The risk-controlling prediction sets (RCPS) framework is a general tool for transforming the output of any machine learning model to design a predictive rule with rigorous error rate control. The key idea behind this framework is to use labeled hold-out calibration data to tune a hyper-parameter that affects the error rate of the resulting prediction rule. However, the limitation of such a calibration scheme is that with limited hold-out data, the tuned hyper-parameter becomes noisy and leads to a prediction rule with an error rate that is often unnecessarily conservative. To overcome this sample-size barrier, we introduce a semi-supervised calibration procedure that leverages unlabeled data to rigorously tune the hyper-parameter without compromising statistical validity. Our procedure builds upon the prediction-powered inference framework, carefully tailoring it to risk-controlling tasks. We demonstrate the benefits and validity of our proposal through two real-data experiments: few-shot image classification and early time series classification.
This paper investigates the lack of research on activation functions for neural network models in time series tasks. It highlights the need to identify essential properties of these activations to improve their effectiveness in specific domains. To this end, the study comprehensively analyzes properties, such as bounded, monotonic, nonlinearity, and periodicity, for activation in time series neural networks. We propose a new activation that maximizes the coverage of these properties, called LeakySineLU. We empirically evaluate the LeakySineLU against commonly used activations in the literature using 112 benchmark datasets for time series classification, obtaining the best average ranking in all comparative scenarios.
Recently, there has been a growing interest in time series foundation models that generalize across different downstream tasks. A key to strong foundation models is a diverse pre-training dataset, which is particularly challenging to collect for time series classification. In this work, we explore the performance of a contrastive-learning-based foundation model as a function of the data used for pre-training. We introduce contrastive accuracy, a new measure to evaluate the quality of the representation space learned by the foundation model. Our experiments reveal the positive correlation between the proposed measure and the accuracy of the model on a collection of downstream tasks. This suggests that the contrastive accuracy can serve as a criterion to search for time series datasets that can enhance the pre-training and improve thereby the foundation model's generalization.
Interpreting complex time series forecasting models is challenging due to the temporal dependencies between time steps and the dynamic relevance of input features over time. Existing interpretation methods are limited by focusing mostly on classification tasks, evaluating using custom baseline models instead of the latest time series models, using simple synthetic datasets, and requiring training another model. We introduce a novel interpretation method called Windowed Temporal Saliency Rescaling (WinTSR) addressing these limitations. WinTSR explicitly captures temporal dependencies among the past time steps and efficiently scales the feature importance with this time importance. We benchmark WinTSR against 10 recent interpretation techniques with 5 state-of-the-art deep-learning models of different architectures, including a time series foundation model. We use 3 real-world datasets for both time-series classification and regression. Our comprehensive analysis shows that WinTSR significantly outranks the other local interpretation methods in overall performance. Finally, we provide a novel and open-source framework to interpret the latest time series transformers and foundation models.
In this paper, we introduce IndMask, a framework for explaining decisions of black-box time series models. While there exists a plethora of methods for providing explanations of machine learning models, time series data requires additional considerations. One needs to consider the time aspect in the explanations as well as deal with a large number of input features. Recent work has proposed explaining a time series prediction by generating a mask over the input time series. Each entry in the mask corresponds to an importance score for each feature at each time step. However, these methods only generate instancewise explanations, which means a mask needs to be computed for each input individually, thereby making them unsuited for inductive settings, where explanations need to be generated for numerous inputs, and instancewise explanation generation is severely prohibitive. Additionally, these methods have mostly been evaluated on simple recurrent neural networks and are often only applicable to a specific downstream task. Our proposed framework IndMask addresses these issues by utilizing a parameterized model for mask generation. We also go beyond recurrent neural networks and deploy IndMask to transformer architectures, thereby genuinely demonstrating its model-agnostic nature. The effectiveness of IndMask is further demonstrated through experiments over real-world datasets and time series classification and forecasting tasks. It is also computationally efficient and can be deployed in conjunction with any time series model.
The success of large language models (LLMs) for time series has been demonstrated in previous work. Utilizing a symbolic time series representation, one can efficiently bridge the gap between LLMs and time series. However, the remaining challenge is to exploit the semantic information hidden in time series by using symbols or existing tokens of LLMs, while aligning the embedding space of LLMs according to the hidden information of time series. The symbolic time series approximation (STSA) method called adaptive Brownian bridge-based symbolic aggregation (ABBA) shows outstanding efficacy in preserving salient time series features by modeling time series patterns in terms of amplitude and period while using existing tokens of LLMs. In this paper, we introduce a method, called LLM-ABBA, that integrates ABBA into large language models for various downstream time series tasks. By symbolizing time series, LLM-ABBA compares favorably to the recent state-of-the-art (SOTA) in UCR and three medical time series classification tasks. Meanwhile, a fixed-polygonal chain trick in ABBA is introduced to \kc{avoid obvious drifting} during prediction tasks by significantly mitigating the effects of cumulative error arising from misused symbols during the transition from symbols to numerical values. In time series regression tasks, LLM-ABBA achieves the new SOTA on Time Series Extrinsic Regression (TSER) benchmarks. LLM-ABBA also shows competitive prediction capability compared to recent SOTA time series prediction results. We believe this framework can also seamlessly extend to other time series tasks.
Recently, time series classification has attracted the attention of a large number of researchers, and hundreds of methods have been proposed. However, these methods often ignore the spatial correlations among dimensions and the local correlations among features. To address this issue, the causal and local correlations based network (CaLoNet) is proposed in this study for multivariate time series classification. First, pairwise spatial correlations between dimensions are modeled using causality modeling to obtain the graph structure. Then, a relationship extraction network is used to fuse local correlations to obtain long-term dependency features. Finally, the graph structure and long-term dependency features are integrated into the graph neural network. Experiments on the UEA datasets show that CaLoNet can obtain competitive performance compared with state-of-the-art methods.
Large language models (LLMs) have demonstrated their effectiveness in multivariate time series classification (MTSC). Effective adaptation of LLMs for MTSC necessitates informative data representations. Existing LLM-based methods directly encode embeddings for time series within the latent space of LLMs from scratch to align with semantic space of LLMs. Despite their effectiveness, we reveal that these methods conceal three inherent bottlenecks: (1) they struggle to encode temporal and channel-specific information in a lossless manner, both of which are critical components of multivariate time series; (2) it is much difficult to align the learned representation space with the semantic space of the LLMs; (3) they require task-specific retraining, which is both computationally expensive and labor-intensive. To bridge these gaps, we propose TableTime, which reformulates MTSC as a table understanding task. Specifically, TableTime introduces the following strategies: (1) convert multivariate time series into a tabular form, thus minimizing information loss to the greatest extent; (2) represent tabular time series in text format to achieve natural alignment with the semantic space of LLMs; (3) design a reasoning framework that integrates contextual text information, neighborhood assistance, multi-path inference and problem decomposition to enhance the reasoning ability of LLMs and realize zero-shot classification. Extensive experiments performed on 10 publicly representative datasets from UEA archive verify the superiorities of the TableTime.
Time series classification is a relevant step supporting decision-making processes in various domains, and deep neural models have shown promising performance. Despite significant advancements in deep learning, the theoretical understanding of how and why complex architectures function remains limited, prompting the need for more interpretable models. Recently, the Kolmogorov-Arnold Networks (KANs) have been proposed as a more interpretable alternative. While KAN-related research is significantly rising, to date, the study of KAN architectures for time series classification has been limited. In this paper, we aim to conduct a comprehensive and robust exploration of the KAN architecture for time series classification on the UCR benchmark. More specifically, we look at a) how reference architectures for forecasting transfer to classification, at the b) hyperparameter and implementation influence on the classification performance in view of finding the one that performs best on the selected benchmark, the c) complexity trade-offs and d) interpretability advantages. Our results show that (1) Efficient KAN outperforms MLP in performance and computational efficiency, showcasing its suitability for tasks classification tasks. (2) Efficient KAN is more stable than KAN across grid sizes, depths, and layer configurations, particularly with lower learning rates. (3) KAN maintains competitive accuracy compared to state-of-the-art models like HIVE-COTE2, with smaller architectures and faster training times, supporting its balance of performance and transparency. (4) The interpretability of the KAN model aligns with findings from SHAP analysis, reinforcing its capacity for transparent decision-making.
Multivariate time series classification is of great importance in practical applications and is a challenging task. However, deep neural network models such as Transformers exhibit high accuracy in multivariate time series classification but lack interpretability and fail to provide insights into the decision-making process. On the other hand, traditional approaches based on decision tree classifiers offer clear decision processes but relatively lower accuracy. Swin Transformer (ST) addresses these issues by leveraging self-attention mechanisms to capture both fine-grained local patterns and global patterns. It can also model multi-scale feature representation learning, thereby providing a more comprehensive representation of time series features. To tackle the aforementioned challenges, we propose ST-Tree with interpretability for multivariate time series classification. Specifically, the ST-Tree model combines ST as the backbone network with an additional neural tree model. This integration allows us to fully leverage the advantages of ST in learning time series context while providing interpretable decision processes through the neural tree. This enables researchers to gain clear insights into the model's decision-making process and extract meaningful interpretations. Through experimental evaluations on 10 UEA datasets, we demonstrate that the ST-Tree model improves accuracy in multivariate time series classification tasks and provides interpretability through visualizing the decision-making process across different datasets.
Quantifying similarities between time series in a meaningful way remains a challenge in time series analysis, despite many advances in the field. Most real-world solutions still rely on a few popular measures, such as Euclidean Distance (EuD), Longest Common Subsequence (LCSS), and Dynamic Time Warping (DTW). The strengths and weaknesses of these measures have been studied extensively, and incremental improvements have been proposed. In this study, however, we present a different similarity measure that fuses the notion of Dubuc's variation from fractal analysis with the Intersection-over-Union (IoU) measure which is widely used in object recognition (also known as the Jaccard Index). In this proof-of-concept paper, we introduce the Multiscale Dubuc Distance (MDD) measure and prove that it is a metric, possessing desirable properties such as the triangle inequality. We use 95 datasets from the UCR Time Series Classification Archive to compare MDD's performance with EuD, LCSS, and DTW. Our experiments show that MDD's overall success, without any case-specific customization, is comparable to DTW with optimized window sizes per dataset. We also highlight several datasets where MDD's performance improves significantly when its single parameter is customized. This customization serves as a powerful tool for gauging MDD's sensitivity to noise. Lastly, we show that MDD's running time is linear in the length of the time series, which is crucial for real-world applications involving very large datasets.
Over the past decade, multivariate time series classification has received great attention. Machine learning (ML) models for multivariate time series classification have made significant strides and achieved impressive success in a wide range of applications and tasks. The challenge of many state-of-the-art ML models is a lack of transparency and interpretability. In this work, we introduce M-CELS, a counterfactual explanation model designed to enhance interpretability in multidimensional time series classification tasks. Our experimental validation involves comparing M-CELS with leading state-of-the-art baselines, utilizing seven real-world time-series datasets from the UEA repository. The results demonstrate the superior performance of M-CELS in terms of validity, proximity, and sparsity, reinforcing its effectiveness in providing transparent insights into the decisions of machine learning models applied to multivariate time series data.
In time-series analysis, many recent works seek to provide a unified view and representation for time-series across multiple domains, leading to the development of foundation models for time-series data. Despite diverse modeling techniques, existing models are black boxes and fail to provide insights and explanations about their representations. In this paper, we present VQShape, a pre-trained, generalizable, and interpretable model for time-series representation learning and classification. By introducing a novel representation for time-series data, we forge a connection between the latent space of VQShape and shape-level features. Using vector quantization, we show that time-series from different domains can be described using a unified set of low-dimensional codes, where each code can be represented as an abstracted shape in the time domain. On classification tasks, we show that the representations of VQShape can be utilized to build interpretable classifiers, achieving comparable performance to specialist models. Additionally, in zero-shot learning, VQShape and its codebook can generalize to previously unseen datasets and domains that are not included in the pre-training process. The code and pre-trained weights are available at https://github.com/YunshiWen/VQShape.
In recent years, spatio-temporal graph neural networks (GNNs) have attracted considerable interest in the field of time series analysis, due to their ability to capture dependencies among variables and across time points. The objective of the presented systematic literature review is hence to provide a comprehensive overview of the various modeling approaches and application domains of GNNs for time series classification and forecasting. A database search was conducted, and over 150 journal papers were selected for a detailed examination of the current state-of-the-art in the field. This examination is intended to offer to the reader a comprehensive collection of proposed models, links to related source code, available datasets, benchmark models, and fitting results. All this information is hoped to assist researchers in future studies. To the best of our knowledge, this is the first systematic literature review presenting a detailed comparison of the results of current spatio-temporal GNN models in different domains. In addition, in its final part this review discusses current limitations and challenges in the application of spatio-temporal GNNs, such as comparability, reproducibility, explainability, poor information capacity, and scalability.
Motion time series collected from mobile and wearable devices such as smartphones and smartwatches offer significant insights into human behavioral patterns, with wide applications in healthcare, automation, IoT, and AR/XR due to their low-power, always-on nature. However, given security and privacy concerns, building large-scale motion time series datasets remains difficult, preventing the development of pre-trained models for human activity analysis. Typically, existing models are trained and tested on the same dataset, leading to poor generalizability across variations in device location, device mounting orientation and human activity type. In this paper, we introduce UniMTS, the first unified pre-training procedure for motion time series that generalizes across diverse device latent factors and activities. Specifically, we employ a contrastive learning framework that aligns motion time series with text descriptions enriched by large language models. This helps the model learn the semantics of time series to generalize across activities. Given the absence of large-scale motion time series data, we derive and synthesize time series from existing motion skeleton data with all-joint coverage. Spatio-temporal graph networks are utilized to capture the relationships across joints for generalization across different device locations. We further design rotation-invariant augmentation to make the model agnostic to changes in device mounting orientations. Our model shows exceptional generalizability across 18 motion time series classification benchmark datasets, outperforming the best baselines by 340% in the zero-shot setting, 16.3% in the few-shot setting, and 9.2% in the full-shot setting.
In multivariate time series classification, although current sequence analysis models have excellent classification capabilities, they show significant shortcomings when dealing with long sequence multivariate data, such as prolonged training times and decreased accuracy. This paper focuses on optimizing model performance for long-sequence multivariate data by mitigating the impact of extended time series and multiple variables on the model. We propose a principal component analysis (PCA)-based temporal streaming compression and dimensionality reduction algorithm for time series data (temporal streaming batch PCA, TSBPCA), which continuously updates the compact representation of the entire sequence through streaming PCA time estimation with time block updates, enhancing the data representation capability of a range of sequence analysis models. We evaluated this method using various models on five real datasets, and the experimental results show that our method performs well in terms of classification accuracy and time efficiency. Notably, our method demonstrates a trend of increasing effectiveness as sequence length grows; on the two longest sequence datasets, accuracy improved by about 7.2%, and execution time decreased by 49.5%.
Leveraging large language models (LLMs) has garnered increasing attention and introduced novel perspectives in time series classification. However, existing approaches often overlook the crucial dynamic temporal information inherent in time series data and face challenges in aligning this data with textual semantics. To address these limitations, we propose HiTime, a hierarchical multi-modal model that seamlessly integrates temporal information into LLMs for multivariate time series classification (MTSC). Our model employs a hierarchical feature encoder to capture diverse aspects of time series data through both data-specific and task-specific embeddings. To facilitate semantic space alignment between time series and text, we introduce a dual-view contrastive alignment module that bridges the gap between modalities. Additionally, we adopt a hybrid prompting strategy to fine-tune the pre-trained LLM in a parameter-efficient manner. By effectively incorporating dynamic temporal features and ensuring semantic alignment, HiTime enables LLMs to process continuous time series data and achieves state-of-the-art classification performance through text generation. Extensive experiments on benchmark datasets demonstrate that HiTime significantly enhances time series classification accuracy compared to most competitive baseline methods. Our findings highlight the potential of integrating temporal features into LLMs, paving the way for advanced time series analysis. The code is publicly available for further research and validation. Our codes are publicly available1.
Time series classification underpins critical applications such as healthcare diagnostics and gesture-driven interactive systems in multimedia scenarios. However, time series class-incremental learning (TSCIL) faces two major challenges: catastrophic forgetting and intra-class variations. Catastrophic forgetting occurs because gradient-based parameter update strategies inevitably erase past knowledge. And unlike images, time series data exhibits subject-specific patterns, also known as intra-class variations, which refer to differences in patterns observed within the same class. While exemplar-based methods fail to cover diverse variation with limited samples, existing exemplar-free methods lack explicit mechanisms to handle intra-class variations. To address these two challenges, we propose TS-ACL, which leverages a gradient-free closed-form solution to avoid the catastrophic forgetting problem inherent in gradient-based optimization methods while simultaneously learning global distributions to resolve intra-class variations. Additionally, it provides privacy protection and efficiency. Extensive experiments on five benchmark datasets covering various sensor modalities and tasks demonstrate that TS-ACL achieves performance close to joint training on four datasets, outperforming existing methods and establishing a new state-of-the-art (SOTA) for TSCIL.
Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions of time series observed at irregular time points, by using a directed acyclic graph to model the conditional dependencies (a form of causal notation) of the system components and learning this graph in tandem with a continuous-time model that parameterizes the solution curves of ordinary differential equations (ODEs). Our technique, a graph neural flow, leads to substantial enhancements over non-graph-based methods, as well as graph-based methods without the modeling of conditional dependencies. We validate our approach on several tasks, including time series classification and forecasting, to demonstrate its efficacy.
Contrastive learning (CL) has emerged as a promising approach for representation learning in time series data by embedding similar pairs closely while distancing dissimilar ones. However, existing CL methods often introduce false negative pairs (FNPs) by neglecting inherent characteristics and then randomly selecting distinct segments as dissimilar pairs, leading to erroneous representation learning, reduced model performance, and overall inefficiency. To address these issues, we systematically define and categorize FNPs in time series into semantic false negative pairs and temporal false negative pairs for the first time: the former arising from overlooking similarities in label categories, which correlates with similarities in non-stationarity and the latter from neglecting temporal proximity. Moreover, we introduce StatioCL, a novel CL framework that captures non-stationarity and temporal dependency to mitigate both FNPs and rectify the inaccuracies in learned representations. By interpreting and differentiating non-stationary states, which reflect the correlation between trends or temporal dynamics with underlying data patterns, StatioCL effectively captures the semantic characteristics and eliminates semantic FNPs. Simultaneously, StatioCL establishes fine-grained similarity levels based on temporal dependencies to capture varying temporal proximity between segments and to mitigate temporal FNPs. Evaluated on real-world benchmark time series classification datasets, StatioCL demonstrates a substantial improvement over state-of-the-art CL methods, achieving a 2.9% increase in Recall and a 19.2% reduction in FNPs. Most importantly, StatioCL also shows enhanced data efficiency and robustness against label scarcity.