While many explainable AI (XAI) methods have been proposed, most are not designed for time-series forecasting models and often rely on the implicit assumption that timestamp features are independent. This assumption ignores the fundamental property of temporal dependence and can lead to explanations that violate the sequential and causal structure of the data. We introduce \textsc{KARMA}, a method for explaining time-series predictors by constructing a Markov surrogate model that captures the temporal dependencies learned by the predictor. Our approach revolves around three main aspects: identifying the minimal history length $K$ that is predictively sufficient for the model, estimating the best-fitting $K$-order Markov transition kernel from the discretized history space, and a five-level global explanation hierarchy that can be derived from the Markov transition kernel, which we illustrate using real-world weather data (Beijing PM 2.5). We also certify using complex synthetic data with known true causal edges that KARMA (i) recovers the data causal structure as learned by the model via a controlled experiment and (ii) identifies temporal dependencies better than established attribution methods such as TimeSHAP.
The multivariate time series forecasting has attracted more and more attention because of its vital role in different fields in the real world, such as finance, traffic, and weather. In recent years, many research efforts have been proposed for forecasting multivariate time series. Although some previous work considers the interdependencies among different variables in the same timestamp, existing work overlooks the inter-connections between different variables at different time stamps. In this paper, we propose a simple yet efficient instance-wise graph-based framework to utilize the inter-de…
Time series forecasting is an important yet challenging task. Though deep learning methods have recently been developed to give superior forecasting results, it is crucial to improve the interpretability of time series models. Previous interpretation methods, including the methods for general neural networks and attention-based methods, mainly consider the interpretation in the feature dimension while ignoring the crucial temporal dimension. In this paper, we present the series saliency framework for temporal interpretation for multivariate time series forecasting, which considers the forecast…
HDT: Hierarchical Discrete Transformer for Multivariate Time Series Forecasting
College of Computing and Data Science, Nanyang Technological University (NTU)（南洋理工大学计算与数据科学学院）；Webank-NTU Joint Research Institute on Fintech, NTU（微众银行-南洋理工大学金融科技联合研究院）；Tencent AI Lab（腾讯人工智能实验室）
In this work, we propose \texttt{TimeGrad}, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion probabilistic models, a class of latent variable models closely connected to score matching and energy-based methods. Our model learns gradients by optimizing a variational bound on the data likelihood and at inference time converts white noise into a sample of the distribution of interest through a Markov chain using Langevin sampling. We demonstrate experi…
Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））；Huawei Technologies Ltd.（华为技术有限公司）
Multivariate time series forecasting has been widely used in various practical scenarios. Recently, Transformer-based models have shown significant potential in forecasting tasks due to the capture of long-range dependencies. However, recent studies in the vision and NLP fields show that the role of attention modules is not clear, which can be replaced by other token aggregation operations. This paper investigates the contributions and deficiencies of attention mechanisms on the performance of time series forecasting. Specifically, we find that (1) attention is not necessary for capturing temp…
Anomalies in univariate time series often refer to abnormal values and deviations from the temporal patterns from majority of historical observations. In multivariate time series, anomalies also refer to abnormal changes in the inter-series relationship, such as correlation, over time. Existing studies have been able to model such inter-series relationships through graph neural networks. However, most works settle on learning a static graph globally or within a context window to assist a time series forecasting task or a reconstruction task, whose objective is not tailored to explicitly detect…
GE Research（通用电气研究中心）；Upstart Power, Inc.（Upstart电力公司）
In this paper, we introduce Masked Multi-Step Multivariate Forecasting (MMMF), a novel and general self-supervised learning framework for time series forecasting with known future information. In many real-world forecasting scenarios, some future information is known, e.g., the weather information when making a short-to-mid-term electricity demand forecast, or the oil price forecasts when making an airplane departure forecast. Existing machine learning forecasting frameworks can be categorized into (1) sample-based approaches where each forecast is made independently, and (2) time series regre…
Probabilistic forecasting of high dimensional multivariate time series is a notoriously challenging task, both in terms of computational burden and distribution modeling. Most previous work either makes simple distribution assumptions or abandons modeling cross-series correlations. A promising line of work exploits scalable matrix factorization for latent-space forecasting, but is limited to linear embeddings, unable to model distributions, and not trainable end-to-end when using deep learning forecasting. We introduce a novel temporal latent auto-encoder method which enables nonlinear factori…
Cross-LKTCN: Modern Convolution Utilizing Cross-Variable Dependency for Multivariate Time Series Forecasting Dependency for Multivariate Time Series Forecasting
Beijing Institute of Technology（北京理工大学）；University of Technology Sydney（悉尼科技大学）；Tongji University（同济大学）；HeFei University of Technology（合肥工业大学）
The key problem in multivariate time series (MTS) analysis and forecasting aims to disclose the underlying couplings between variables that drive the co-movements. Considerable recent successful MTS methods are built with graph neural networks (GNNs) due to their essential capacity for relational modeling. However, previous work often used a static graph structure of time-series variables for modeling MTS failing to capture their ever-changing correlations over time. To this end, a fully-connected supra-graph connecting any two variables at any two timestamps is adaptively learned to capture t…
University of Science and Technology of China（中国科学技术大学）；Institute of Advanced Technology, University of Science and Technology of China（中国科学技术大学先进技术研究院）；Jiaxing University（嘉兴学院）
Large-scale self-supervised pre-training Transformer architecture have significantly boosted the performance for various tasks in natural language processing (NLP) and computer vision (CV). However, there is a lack of researches on processing multivariate time-series by pre-trained Transformer, and especially, current study on masking time-series for self-supervised learning is still a gap. Different from language and image processing, the information density of time-series increases the difficulty of research. The challenge goes further with the invalidity of the previous patch embedding and …
SCFormer: Structured Channel-wise Transformer with Cumulative Historical State for Multivariate Time Series Forecasting
Xinjiang Technical Institute of Physics and Chemistry, Chinese Academy of Sciences（新疆物理化学技术研究所，中国科学院）；University of Chinese Academy of Sciences（中国科学院大学）；Xinjiang Laboratory of Minority Speech and Language Information Processing（新疆少数民族语言信息处理实验室）
Ister: Linear Transformer for Efficient Multivariate Time Series Forecasting
Hong Kong University of Science and Technology (Guangzhou)（香港理工大学（广州））；ShenZhen University（深圳大学）；Shenzhen Energy Group Co., Ltd.（深圳能源集团有限公司）；South China University of Technology（华南理工大学）
Tsinghua University（清华大学）；Microsoft Research of Asia（微软亚洲研究院）
Multivariate time series forecasting has seen widely ranging applications in various domains, including finance, traffic, energy, and healthcare. To capture the sophisticated temporal patterns, plenty of research studies designed complex neural network architectures based on many variants of RNNs, GNNs, and Transformers. However, complex models are often computationally expensive and thus face a severe challenge in training and inference efficiency when applied to large-scale real-world datasets. In this paper, we introduce LightTS, a light deep learning architecture merely based on simple MLP…
ITS-Mina: A Harris Hawks Optimization-Based All-MLP Framework with Iterative Refinement and External Attention for Multivariate Time Series Forecasting
Department of Computer Science and Engineering, Shahid Beheshti University, Iran（伊朗谢赫·贝赫什提大学计算机科学与工程系）；School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Iran（伊朗基础科学研究院（IPM）计算机科学学院）
vLinear: A Powerful Linear Model for Multivariate Time Series Forecasting
State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University（人工智能通用基础理论国家重点实验室，智能科学与技术学院，北京大学）
HTMformer: Hybrid Time and Multivariate Transformer for Time Series Forecasting
Northwestern Polytechnical University（北华理工大学）；MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University（人工智能教育部重点实验室，上海交通大学AI研究院）；Ningbo Institute of Digital Twin, Eastern Institute of Technology（宁波数字孪生研究所，东部技术研究所）；Ningbo Key Laboratory of Spatial Intelligence and Digital Derivative（宁波空间智能与数字衍生关键实验室）
Deep Coupling Network For Multivariate Time Series Forecasting
School of Computer Science, Beijing Institute of Technology（北京理工大学计算机学院）；School of Electronic and Information Engineering, Tongji University（同济大学电子与信息工程学院）；School of Medical Technology, Beijing Institute of Technology（北京理工大学医学技术学院）；Faculty of Engineering and Information Technology, University of Technology Sydney（悉尼科技大学工程与信息技术学院）；School of Computer Science and Information Engineering, HeFei University of Technology（合肥工业大学计算机与信息工程学院）
VFEM: Visual Feature Empowered Multivariate Time Series Forecasting with Cross-Modal Fusion
Tsinghua Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院，清华大学）；Pengcheng Laboratory（鹏城实验室）；Ant Group（蚂蚁集团）；Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ)（广东人工智能与数字经济实验室（深圳））；University of Pennsylvania（宾夕法尼亚大学）
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Huazhong University of Science and Technology（华中科技大学）
Multivariate Time Series (MTS) forecasting plays a vital role in a wide range of applications. Recently, Spatial-Temporal Graph Neural Networks (STGNNs) have become increasingly popular MTS forecasting methods due to their state-of-the-art performance. However, recent works are becoming more sophisticated with limited performance improvements. This phenomenon motivates us to explore the critical factors of MTS forecasting and design a model that is as powerful as STGNNs, but more concise and efficient. In this paper, we identify the indistinguishability of samples in both spatial and temporal …
