Leveraging graph structures for time-series forecasting has garnered significant attention due to their effective relationship modeling between nodes and their associated time-series. However, in scenarios entities communicate in a broadcasting manner, graph models fall short of pairwise modeling. Hypergraph models address this by capturing beyond-pairwise interactions among node time-series. Nevertheless, most hypergraph models overlook the dynamics between nodes and their incident hyperedges, assuming constant node-hyperedge connections. In this paper, we introduce a novel model, Probabilistic Hypergraph Recurrent Neural Networks (PHRNN), which leverages node-hyperedge dynamics for accurate time-series forecasting. PHRNN associates each time-series with a node and models node interactions on a hypergraph, capturing beyond-pairwise interactions. Moreover, PHRNN learns a probabilistic hypergraph in which node-hyperedge relations are modeled as probabilistic distributions instead of fixed values, capturing dynamic node-hyperedge relations. PHRNN further integrates a prior knowledge KNN hypergraph as regularization when learning the probabilistic hypergraph structure. To the best of our knowledge, PHRNN is the first time-series forecasting model that incorporates hypergraph modeling and probabilistic relationship modeling. Forecasting results from extensive experiments show that PHRNN outperforms state-of-the-art graph and hypergraph baselines on real-world datasets.

Recent advances in time series research have created a significant demand for better time series visualization techniques, especially for large-scale datasets that contain millions of time series or more. In this paper, we consider a common use scenario where analysts aim to identify representative time series from a large collection. These representative time series generalize as many time series as possible and can be used for downstream tasks. Building a visualization system for this scenario involves many challenges, including visualizing, selecting, and highlighting a subset of time series from the overall dataset. Moreover, the potential for time series to be incomplete due to missing records adds an extra layer of difficulty. To address these challenges, we propose a novel visualization system, called the Locality Sensitive Hashing-based Interactive Visualization Explorer for large-scale Incomplete Time Series (LIVE-ITS). On the frontend, LIVE-ITS allows analysts to interact with the system and select representative time series in areas of interest. In the backend, LIVE-ITS not only selects an optimal subset that represents as many time series as possible, but also achieves the best possible time complexity. Experiments on both synthetic dataset and real-world datasets show that LIVE-ITS exhibits high partition accuracy and high response efficiency, further validating the effectiveness of our proposed visualization system.

Recent successes of foundation models in large language models have inspired researchers to apply similar technologies to time-series forecasting. Unlike conventional time-series forecasting models, which are trained on the training subset of the target dataset, foundation models are trained on a large collection of source datasets that do not necessarily include the target dataset, with the assumption that foundation models can capture the complex patterns between the input time-series values and the desired predictions. Although many foundation models have claimed superior prediction performance compared to conventional models, one question remains unanswered: Do foundation models for time-series forecasting, which train on many datasets other than the target dataset, perform better than conventional models that train on only (the training subset of) the target dataset? To answer this question, this paper adapts a diffusion-based foundation model and conducts extensive experiments using both small datasets and a large collection of over 100 datasets. Our results show that training on large-scale datasets does not necessarily guarantee a better performance than a conventional model that trains only on the dataset from the same domain. Hence, this paper provides insights for future foundation model research in large-scale time-series forecasting, emphasizing that the usage of target datasets should be considered in addition to training on large-scale source datasets.

Time-series and graphs have been extensively studied for their ubiquitous existence in numerous domains. Both topics have been separately explored in the field of deep learning. For time-series modeling, recurrent neural networks or convolutional neural networks model the relations between values across timesteps, while for graph modeling, graph neural networks model the inter-relations between nodes. Recent research in deep learning requires simultaneous modeling for time-series and graphs when both representations are present. For example, both types of modeling are necessary for time-series classification, regression, and anomaly detection in graphs. This article aims to provide a comprehensive summary of these models, which we call graph time-series models. To the best of our knowledge, this is the first survey article that provides a picture of related models from the perspective of deep graph time-series modeling to address a range of time-series tasks, including regression, classification, and anomaly detection. Graph time-series models are split into two categories: (a) graph recurrent/convolutional neural networks and (b) graph attention neural networks. Under each category, we further categorize models based on their properties. Additionally, we compare representative models and discuss how distinctive model characteristics are utilized with respect to various model components and data challenges. Pointers to commonly used datasets and code are included to facilitate access for further research. In the end, we discuss potential directions for future research.

Many existing deep graph models have shown that forecasting time-series values benefits from modeling the mutual relations between time-series. For example, graph neural networks can exploit the correlations between two CPU utilization time-series, facilitating more accurate predictions. However, the implied pairwise interactions between entities in the graph structure do not always reflect the actual interactions. In a cloud system, for instance, computing tasks are assigned to groups of machines, and CPU utilization time-series within the same group simultaneously interact with one another. Hence, such interactions are beyond-pairwise. In this paper, we propose a novel model called Hypergraph Recurrent Neural Networks (HGRNN) for time-series forecasting. Our model employs a hypergraph to model beyond-pairwise relations, which naturally reflect the actual interactions among entities. We also introduce a novel semi-principled hypergraph construction method to address the challenge of missing hypergraph information. Our model adopts the encoder-decoder framework where historical time-series are digested into an encoded state which is decoded to yield prediction. We further integrate a temporal component to enhance learning from temporal locality. Extensive experiments on large-scale datasets show that our model achieves better forecasting performance compared to state-of-the-art baselines.

Effective time-series forecasting methods are of significant importance to solve a broad spectrum of research problems. Deep probabilistic forecasting techniques have recently been proposed for modeling large collections of time-series. However, these techniques explicitly assume either complete independence (local model) or complete dependence (global model) between time-series in the collection. This corresponds to the two extreme cases where every time-series is disconnected from every other time-series in the collection or likewise, that every time-series is related to every other time-series resulting in a completely connected graph. In this work, we propose a deep hybrid probabilistic graph-based forecasting framework called Graph Deep Factors (GraphDF) that goes beyond these two extremes by allowing nodes and their time-series to be connected to others in an arbitrary fashion. GraphDF is a hybrid forecasting framework that consists of a relational global and relational local model. In particular, a relational global model learns complex non-linear time-series patterns globally using the structure of the graph to improve both forecasting accuracy and computational efficiency. Similarly, instead of modeling every time-series independently, a relational local model not only considers its individual time-series but also the time-series of nodes that are connected in the graph. The experiments demonstrate the effectiveness of the proposed deep hybrid graph-based forecasting model compared to the state-of-the-art methods in terms of its forecasting accuracy, runtime, and scalability. Our case study reveals that GraphDF can successfully generate cloud usage forecasts and opportunistically schedule workloads to increase cloud cluster utilization by 47.5% on average. Furthermore, we target addressing the common nature of many time-series forecasting applications where time-series are provided in a streaming version; however, most methods fail to leverage the newly incoming time-series values and result in worse performance over time. In this article, we propose an online incremental learning framework for probabilistic forecasting. The framework is theoretically proven to have lower time and space complexity. The framework can be universally applied to many other machine learning-based methods.

Traditional resource (demand or supply) forecasting models mainly focus on modeling temporal dependency. However, spatio-temporal data include complex non-linear relational and spatial dependencies. In addition, dynamic contextual information also impacts resources. Methods that consider context assume that the impact of context on resources is fixed, which is not realistic. For example, in a bicycle-sharing system, bike supply in stations is affected by the weather, and that effect changes over time. We propose a novel graph-based context integrated relational model, Context Integrated Graph Neural Network (CIGNN), which models temporal, relational, spatial, and dynamic contextual dependencies for multi-step ahead resource forecasting. We define a resource graph, where nodes represent locations with associated resource time-series, and context graphs (one for each type of context), where nodes represent locations with associated contextual time-series. Assuming that various contexts have dynamic impact on resources, our proposed CIGNN model employs a novel fusion mechanism that jointly learns from multiple contextual time-series. To the best of our knowledge, CIGNN is the first approach that integrates dynamic contextual information using graph neural networks for resource forecasting. Empirical results on two real-world datasets demonstrate that CIGNN consistently outperforms state-of-the-art approaches.

Deep probabilistic forecasting techniques have recently been proposed for modeling large collections of time-series. However, these techniques explicitly assume either complete independence (local model) or complete dependence (global model) between time-series in the collection. This corresponds to the two extreme cases where every time-series is disconnected from every other time-series in the collection or likewise, that every time-series is related to every other time-series resulting in a completely connected graph. In this work, we propose a deep hybrid probabilistic graph-based forecasting framework called Graph Deep Factors (GraphDF) that goes beyond these two extremes by allowing nodes and their time-series to be connected to others in an arbitrary fashion. GraphDF is a hybrid forecasting framework that consists of a relational global and relational local model. In particular, we propose a relational global model that learns complex non-linear time-series patterns globally using the structure of the graph to improve both forecasting accuracy and computational efficiency. Similarly, instead of modeling every time-series independently, we learn a relational local model that not only considers its individual time-series but also the time-series of nodes that are connected in the graph. The experiments demonstrate the effectiveness of the proposed deep hybrid graph-based forecasting model compared to the state-of-the-art methods in terms of its forecasting accuracy, runtime, and scalability. Our case study reveals that GraphDF can successfully generate cloud usage forecasts and opportunistically schedule workloads to increase cloud cluster utilization by 47.5% on average.