EDformer: Embedded Decomposition Transformer for Interpretable Multivariate Time Series Predictions

Time series forecasting is a crucial challenge with significant applications in areas such as weather prediction, stock market analysis, and scientific simulations. This paper introduces an embedded decomposed transformer, 'EDformer', for multivariate time series forecasting tasks. Without altering the fundamental elements, we reuse the Transformer architecture and consider the capable functions of its constituent parts in this work. Edformer first decomposes the input multivariate signal into seasonal and trend components. Next, the prominent multivariate seasonal component is reconstructed across the reverse dimensions, followed by applying the attention mechanism and feed-forward network in the encoder stage. In particular, the feed-forward network is used for each variable frame to learn nonlinear representations, while the attention mechanism uses the time points of individual seasonal series embedded within variate frames to capture multivariate correlations. Therefore, the trend signal is added with projection and performs the final forecasting. The EDformer model obtains state-of-the-art predicting results in terms of accuracy and efficiency on complex real-world time series datasets. This paper also addresses model explainability techniques to provide insights into how the model makes its predictions and why specific features or time steps are important, enhancing the interpretability and trustworthiness of the forecasting results.

DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting

Multivariate time series forecasting is crucial for various applications, such as financial investment, energy management, weather forecasting, and traffic optimization. However, accurate forecasting is challenging due to two main factors. First, real-world time series often show heterogeneous temporal patterns caused by distribution shifts over time. Second, correlations among channels are complex and intertwined, making it hard to model the interactions among channels precisely and flexibly. In this study, we address these challenges by proposing a general framework called \textbf{DUET}, which introduces \underline{DU}al clustering on the temporal and channel dimensions to \underline{E}nhance multivariate \underline{T}ime series forecasting. First, we design a Temporal Clustering Module (TCM) that clusters time series into fine-grained distributions to handle heterogeneous temporal patterns. For different distribution clusters, we design various pattern extractors to capture their intrinsic temporal patterns, thus modeling the heterogeneity. Second, we introduce a novel Channel-Soft-Clustering strategy and design a Channel Clustering Module (CCM), which captures the relationships among channels in the frequency domain through metric learning and applies sparsification to mitigate the adverse effects of noisy channels. Finally, DUET combines TCM and CCM to incorporate both the temporal and channel dimensions. Extensive experiments on 25 real-world datasets from 10 application domains, demonstrate the state-of-the-art performance of DUET.

Toward Foundation Model for Multivariate Wearable Sensing of Physiological Signals

Time-series foundation models have the ability to run inference, mainly forecasting, on any type of time series data, thanks to the informative representations comprising waveform features. Wearable sensing data, on the other hand, contain more variability in both patterns and frequency bands of interest and generally emphasize more on the ability to infer healthcare-related outcomes. The main challenge of crafting a foundation model for wearable sensing physiological signals is to learn generalizable representations that support efficient adaptation across heterogeneous sensing configurations and applications. In this work, we propose NormWear, a step toward such a foundation model, aiming to extract generalized and informative wearable sensing representations. NormWear has been pretrained on a large set of physiological signals, including PPG, ECG, EEG, GSR, and IMU, from various public resources. For a holistic assessment, we perform downstream evaluation on 11 public wearable sensing datasets, spanning 18 applications in the areas of mental health, body state inference, biomarker estimations, and disease risk evaluations. We demonstrate that NormWear achieves a better performance improvement over competitive baselines in general time series foundation modeling. In addition, leveraging a novel representation-alignment-match-based method, we align physiological signals embeddings with text embeddings. This alignment enables our proposed foundation model to perform zero-shot inference, allowing it to generalize to previously unseen wearable signal-based health applications. Finally, we perform nonlinear dynamic analysis on the waveform features extracted by the model at each intermediate layer. This analysis quantifies the model's internal processes, offering clear insights into its behavior and fostering greater trust in its inferences among end users.

PowerMamba: A Deep State Space Model and Comprehensive Benchmark for Time Series Prediction in Electric Power Systems

The electricity sector is undergoing substantial transformations due to the rising electrification of demand, enhanced integration of renewable energy resources, and the emergence of new technologies. These changes are rendering the electric grid more volatile and unpredictable, making it difficult to maintain reliable operations. In order to address these issues, advanced time series prediction models are needed for closing the gap between the forecasted and actual grid outcomes. In this paper, we introduce a multivariate time series prediction model that combines traditional state space models with deep learning methods to simultaneously capture and predict the underlying dynamics of multiple time series. Additionally, we design a time series processing module that incorporates high-resolution external forecasts into sequence-to-sequence prediction models, achieving this with negligible increases in size and no loss of accuracy. We also release an extended dataset spanning five years of load, electricity price, ancillary service price, and renewable generation. To complement this dataset, we provide an open-access toolbox that includes our proposed model, the dataset itself, and several state-of-the-art prediction models, thereby creating a unified framework for benchmarking advanced machine learning approaches. Our findings indicate that the proposed model outperforms existing models across various prediction tasks, improving state-of-the-art prediction error by an average of 7% and decreasing model parameters by 43%.

Higher Order Transformers: Efficient Attention Mechanism for Tensor Structured Data

Transformers are now ubiquitous for sequence modeling tasks, but their extension to multi-dimensional data remains a challenge due to the quadratic cost of the attention mechanism. In this paper, we propose Higher-Order Transformers (HOT), a novel architecture designed to efficiently process data with more than two axes, i.e. higher-order tensors. To address the computational challenges associated with high-order tensor attention, we introduce a novel Kronecker factorized attention mechanism that reduces the attention cost to quadratic in each axis' dimension, rather than quadratic in the total size of the input tensor. To further enhance efficiency, HOT leverages kernelized attention, reducing the complexity to linear. This strategy maintains the model's expressiveness while enabling scalable attention computation. We validate the effectiveness of HOT on two high-dimensional tasks, including multivariate time series forecasting, and 3D medical image classification. Experimental results demonstrate that HOT achieves competitive performance while significantly improving computational efficiency, showcasing its potential for tackling a wide range of complex, multi-dimensional data.

MTS-UNMixers: Multivariate Time Series Forecasting via Channel-Time Dual Unmixing

Multivariate time series data provide a robust framework for future predictions by leveraging information across multiple dimensions, ensuring broad applicability in practical scenarios. However, their high dimensionality and mixing patterns pose significant challenges in establishing an interpretable and explicit mapping between historical and future series, as well as extracting long-range feature dependencies. To address these challenges, we propose a channel-time dual unmixing network for multivariate time series forecasting (named MTS-UNMixer), which decomposes the entire series into critical bases and coefficients across both the time and channel dimensions. This approach establishes a robust sharing mechanism between historical and future series, enabling accurate representation and enhancing physical interpretability. Specifically, MTS-UNMixers represent sequences over time as a mixture of multiple trends and cycles, with the time-correlated representation coefficients shared across both historical and future time periods. In contrast, sequence over channels can be decomposed into multiple tick-wise bases, which characterize the channel correlations and are shared across the whole series. To estimate the shared time-dependent coefficients, a vanilla Mamba network is employed, leveraging its alignment with directional causality. Conversely, a bidirectional Mamba network is utilized to model the shared channel-correlated bases, accommodating noncausal relationships. Experimental results show that MTS-UNMixers significantly outperform existing methods on multiple benchmark datasets. The code is available at https://github.com/ZHU-0108/MTS-UNMixers.

MuSiCNet: A Gradual Coarse-to-Fine Framework for Irregularly Sampled Multivariate Time Series Analysis

Irregularly sampled multivariate time series (ISMTS) are prevalent in reality. Most existing methods treat ISMTS as synchronized regularly sampled time series with missing values, neglecting that the irregularities are primarily attributed to variations in sampling rates. In this paper, we introduce a novel perspective that irregularity is essentially relative in some senses. With sampling rates artificially determined from low to high, an irregularly sampled time series can be transformed into a hierarchical set of relatively regular time series from coarse to fine. We observe that additional coarse-grained relatively regular series not only mitigate the irregularly sampled challenges to some extent but also incorporate broad-view temporal information, thereby serving as a valuable asset for representation learning. Therefore, following the philosophy of learning that Seeing the big picture first, then delving into the details, we present the Multi-Scale and Multi-Correlation Attention Network (MuSiCNet) combining multiple scales to iteratively refine the ISMTS representation. Specifically, within each scale, we explore time attention and frequency correlation matrices to aggregate intra- and inter-series information, naturally enhancing the representation quality with richer and more intrinsic details. While across adjacent scales, we employ a representation rectification method containing contrastive learning and reconstruction results adjustment to further improve representation consistency. MuSiCNet is an ISMTS analysis framework that competitive with SOTA in three mainstream tasks consistently, including classification, interpolation, and forecasting.

Knowledge-enhanced Transformer for Multivariate Long Sequence Time-series Forecasting

Multivariate Long Sequence Time-series Forecasting (LSTF) has been a critical task across various real-world applications. Recent advancements focus on the application of transformer architectures attributable to their ability to capture temporal patterns effectively over extended periods. However, these approaches often overlook the inherent relationships and interactions between the input variables that could be drawn from their characteristic properties. In this paper, we aim to bridge this gap by integrating information-rich Knowledge Graph Embeddings (KGE) with state-of-the-art transformer-based architectures. We introduce a novel approach that encapsulates conceptual relationships among variables within a well-defined knowledge graph, forming dynamic and learnable KGEs for seamless integration into the transformer architecture. We investigate the influence of this integration into seminal architectures such as PatchTST, Autoformer, Informer, and Vanilla Transformer. Furthermore, we thoroughly investigate the performance of these knowledge-enhanced architectures along with their original implementations for long forecasting horizons and demonstrate significant improvement in the benchmark results. This enhancement empowers transformer-based architectures to address the inherent structural relation between variables. Our knowledge-enhanced approach improves the accuracy of multivariate LSTF by capturing complex temporal and relational dynamics across multiple domains. To substantiate the validity of our model, we conduct comprehensive experiments using Weather and Electric Transformer Temperature (ETT) datasets.

Conformal Prediction for Hierarchical Data

Reconciliation has become an essential tool in multivariate point forecasting for hierarchical time series. However, there is still a lack of understanding of the theoretical properties of probabilistic Forecast Reconciliation techniques. Meanwhile, Conformal Prediction is a general framework with growing appeal that provides prediction sets with probabilistic guarantees in finite sample. In this paper, we propose a first step towards combining Conformal Prediction and Forecast Reconciliation by analyzing how including a reconciliation step in the Split Conformal Prediction (SCP) procedure enhances the resulting prediction sets. In particular, we show that the validity granted by SCP remains while improving the efficiency of the prediction sets. We also advocate a variation of the theoretical procedure for practical use. Finally, we illustrate these results with simulations.

Disentangled Interpretable Representation for Efficient Long-term Time Series Forecasting

Industry 5.0 introduces new challenges for Long-term Time Series Forecasting (LTSF), characterized by high-dimensional, high-resolution data and high-stakes application scenarios. Against this backdrop, developing efficient and interpretable models for LTSF becomes a key challenge. Existing deep learning and linear models often suffer from excessive parameter complexity and lack intuitive interpretability. To address these issues, we propose DiPE-Linear, a Disentangled interpretable Parameter-Efficient Linear network. DiPE-Linear incorporates three temporal components: Static Frequential Attention (SFA), Static Temporal Attention (STA), and Independent Frequential Mapping (IFM). These components alternate between learning in the frequency and time domains to achieve disentangled interpretability. The decomposed model structure reduces parameter complexity from quadratic in fully connected networks (FCs) to linear and computational complexity from quadratic to log-linear. Additionally, a Low-Rank Weight Sharing policy enhances the model's ability to handle multivariate series. Despite operating within a subspace of FCs with limited expressive capacity, DiPE-Linear demonstrates comparable or superior performance to both FCs and nonlinear models across multiple open-source and real-world LTSF datasets, validating the effectiveness of its sophisticatedly designed structure. The combination of efficiency, accuracy, and interpretability makes DiPE-Linear a strong candidate for advancing LTSF in both research and real-world applications. The source code is available at https://github.com/wintertee/DiPE-Linear.