific classes of distributions for their validity and power. Our first framework allows us to convert any conditional independence test into a conditional two-sample test in a black-box manner, while preserving the asymptotic properties of the original conditional independence test. The second framework transforms the problem into comparing marginal distributions with estimated density ratios, which allows us to leverage existing methods for marginal two-sample testing. We demonstrate this idea in a concrete manner with classification and kernel-based methods. Finally, simulation studies are conducted to illustrate the proposed frameworks in finite-sample scenarios.

Infectious diseases occur when pathogens from other individuals or animals infect a person, resulting in harm to both individuals and society as a whole. The outbreak of such diseases can pose a significant threat to human health. However, early detection and tracking of these outbreaks have the potential to reduce the mortality impact. To address these threats, public health authorities have endeavored to establish comprehensive mechanisms for collecting disease data. Many countries have implemented infectious disease surveillance systems, with the detection of epidemics being a primary objective. The clinical healthcare system, local/state health agencies, federal agencies, academic/professional groups, and collaborating governmental entities all play pivotal roles within this system. Moreover, nowadays, search engines and social media platforms can serve as valuable tools for monitoring disease trends. The Internet and social media have become significant platforms where users share information about their preferences and relationships. This real-time information can be harnessed to gauge the influence of ideas and societal opinions, making it highly useful across various domains and research areas, such as marketing campaigns, financial predictions, and public health, among others. This article provides a review of the existing standard methods developed by researchers for detecting outbreaks using time series data. These methods leverage various data sources, including conventional data sources and social media data or Internet data sources. The review particularly concentrates on works published within the timeframe of 2015 to 2022.

Conformal prediction has emerged as a powerful tool for building prediction intervals that are valid in a distribution-free way. However, its evaluation may be computationally costly, especially in the high-dimensional setting where the dimensionality and sample sizes are both large and of comparable magnitudes. To address this challenge in the context of generalized linear regression, we propose a novel algorithm based on Approximate Message Passing (AMP) to accelerate the computation of prediction intervals using full conformal prediction, by approximating the computation of conformity scores. Our work bridges a gap between modern uncertainty quantification techniques and tools for high-dimensional problems involving the AMP algorithm. We evaluate our method on both synthetic and real data, and show that it produces prediction intervals that are close to the baseline methods, while being orders of magnitude faster. Additionally, in the high-dimensional limit and under assumptions on the data distribution, the conformity scores computed by AMP converge to the one computed exactly, which allows theoretical study and benchmarking of conformal methods in high dimensions.

Scientific document classification is a critical task and often involves many classes. However, collecting human-labeled data for many classes is expensive and usually leads to label-scarce scenarios. Moreover, recent work has shown that sentence embedding model fine-tuning for few-shot classification is efficient, robust, and effective. In this work, we propose FusionSent (Fusion-based Sentence Embedding Fine-tuning), an efficient and prompt-free approach for few-shot classification of scientific documents with many classes. FusionSent uses available training examples and their respective label texts to contrastively fine-tune two different sentence embedding models. Afterward, the parameters of both fine-tuned models are fused to combine the complementary knowledge from the separate fine-tuning steps into a single model. Finally, the resulting sentence embedding model is frozen to embed the training instances, which are then used as input features to train a classification head. Our experiments show that FusionSent significantly outperforms strong baselines by an average of $6.0$ $F_{1}$ points across multiple scientific document classification datasets. In addition, we introduce a new dataset for multi-label classification of scientific documents, which contains 203,961 scientific articles and 130 classes from the arXiv category taxonomy. Code and data are available at https://github.com/sebischair/FusionSent.

Data imputation addresses the challenge of imputing missing values in database instances, ensuring consistency with the overall semantics of the dataset. Although several heuristics which rely on statistical methods, and ad-hoc rules have been proposed. These do not generalise well and often lack data context. Consequently, they also lack explainability. The existing techniques also mostly focus on the relational data context making them unsuitable for wider application contexts such as in graph data. In this paper, we propose a graph data imputation approach called GIG which relies on graph differential dependencies (GDDs). GIG, learns the GDDs from a given knowledge graph, and uses these rules to train a transformer model which then predicts the value of missing data within the graph. By leveraging GDDs, GIG incoporates semantic knowledge into the data imputation process making it more reliable and explainable. Experimental results on seven real-world datasets highlight GIG's effectiveness compared to existing state-of-the-art approaches.