As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how data encoding and perturbation modeling approaches can be matched to achieve meaningful robustness certificates. By utilizing an innovative approach integrating Grover's algorithm, a quadratic sampling advantage over classical randomized smoothing is achieved. This strategy necessitates a basis state encoding, thus restricting the space of meaningful perturbations. We show how constrained $k$-distant Hamming weight perturbations are a suitable noise distribution here, and elucidate how they can be constructed on a quantum computer. The efficacy of the proposed framework is demonstrated on a time series classification task employing a Bag-of-Words pre-processing solution. The advantage of quadratic sample reduction is recovered especially in the regime with large number of samples. This may allow quantum computers to efficiently scale randomized smoothing to more complex tasks beyond the reach of classical methods.

Time series classification stands as a pivotal and intricate challenge across various domains, including finance, healthcare, and industrial systems. In contemporary research, there has been a notable upsurge in exploring feature extraction through random sampling. Unlike deep convolutional networks, these methods sidestep elaborate training procedures, yet they often necessitate generating a surplus of features to comprehensively encapsulate time series nuances. Consequently, some features may lack relevance to labels or exhibit multi-collinearity with others. In this paper, we propose a novel hierarchical feature selection method aided by ANOVA variance analysis to address this challenge. Through meticulous experimentation, we demonstrate that our method substantially reduces features by over 94% while preserving accuracy -- a significant advancement in the field of time series analysis and feature selection.

Frequency domain representation of time series feature offers a concise representation for handling real-world time series data with inherent complexity and dynamic nature. However, current frequency-based methods with complex operations still fall short of state-of-the-art time domain methods for general time series analysis. In this work, we present Omni-Dimensional Frequency Learner (ODFL) model based on a in depth analysis among all the three aspects of the spectrum feature: channel redundancy property among the frequency dimension, the sparse and un-salient frequency energy distribution among the frequency dimension, and the semantic diversity among the variable dimension. Technically, our method is composed of a semantic-adaptive global filter with attention to the un-salient frequency bands and partial operation among the channel dimension. Empirical results show that ODFL achieves consistent state-of-the-art in five mainstream time series analysis tasks, including short- and long-term forecasting, imputation, classification, and anomaly detection, offering a promising foundation for time series analysis.

Time series analysis stands as a focal point within the data mining community, serving as a cornerstone for extracting valuable insights crucial to a myriad of real-world applications. Recent advances in Foundation Models (FMs) have fundamentally reshaped the paradigm of model design for time series analysis, boosting various downstream tasks in practice. These innovative approaches often leverage pre-trained or fine-tuned FMs to harness generalized knowledge tailored for time series analysis. This survey aims to furnish a comprehensive and up-to-date overview of FMs for time series analysis. While prior surveys have predominantly focused on either application or pipeline aspects of FMs in time series analysis, they have often lacked an in-depth understanding of the underlying mechanisms that elucidate why and how FMs benefit time series analysis. To address this gap, our survey adopts a methodology-centric classification, delineating various pivotal elements of time-series FMs, including model architectures, pre-training techniques, adaptation methods, and data modalities. Overall, this survey serves to consolidate the latest advancements in FMs pertinent to time series analysis, accentuating their theoretical underpinnings, recent strides in development, and avenues for future exploration.

Time series data analysis is a critical component in various domains such as finance, healthcare, and meteorology. Despite the progress in deep learning for time series analysis, there remains a challenge in addressing the non-stationary nature of time series data. Traditional models, which are built on the assumption of constant statistical properties over time, often struggle to capture the temporal dynamics in realistic time series, resulting in bias and error in time series analysis. This paper introduces the Adaptive Wavelet Network (AdaWaveNet), a novel approach that employs Adaptive Wavelet Transformation for multi-scale analysis of non-stationary time series data. AdaWaveNet designed a lifting scheme-based wavelet decomposition and construction mechanism for adaptive and learnable wavelet transforms, which offers enhanced flexibility and robustness in analysis. We conduct extensive experiments on 10 datasets across 3 different tasks, including forecasting, imputation, and a newly established super-resolution task. The evaluations demonstrate the effectiveness of AdaWaveNet over existing methods in all three tasks, which illustrates its potential in various real-world applications.

Data is essential to performing time series analysis utilizing machine learning approaches, whether for classic models or today's large language models. A good time-series dataset is advantageous for the model's accuracy, robustness, and convergence, as well as task outcomes and costs. The emergence of data-centric AI represents a shift in the landscape from model refinement to prioritizing data quality. Even though time-series data processing methods frequently come up in a wide range of research fields, it hasn't been well investigated as a specific topic. To fill the gap, in this paper, we systematically review different data-centric methods in time series analysis, covering a wide range of research topics. Based on the time-series data characteristics at sample, feature, and period, we propose a taxonomy for the reviewed data selection methods. In addition to discussing and summarizing their characteristics, benefits, and drawbacks targeting time-series data, we also introduce the challenges and opportunities by proposing recommendations, open problems, and possible research topics.

Unsupervised (a.k.a. Self-supervised) representation learning (URL) has emerged as a new paradigm for time series analysis, because it has the ability to learn generalizable time series representation beneficial for many downstream tasks without using labels that are usually difficult to obtain. Considering that existing approaches have limitations in the design of the representation encoder and the learning objective, we have proposed Contrastive Shapelet Learning (CSL), the first URL method that learns the general-purpose shapelet-based representation through unsupervised contrastive learning, and shown its superior performance in several analysis tasks, such as time series classification, clustering, and anomaly detection. In this paper, we develop TimeCSL, an end-to-end system that makes full use of the general and interpretable shapelets learned by CSL to achieve explorable time series analysis in a unified pipeline. We introduce the system components and demonstrate how users interact with TimeCSL to solve different analysis tasks in the unified pipeline, and gain insight into their time series by exploring the learned shapelets and representation.

Time series analysis is a vital task with broad applications in various domains. However, effectively capturing cross-dimension and cross-time dependencies in non-stationary time series poses significant challenges, particularly in the context of environmental factors. The spurious correlation induced by the environment confounds the causal relationships between cross-dimension and cross-time dependencies. In this paper, we introduce a novel framework called Caformer (\underline{\textbf{Ca}}usal Trans\underline{\textbf{former}}) for time series analysis from a causal perspective. Specifically, our framework comprises three components: Dynamic Learner, Environment Learner, and Dependency Learner. The Dynamic Learner unveils dynamic interactions among dimensions, the Environment Learner mitigates spurious correlations caused by environment with a back-door adjustment, and the Dependency Learner aims to infer robust interactions across both time and dimensions. Our Caformer demonstrates consistent state-of-the-art performance across five mainstream time series analysis tasks, including long- and short-term forecasting, imputation, classification, and anomaly detection, with proper interpretability.

Social media platforms hold valuable insights, yet extracting essential information can be challenging. Traditional top-down approaches often struggle to capture critical signals in rapidly changing events. As global events evolve swiftly, social media narratives, including instances of disinformation, become significant sources of insights. To address the need for an inductive strategy, we explore a niche social media platform GAB and an established messaging service Telegram, to develop methodologies applicable on a broader scale. This study investigates narrative evolution on these platforms using quantitative corpus-based discourse analysis techniques. Our approach is a novel mode to study multiple social media domains to distil key information which may be obscured otherwise, allowing for useful and actionable insights. The paper details the technical and methodological aspects of gathering and preprocessing GAB and Telegram data for a keyness (Log Ratio) metric analysis, identifying crucial nouns and verbs for deeper exploration. Empirically, this approach is applied to a case study of a well defined event that had global impact: the 2023 Wagner mutiny. The main findings are: (1) the time line can be deconstructed to provide useful data features allowing for improved interpretation; (2) a methodology is applied which provides a basis for generalization. The key contribution is an approach, that in some cases, provides the ability to capture the dynamic narrative shifts over time with elevated confidence. The approach can augment near-real-time assessment of key social movements, allowing for informed governance choices. This research is important because it lays out a useful methodology for time series relevant info-culling, which can enable proactive modes for positive social engagement.

Over a significant period in the past, the convolutional network [He et al., 2016; Zheng et al., 2014; Middlehurst This paper introduces ConvTimeNet, a novel deep et al., 2023] has played a crucial role in time series analysis, hierarchical fully convolutional network designed largely due to its inherent properties that strike an excellent to serve as a general-purpose model for time series balance between computational efficiency and representation analysis. The key design of this network is twofold, quality. Data back to the past years, many representative designed to overcome the limitations of traditional works [Bagnall et al., 2017] of time series analysis typically convolutional networks. Firstly, we propose an employ convolutional networks as the backbone. For adaptive segmentation of time series into sub-series instance, temporal convolutional network (TCN[Bai et al., level patches, treating these as fundamental modeling 2018]) and its variants are widely used in modeling temporal units. This setting avoids the sparsity semantics variation dependence for the time series forecasting task. Furthermore, associated with raw point-level time steps. Secondly, a large number of works (such as InceptionTime[Ismail we design a fully convolutional block by Fawaz et al., 2020], MiniRocket[Dempster et al., 2021], skillfully integrating deepwise and pointwise convolution and MCNN[Cui et al., 2016]) are also proposed by employing operations, following the advanced building convolutional networks to identify informative patterns block style employed in Transformer encoders.