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1. A Windowed Temporal Saliency Rescaling Method for Interpreting Time Series Deep Learning Models

   Islam, Md Khairul; Fox, Judy (March 2025, AAAI'25 Workshop: AI for Time Series Analysis: Theory, Algorithms, and Applications (AI4TS))

   Song, Dongjin; Xie, Yao; Purushotham, Sanjay; Chen, Haifeng; Shen, Cong (Ed.)

   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, 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. 

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2. Correlating Time Series With Interpretable Convolutional Kernels

   https://doi.org/10.1109/TKDE.2025.3550877  

   Chen, Xinyu; Cai, HanQin; Liu, Fuqiang; Zhao, Jinhua (June 2025, IEEE Transactions on Knowledge and Data Engineering)

   This study addresses the problem of convolutional kernel learning in univariate, multivariate, and multidimensional time series data, which is crucial for interpreting temporal patterns in time series and supporting downstream machine learning tasks. First, we propose formulating convolutional kernel learning for univariate time series as a sparse regression problem with a non-negative constraint, leveraging the properties of circular convolution and circulant matrices. Second, to generalize this approach to multivariate and multidimensional time series data, we use tensor computations, reformulating the convolutional kernel learning problem in the form of tensors. This is further converted into a standard sparse regression problem through vectorization and tensor unfolding operations. In the proposed methodology, the optimization problem is addressed using the existing non-negative subspace pursuit method, enabling the convolutional kernel to capture temporal correlations and patterns. To evaluate the proposed model, we apply it to several real-world time series datasets. On the multidimensional ridesharing and taxi trip data from New York City and Chicago, the convolutional kernels reveal interpretable local correlations and cyclical patterns, such as weekly seasonality. For the monthly temperature time series data in North America, the proposed model can quantify the yearly seasonality and make it comparable across different decades. In the context of multidimensional fluid flow data, both local and nonlocal correlations captured by the convolutional kernels can reinforce tensor factorization, leading to performance improvements in fluid flow reconstruction tasks. Thus, this study lays an insightful foundation for automatically learning convolutional kernels from time series data, with an emphasis on interpretability through sparsity and non-negativity constraints. 

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3. Capturing Temporal Components for Time Series Classification

   Vavilthota, Venkata Ragavendra; Ramanathan, Ranjith; Aakur, Sathyanarayanan N (September 2024, Springer)

   Analyzing sequential data is crucial in many domains, particularly due to the abundance of data collected from the Internet of Things paradigm. Time series classification, the task of categorizing sequential data, has gained prominence, with machine learning approaches demonstrating remarkable performance on public benchmark datasets. However, progress has primarily been in designing architectures for learning representations from raw data at fixed (or ideal) time scales, which can fail to generalize to longer sequences. This work introduces a \textit{compositional representation learning} approach trained on statistically coherent components extracted from sequential data. Based on a multi-scale change space, an unsupervised approach is proposed to segment the sequential data into chunks with similar statistical properties. A sequence-based encoder model is trained in a multi-task setting to learn compositional representations from these temporal components for time series classification. We demonstrate its effectiveness through extensive experiments on publicly available time series classification benchmarks. Evaluating the coherence of segmented components shows its competitive performance on the unsupervised segmentation task. 

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4. Trainable Time Warping: Aligning Time-series in the Continuous-time Domain

   https://doi.org/10.1109/icassp.2019.8682322  

   Khorram, Soheil; McInnis, Melvin G; Mower Provost, Emily (May 2019, International Conference on Acoustics, Speech, and Signal Processing (ICASSP))

   DTW calculates the similarity or alignment between two signals, subject to temporal warping. However, its computational complexity grows exponentially with the number of time-series. Although there have been algorithms developed that are linear in the number of time-series, they are generally quadratic in time-series length. The exception is generalized time warping (GTW), which has linear computational cost. Yet, it can only identify simple time warping functions. There is a need for a new fast, high-quality multisequence alignment algorithm. We introduce trainable time warping (TTW), whose complexity is linear in both the number and the length of time-series. TTW performs alignment in the continuoustime domain using a sinc convolutional kernel and a gradient-based optimization technique. We compare TTW and GTW on S5 UCR datasets in time-series averaging and classification. TTW outperforms GTW on 67.1% of the datasets for the averaging tasks, and 61.2% of the datasets for the classification tasks. 

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5. Generative Anomaly Detection for Time Series Datasets

   Kang, Zhuangwei; Mukhopadhyay, Ayan; Gokhale, Aniruddha; Wen, Shijie and (January 2022, ITSC)

   Traffic congestion anomaly detection is of paramount importance in intelligent traffic systems. The goals of transportation agencies are two-fold: to monitor the general traffic conditions in the area of interest and to locate road segments under abnormal congestion states. Modeling congestion patterns can achieve these goals for citywide roadways, which amounts to learning the distribution of multivariate time series (MTS). However, existing works are either not scalable or unable to capture the spatial-temporal information in MTS simultaneously. To this end, we propose a principled and comprehensive framework consisting of a data-driven generative approach that can perform tractable density estimation for detecting traffic anomalies. Our approach first clusters segments in the feature space and then uses conditional normalizing flow to identify anomalous temporal snapshots at the cluster level in an unsupervised setting. Then, we identify anomalies at the segment level by using a kernel density estimator on the anomalous cluster. Extensive experiments on synthetic datasets show that our approach significantly outperforms several state-of-the-art congestion anomaly detection and diagnosis methods in terms of Recall and F1-Score. We also use the generative model to sample labeled data, which can train classifiers in a supervised setting, alleviating the lack of labeled data for anomaly detection in sparse settings. 

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