The forecasting of multi-variate time processes through graph-based techniques has recently been addressed under the graph signal processing framework. However, problems in the representation and the processing arise when each time series carries a vector of quantities rather than a scalar one. To tackle this issue, we devise a new framework and propose new methodologies based on the graph vector autoregressive model. More explicitly, we leverage product graphs to model the high-dimensional graph data and develop multi-dimensional graph-based vector autoregressive models to forecast future trends with a number of parameters that is independent of the number of time series and a linear computational complexity. Numerical results demonstrating the prediction of moving point clouds corroborate our findings.
Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product graphs to combine this multidimensional information, at the expense of creating a larger graph. In this paper, we show the limitations of such approaches, and propose extensions to tackle them. Then, we propose a recursive multiple-input multiple-output graph filter which encompasses many already existing models in the literature while being more flexible. N…
Multivariate time series (MTS) forecasting is an essential problem in many fields. Accurate forecasting results can effectively help decision-making. To date, many MTS forecasting methods have been proposed and widely applied. However, these methods assume that the predicted value of a single variable is affected by all other variables, which ignores the causal relationship among variables. To address the above issue, we propose a novel end-to-end deep learning model, termed graph neural network with Neural Granger Causality (CauGNN) in this paper. To characterize the causal information among …
Traffic speed forecasting is one of the core problems in transportation systems. For a more accurate prediction, recent studies started using not only the temporal speed patterns but also the spatial information on the road network through the graph convolutional networks. Even though the road network is highly complex due to its non-Euclidean and directional characteristics, previous approaches mainly focused on modeling the spatial dependencies using the distance only. In this paper, we identify two essential spatial dependencies in traffic forecasting in addition to distance, direction and …
Prediction of movements is essential for successful cooperation with intelligent systems. We propose a model that integrates organized spatial information as given through the moving body's skeletal structure. This inherent structure is exploited in our model through application of Graph Convolutions and we demonstrate how this allows leveraging the structured spatial information into competitive predictions that are based on a lightweight model that requires a comparatively small number of parameters.
University of Washington（华盛顿大学）；Beihang University（北京航空航天大学）
Traffic forecasting is a classical task for traffic management and it plays an important role in intelligent transportation systems. However, since traffic data are mostly collected by traffic sensors or probe vehicles, sensor failures and the lack of probe vehicles will inevitably result in missing values in the collected raw data for some specific links in the traffic network. Although missing values can be imputed, existing data imputation methods normally need long-term historical traffic state data. As for short-term traffic forecasting, especially under edge computing and online predicti…
Boğaziçi University（博阿齐奇大学）；AWS AI Labs（AWS人工智能实验室）
Intermittent demand, where demand occurrences appear sporadically in time, is a common and challenging problem in forecasting. In this paper, we first make the connections between renewal processes, and a collection of current models used for intermittent demand forecasting. We then develop a set of models that benefit from recurrent neural networks to parameterize conditional interdemand time and size distributions, building on the latest paradigm in "deep" temporal point processes. We present favorable empirical findings on discrete and continuous time intermittent demand data, validating th…
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 forecast…
In recent years, marked temporal point processes (MTPPs) have emerged as a powerful modeling machinery to characterize asynchronous events in a wide variety of applications. MTPPs have demonstrated significant potential in predicting event-timings, especially for events arriving in near future. However, due to current design choices, MTPPs often show poor predictive performance at forecasting event arrivals in distant future. To ameliorate this limitation, in this paper, we design DualTPP which is specifically well-suited to long horizon event forecasting. DualTPP has two components. The first…
Traffic forecasting influences various intelligent transportation system (ITS) services and is of great significance for user experience as well as urban traffic control. It is challenging due to the fact that the road network contains complex and time-varying spatial-temporal dependencies. Recently, deep learning based methods have achieved promising results by adopting graph convolutional network (GCN) to extract the spatial correlations and recurrent neural network (RNN) to capture the temporal dependencies. However, the existing methods often construct the graph only based on road network …
Central South University（中南大学）；Hisense TransTech Co., Ltd.（海信网络科技股份有限公司）；Zhejiang University（浙江大学）
Traffic forecasting is a fundamental and challenging task in the field of intelligent transportation. Accurate forecasting not only depends on the historical traffic flow information but also needs to consider the influence of a variety of external factors, such as weather conditions and surrounding POI distribution. Recently, spatiotemporal models integrating graph convolutional networks and recurrent neural networks have become traffic forecasting research hotspots and have made significant progress. However, few works integrate external factors. Therefore, based on the assumption that intro…
University of Amsterdam（阿姆斯特丹大学）；Amazon（亚马逊）；Zalando（Zalando（扎兰多））
This paper introduces a new approach for Multivariate Time Series forecasting that jointly infers and leverages relations among time series. Its modularity allows it to be integrated with current univariate methods. Our approach allows to trade-off accuracy and computational efficiency gradually via offering on one extreme inference of a potentially fully-connected graph or on another extreme a bipartite graph. In the potentially fully-connected case we consider all pair-wise interactions among time-series which yields the best forecasting accuracy. Conversely, the bipartite case leverages the…
We study epidemic forecasting on real-world health data by a graph-structured recurrent neural network (GSRNN). We achieve state-of-the-art forecasting accuracy on the benchmark CDC dataset. To improve model efficiency, we sparsify the network weights via transformed-$\ell_1$ penalty and maintain prediction accuracy at the same level with 70% of the network weights being zero.
Accurate forecasting of multivariate time series is an extensively studied subject in finance, transportation, and computer science. Fully mining the correlation and causation between the variables in a multivariate time series exhibits noticeable results in improving the performance of a time series model. Recently, some models have explored the dependencies between variables through end-to-end graph structure learning without the need for predefined graphs. However, current models do not incorporate the trade-off between efficiency and flexibility and lack the guidance of domain knowledge in…
We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows the use of general gradient optimization algorithms for training and incurs only a small computational overhead on training and prediction. The model finds its applications in forecasting in non-stationary time series with either gradually varying volatility, presence of change points, or a combination thereof. We evaluate the model on synthetic and real-world…
Geometric deep learning has gained tremendous attention in both academia and industry due to its inherent capability of representing arbitrary structures. Due to exponential increase in interest towards renewable sources of energy, especially wind energy, accurate wind speed forecasting has become very important. . In this paper, we propose a novel deep learning architecture, Multi Scale Graph Wavenet for wind speed forecasting. It is based on a graph convolutional neural network and captures both spatial and temporal relationships in multivariate time series weather data for wind speed foreca…
SAMSGL: Series-Aligned Multi-Scale Graph Learning for Spatio-Temporal Forecasting
East China University of Science and Technology（华东理工大学）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）；Humboldt University of Berlin（柏林洪堡大学）
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…
Forecasting of multivariate time-series is an important problem that has applications in traffic management, cellular network configuration, and quantitative finance. A special case of the problem arises when there is a graph available that captures the relationships between the time-series. In this paper we propose a novel learning architecture that achieves performance competitive with or better than the best existing algorithms, without requiring knowledge of the graph. The key element of our proposed architecture is the learnable fully connected hard graph gating mechanism that enables the…
Beijing University of Posts and Telecommunications（北京邮电大学）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Institute for Interdisciplinary Information Sciences (IIIS), Tsinghua University（清华大学交叉信息研究院）
Traffic forecasting is crucial for public safety and resource optimization, yet is very challenging due to three aspects: i) current existing works mostly exploit intricate temporal patterns (e.g., the short-term thunderstorm and long-term daily trends) within a single method, which fail to accurately capture spatio-temporal dependencies under different schemas; ii) the under-exploration of the graph positional encoding limit the extraction of spatial information in the commonly used full graph attention network; iii) the quadratic complexity of the full graph attention introduces heavy comput…
Beijing University of Posts and Telecommunications（北京邮电大学）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Tsinghua University（清华大学）；Auburn University（奥本大学）
Traffic forecasting is important in intelligent transportation systems of webs and beneficial to traffic safety, yet is very challenging because of the complex and dynamic spatio-temporal dependencies in real-world traffic systems. Prior methods use the pre-defined or learnable static graph to extract spatial correlations. However, the static graph-based methods fail to mine the evolution of the traffic network. Researchers subsequently generate the dynamic graph for each time slice to reflect the changes of spatial correlations, but they follow the paradigm of independently modeling spatio-te…
As an important part of intelligent transportation systems, traffic forecasting has attracted tremendous attention from academia and industry. Despite a lot of methods being proposed for traffic forecasting, it is still difficult to model complex spatial-temporal dependency. Temporal dependency includes short-term dependency and long-term dependency, and the latter is often overlooked. Spatial dependency can be divided into two parts: distance-based spatial dependency and hidden spatial dependency. To model complex spatial-temporal dependency, we propose a novel framework for traffic forecasti…
Monash University（莫纳什大学）；La Trobe University（乐卓博大学）；Shanghai Jiao Tong University（上海交通大学）；East China Normal University（华东师范大学）；Griffith University（格里菲斯大学）
Multivariate time series forecasting has long received significant attention in real-world applications, such as energy consumption and traffic prediction. While recent methods demonstrate good forecasting abilities, they have three fundamental limitations. (i) Discrete neural architectures: Interlacing individually parameterized spatial and temporal blocks to encode rich underlying patterns leads to discontinuous latent state trajectories and higher forecasting numerical errors. (ii) High complexity: Discrete approaches complicate models with dedicated designs and redundant parameters, leadin…
University of Washington（华盛顿大学）；INRIX, Inc.（因瑞克斯公司）
Traffic forecasting is a particularly challenging application of spatiotemporal forecasting, due to the time-varying traffic patterns and the complicated spatial dependencies on road networks. To address this challenge, we learn the traffic network as a graph and propose a novel deep learning framework, Traffic Graph Convolutional Long Short-Term Memory Neural Network (TGC-LSTM), to learn the interactions between roadways in the traffic network and forecast the network-wide traffic state. We define the traffic graph convolution based on the physical network topology. The relationship between t…
Amazon Web Services AI Labs（亚马逊云科技人工智能实验室）；Boğaziçi University（博阿齐奇大学）
Intermittency is a common and challenging problem in demand forecasting. We introduce a new, unified framework for building intermittent demand forecasting models, which incorporates and allows to generalize existing methods in several directions. Our framework is based on extensions of well-established model-based methods to discrete-time renewal processes, which can parsimoniously account for patterns such as aging, clustering and quasi-periodicity in demand arrivals. The connection to discrete-time renewal processes allows not only for a principled extension of Croston-type models, but also…
Multivariate de Bruijn Graphs: A Symbolic Graph Framework for Time Series Forecasting
Department of Computer Science, Indiana University Bloomington, IN, USA（印第安纳大学布卢明顿分校计算机科学系）；College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar（哈马德·本·卡西姆大学科学与工程学院）；Department of Computer Science, University of Illinois Springfield, IL, USA（伊利诺伊大学斯普林菲尔德分校计算机科学系）
Ant Group（蚂蚁集团）；AI School, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）
Multivariate time-series forecasting is a critical task for many applications, and graph time-series network is widely studied due to its capability to capture the spatial-temporal correlation simultaneously. However, most existing works focus more on learning with the explicit prior graph structure, while ignoring potential information from the implicit graph structure, yielding incomplete structure modeling. Some recent works attempt to learn the intrinsic or implicit graph structure directly while lacking a way to combine explicit prior structure with implicit structure together. In this pa…
FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective
Beijing Institute of Technology（北京理工大学）；Tongji University（同济大学）；University of Oxford（牛津大学）；University of Macau（澳门大学）；HeFei University of Technology（合肥工业大学）；Macquarie University（麦考瑞大学）
Beijing University of Posts and Telecommunications（北京邮电大学）；Didi Research Institute, Didi Chuxing（滴滴出行滴滴研究院）
Traffic forecasting is one canonical example of spatial-temporal learning task in Intelligent Traffic System. Existing approaches capture spatial dependency with a pre-determined matrix in graph convolution neural operators. However, the explicit graph structure losses some hidden representations of relationships among nodes. Furthermore, traditional graph convolution neural operators cannot aggregate long-range nodes on the graph. To overcome these limits, we propose a novel network, Spatial-Temporal Adaptive graph convolution with Attention Network (STAAN) for traffic forecasting. Firstly, w…
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）
In traffic forecasting, graph convolutional networks (GCNs), which model traffic flows as spatio-temporal graphs, have achieved remarkable performance. However, existing GCN-based methods heuristically define the graph structure as the physical topology of the road network, ignoring potential dependence of the graph structure over traffic data. And the defined graph structure is deterministic, which lacks investigation of uncertainty. In this paper, we propose a Bayesian Spatio-Temporal Graph Convolutional Network (BSTGCN) for traffic prediction. The graph structure in our network is learned f…
Institute of Informatics, LMU Munich（慕尼黑大学信息学研究所）；Corporate Technology, Siemens AG（西门子股份公司企业技术部）；Technical University of Munich（慕尼黑工业大学）
There has been an increasing interest in inferring future links on temporal knowledge graphs (KG). While links on temporal KGs vary continuously over time, the existing approaches model the temporal KGs in discrete state spaces. To this end, we propose a novel continuum model by extending the idea of neural ordinary differential equations (ODEs) to multi-relational graph convolutional networks. The proposed model preserves the continuous nature of dynamic multi-relational graph data and encodes both temporal and structural information into continuous-time dynamic embeddings. In addition, a nov…
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…
University of Verona（维罗纳大学）；Humatics Srl（Humatics有限公司）
The fashion industry is one of the most active and competitive markets in the world, manufacturing millions of products and reaching large audiences every year. A plethora of business processes are involved in this large-scale industry, but due to the generally short life-cycle of clothing items, supply-chain management and retailing strategies are crucial for good market performance. Correctly understanding the wants and needs of clients, managing logistic issues and marketing the correct products are high-level problems with a lot of uncertainty associated to them given the number of influen…
Short-term demand forecasting models commonly combine convolutional and recurrent layers to extract complex spatiotemporal patterns in data. Long-term histories are also used to consider periodicity and seasonality patterns as time series data. In this study, we propose an efficient architecture, Temporal-Guided Network (TGNet), which utilizes graph networks and temporal-guided embedding. Graph networks extract invariant features to permutations of adjacent regions instead of convolutional layers. Temporal-guided embedding explicitly learns temporal contexts from training data and is substitut…
The University of Tokyo（东京大学）；Toyota Motor Corporation（丰田汽车公司）
Traffic forecasting as a canonical task of multivariate time series forecasting has been a significant research topic in AI community. To address the spatio-temporal heterogeneity and non-stationarity implied in the traffic stream, in this study, we propose Spatio-Temporal Meta-Graph Learning as a novel Graph Structure Learning mechanism on spatio-temporal data. Specifically, we implement this idea into Meta-Graph Convolutional Recurrent Network (MegaCRN) by plugging the Meta-Graph Learner powered by a Meta-Node Bank into GCRN encoder-decoder. We conduct a comprehensive evaluation on two bench…
Traffic forecasting is one of the most popular spatio-temporal tasks in the field of machine learning. A prevalent approach in the field is to combine graph convolutional networks and recurrent neural networks for the spatio-temporal processing. There has been fierce competition and many novel methods have been proposed. In this paper, we present the method of spatio-temporal graph neural controlled differential equation (STG-NCDE). Neural controlled differential equations (NCDEs) are a breakthrough concept for processing sequential data. We extend the concept and design two NCDEs: one for the…
Siemens AG（西门子股份公司）；Ludwig Maximilian University of Munich（慕尼黑大学）
Conventional static knowledge graphs model entities in relational data as nodes, connected by edges of specific relation types. However, information and knowledge evolve continuously, and temporal dynamics emerge, which are expected to influence future situations. In temporal knowledge graphs, time information is integrated into the graph by equipping each edge with a timestamp or a time range. Embedding-based methods have been introduced for link prediction on temporal knowledge graphs, but they mostly lack explainability and comprehensible reasoning chains. Particularly, they are usually not…
Sun Yat-sen University（中山大学）；Microsoft Research（微软研究院）
Stock trend forecasting, which forecasts stock prices' future trends, plays an essential role in investment. The stocks in a market can share information so that their stock prices are highly correlated. Several methods were recently proposed to mine the shared information through stock concepts (e.g., technology, Internet Retail) extracted from the Web to improve the forecasting results. However, previous work assumes the connections between stocks and concepts are stationary, and neglects the dynamic relevance between stocks and concepts, limiting the forecasting results. Moreover, existing …
