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A multiple multivariate time-series forecasting problem, where each multivariate time-series (i.e., sample) shares the same domain, timestream, and variables. When stacking the time-series together, we assemble a tridimensional tensor with the axes describing samples, timestamps, and variables. The multiple samples have equal variables recorded during the same timestamps, meaning that samples are unique but all observed in the same way. By tackling the problem altogether, we leverage inner and outer variables besides intra-and inter-temporal relationships to improve forecasting.
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Time-series forecasting is one of the most active research topics in artificial intelligence. A still open gap in that literature is that statistical and ensemble learning approaches systematically present lower predictive performance than deep learning methods. They generally disregard the data sequence aspect entangled with multivariate data repr...
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... of the pandemic in each country, one can describe the problem in terms of multiple variables, like the number of confirmed cases, recovered people, and deaths. However, when looking at all countries at once, the problem yields an additional data dimension, and each country becomes a multivariate sample of a broader problem, such as depicted in Fig. 1. In linguistic terms, we refer to such a problem as multiple multivariate time-series ...
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... the past of other patients. Nevertheless, we must be careful about drawing any understanding about these results, as the reason each patient is in the ICU is different, and while some explanations might be suited for a small set of patients, it tends not to generalize to a significant number of patients. When analyzing the Evolution Weights in Fig. 10 aided by a physician, we can say that there is a relationship between the amount of urine excreted by a patient and the arterial blood pressure, and also that there is a relation between the systolic and diastolic blood pressure. However, even aided by the Evolution Weights, we cannot further describe these relations once there are ...
Citations
... For example, the MTGNN model [49] uses a graph structure to represent series when initial inter-series relationships are unknown, calculates pairwise correlations and uses a graph convolutional network for message propagation. The ReGENN network [50] identifies potential inter-series relationships in the spectral domain. Literature [51] highlights traffic flow prediction, uncovering long and short-term correlation patterns in multivariate time series and proposing a learning paradigm that combines static and dynamic graphs. ...
Multivariate time series classification (MVTSC) has significant potential for Internet of Things applications. Recently, deep learning (DL) and graph neural network (GNN) methods have been applied to MVTSC tasks. Unfortunately, DL-based methods ignore explicit inter-series correlation modeling. Most existing GNN-based methods treat MVTS data as a static graph spanning the entire temporal trajectory, which inadequately captures changes in inter-series local correlations. To address this problem, we propose the spatial-temporal attention dynamic GNN (STADGNN), which explicitly models dynamic inter-series correlations by constructing the MVTS data into a dynamic graph structure at a finer granularity. It combines discrete Fourier transform (DFT) and discrete wavelet transform (DWT), which extract the global and local features of MVTS data in an end-to-end framework. In dynamic graph learning, spatial-temporal attention mechanisms are employed to simultaneously capture changes in inter-series local correlations and intra-series temporal dependencies without relying on predefined priors. Experimental results on 25 UEA datasets indicate that the STADGNN outperforms existing DL-based and GNN-based baseline models in MVTSC tasks.
... Grazing land Grazing land is land used for livestock grazing and browsing which is covered with grasses or shrubs forecasts of the response variables Wei, 2019). Time series can be regarded as univariate or multivariate describing, respectively, single and multiple endogenous variables varying over time (Spadon et al., 2022). The term "univariate time series" refers to a time series that consists of single observations recorded sequentially over equal time (Sharma & Ghosh, 2016), whereas multivariate time series models are designed to capture the dynamics of multiple time series simultaneously and leverage dependencies across these series for more reliable predictions (Sagar et al., 2021). ...
This study gives empirical evidence on the drivers of land use change by conducting a qualitative assessment and then using time series data to quantify the relationship between land use land cover change and factors that cause the change. Vector autoregressive models with exogenous variables were used to analyze the time series data. The findings revealed demographic and environmental factors were the primary causes of land use and land cover change. Population growth was found among the key drivers for losses of the natural vegetation on the one hand and rehabilitation of bare lands and grazing lands on the other hand. Despite its pressure on the natural vegetation, the increase in population contributes to a productive labor force for improving land management through rehabilitating degraded grazing lands, implementing soil and water conservation measures, and planting trees on degraded lands. This implies that population growth can be an opportunity or a threat for sustainable natural resources management, depending on how the available labor force is used. Climatic factors like maximum temperature and precipitation were also important causes of change in land use land cover. The study has important contributions to improving land use practices through designing appropriate land resources management policies.
... In this sense, by adjusting vessel routes (see Fig. 2B) to avoid these critical areas (see Fig. 2A), the smartWhales initiative aims to contribute to a significant reduction in the likelihood of harmful vessel-whale encounters mainly when vessel paths navigate across collision hotspot areas (see Fig. 3). As vessels navigate, their historical data provide us with insights into their likely trajectory, along with observations on collective vessel movement patterns (Song et al., 2024;Alam et al., 2024); the same can be observed among people commuting (Spadon et al., 2019b;Lei et al., 2022;Alves et al., 2021), patient trajectories in hospitals (Rodrigues-Jr et al., 2021), and disease-spreading phenomena (Spadon et al., 2022b). ...
... In [20], a new neural network architecture for time series forecasting called Recurrent Graph Evolution Neural Network (REGENN) is presented, combining graph evolution and deep recurrent learning. Specifically, REGENN consists, in parallel, of a linear component with a feed-forward layer and a nonlinear component with an autoencoder. ...
... Finally, the third, also from the medical field, corresponds to the 2012 PhysioNet Computing in Cardiology Challenge [22]. As can be intuitively observed in Figures 5,7, and 9 of Ref. [20] (exact values are not provided), REGENN achieves better results than other state-of-the-art techniques. ...
... The features are the number of recovered patients, the number of infected patients, and the number of deaths. • Brazilian Weather: Dataset generated by collecting data from 253 sensors over 1095 days [20]. It consists of four variables: minimum temperature, maximum temperature, solar radiation, and rainfall. ...
Time series forecasting is undoubtedly a key area in machine learning due to the numerous fields where it is crucial to estimate future data points of sequences based on a set of previously observed values. Deep learning has been successfully applied to this area. On the other hand, growing concerns about the steady increase in the amount of resources required by deep learning-based tools have made Green AI gain traction as a move towards making machine learning more sustainable. In this paper, we present a deep learning-based time series forecasting methodology called GreeNNTSF, which aims to reduce the size of the resulting model, thereby diminishing the associated computational and energetic costs without giving up adequate forecasting performance. The methodology, based on the ODF2NNA algorithm, produces models that outperform state-of-the-art techniques not only in terms of prediction accuracy but also in terms of computational costs and memory footprint. To prove this claim, after presenting the main state-of-the-art methods that utilize deep learning for time series forecasting and introducing our methodology we test GreeNNTSF on a selection of real-world forecasting problems that are commonly used as benchmarks, such as SARS-CoV-2 and PhysioNet (medicine), Brazilian Weather (climate), WTI and Electricity (economics), and Traffic (smart cities). The results of each experiment conducted objectively demonstrate, rigorously following the experimentation presented in the original papers that addressed these problems, that our method is more competitive than other state-of-the-art approaches, producing more accurate and efficient models.
... Structure learning has recently gained much attention, such as (Li et al., 2018;Wu et al., 2020;Zhao et al., 2020;Cao et al., 2020;Shang et al., 2021;Deng & Hooi, 2021;Marcinkevics & Vogt, 2021;Geffner et al., 2022;Tank et al., 2022;Spadon et al., 2022;Fu & He, 2022;Zhou et al., 2022;Gong et al., 2023;Fu et al., 2023;Li et al., 2023b;Fu et al., 2024). Among others, causal graphs as a directed acrylic graph structure provide more explicit and interpretable correlations between variables, thus enabling a better understanding of the underlying physical mechanisms and dynamic systems for time series (Kofinas et al., 2023;. ...
... Noteworthy applications of graph learning techniques in time series forecasting span in climate domains, including but not limited to heatwave prediction (Li et al., 2023a), and frost forecasts (Lira et al., 2022). To improve the the time series analysis effectiveness, there has been a growing focus on structured learning in the context of tabular time series data (Li et al., 2018;Wu et al., 2020;Zhao et al., 2020;Cao et al., 2020;Shang et al., 2021;Deng & Hooi, 2021;Marcinkevics & Vogt, 2021;Geffner et al., 2022;Tank et al., 2022;Spadon et al., 2022;Gong et al., 2023), which learned structures contribute to various time series analysis tasks like forecasting, anomaly detection, imputation, etc. As a directed and interpretable structure, causal graphs attract much research attention in this research topic (Guo et al., 2021). ...
Understanding the causal interaction of time series variables can contribute to time series data analysis for many real-world applications, such as climate forecasting and extreme weather alerts. However, causal relationships are difficult to be fully observed in real-world complex settings, such as spatial-temporal data from deployed sensor networks. Therefore, to capture fine-grained causal relations among spatial-temporal variables for further a more accurate and reliable time series analysis, we first design a conceptual fine-grained causal model named TBN Granger Causality, which adds time-respecting Bayesian Networks to the previous time-lagged Neural Granger Causality to offset the instantaneous effects. Second, we propose an end-to-end deep generative model called TacSas, which discovers TBN Granger Causality in a generative manner to help forecast time series data and detect possible anomalies during the forecast. For evaluations, besides the causality discovery benchmark Lorenz-96, we also test TacSas on climate benchmark ERA5 for climate forecasting and the extreme weather benchmark of NOAA for extreme weather alerts.
... Next, the titles and abstracts were scanned to ensure that the chosen articles were relevant to the main goal of this research. By this criterion, we excluded studies such as the use of non-OULAD for predictions (e.g., the use of the International University of La Rioja educational dataset to predict learner performance by [10] and non-education contexts [22]. This reduced the number of shortlisted articles to 29. ...
Higher education has experienced an unparalleled digital transformation, driven by the widespread adoption of online learning with massive users, which has risen to an explosive growth in the generation and analysis of student-related data. Within this transformation, predictive modeling has emerged as a useful tool for predicting critical indicators in the learning process, encompassing students’ academic performance, class retention, and dropout rates. With this backdrop, this study aims to conduct a systematic review of recent publications focused on predictive modeling, with a specific emphasis on the Open University Learning Analytics Datasets (OULAD). Following the PRISMA process, we identified 17 research articles published from 2017 to 2024, concentrating on OULAD in higher education. For our analysis, we categorized the purpose of predictive modeling into three types: (a) predicting students' performance, (b) identifying at-risk students, and (c) predicting student engagement. The central focus lies on the identification of algorithms predominantly employed in these studies, including machine learning, deep learning, and statistical models. By investigating the methodologies and algorithms employed, this review informs researchers in learning analytics and educational data mining of the potential opportunities and challenges associated with predictive modeling using OULAD in higher education.
... Up until now, types of technologies have been developed to realize the predictions of IvTS. According to our literature review, current IvTS analysis methods can be mainly divided into three categories, i.e., regression based forecasting method [12][13][14][15] , data decomposition based forecasting method [6,7] , and artificial intelligence based forecasting method [16][17][18][19][20] . Studies on forecasting methods and applications of IvTS have been widely considered by academia and industry. ...
Long-memory process has been widely studied in classical financial time series analysis, which has merely been reported in the field of interval-valued financial time series. The aim of this paper is to explore long-memory process in the prediction of interval-valued time series (IvTS). To model the long-memory process, two novel interval-valued time series prediction models named as interval-valued vector autoregressive fractionally integrated moving average (IV-VARFIMA) and ARFIMAX-FIGARCH were established. In the developed long-memory pattern, both of the short term and long-term influences contained in IvTS can be included. As an application of the proposed models, interval-valued form of WTI crude oil futures price series is predicted. Compared to current IvTS prediction models, IV-VARFIMA and ARFIMAX-FIGARCH can provide better in-sample and out-of-sample forecasts.
... Time series can be regarded as univariate or multivariate describing, respectively, single and multiple endogenous variables varying over time (Spadon et al., 2022). The term "univariate time series" refers to a time series that consists of single observations recorded sequentially over equal time (S. ...
This study gives empirical evidence on the drivers of land use land cover change by conducting qualitative assessment first, and then making use of time series data for quantifying the relationship between land use land cover change and factors that cause the change. Analyzing the drivers of land use land cover change employing a mixed method approach gives good ground for the selection of exogenous variables as well as justification of the results of the quantitative analysis. Temporal changes of land use land cover in a given time are interdependent with changes in the previous years which needs time series data analysis. Vector autoregressive models with exogenous variables were used to analyze the time series data. The findings revealed demographic and environmental factors were the main causes of land use and land cover change. Population growth was found among the key drivers for losses of the natural vegetation on the one hand and rehabilitation of bare lands and grazing lands on the other hand, through contributing productive labor force for rehabilitating gullies, construction of soil and water conservation structures, and plantations of trees on degraded lands. This implies population growth can be an opportunity or a threat for sustainable natural resources management depending on how the available labor force is used. Climatic factors like maximum temperature and precipitation were also important causes of change in land use land cover. The study has important contributions to improving land use practices through designing appropriate land resources management policies.
... Prediction speed, accuracy, over-fitting, robustness and process memory are common evaluation indexes of indoor environment prediction [53]. Prediction model LSTM, BPNN, ARIMA and SVM were compared in terms of this evaluation. ...
... Fully mining and accurately modeling the potential spatio-temporal features in multivariate time series can be used to explore the future state of the system and provide a theoretical basis for the regulation and decision-making of complex systems [2,3]. For example, the study of individual indicators of air pollutants can help the state in the macro-regulation of pollutant emissions [4]. The analysis of water quality guarantees the quality of drinking water and the health of the local residents [5]. ...
In recent years, multivariate time series prediction has attracted extensive research interests. However, the dynamic changes of the spatial topology and the temporal evolution of multivariate variables bring great challenges to the spatio-temporal time series prediction. In this paper, a novel Dirichlet graph convolution module is introduced to automatically learn the spatio-temporal representation, and we combine graph attention (GAT) and neural differential equation (NDE) based on nonlinear state transition to model spatio-temporal state evolution of nonlinear systems. Specifically, the spatial topology is revealed by the cosine similarity of node embeddings. The use of multi-layer Dirichlet graph convolution aims to enhance the representation ability of the model while suppressing the phenomenon of over-smoothing or over-separation. The GCN and LSTM-based network is used as the nonlinear operator to model the evolution law of the dynamic system, and the GAT updates the strength of the connection. In addition, the Euler trapezoidal integral method is used to model the temporal dynamics and makes medium and long-term prediction in latent space from the perspective of nonlinear state transition. The proposed model can adaptively mine spatial correlations and discover spatio-temporal dynamic evolution patterns through the coupled NDE, which makes the modeling process more interpretable. Experiment results demonstrate the effectiveness of spatio-temporal dynamic discovery on predictive performance.