Multivariate time series modeling and prediction problems are abundant in many machine learning application domains. Accurate interpretation of such prediction outcomes from a machine learning model that explicitly captures temporal correlations can significantly benefit the domain experts. In this context, temporal attention has been successfully applied to isolate the important time steps for the input time series. However, in multivariate time series problems, spatial interpretation is also critical to understand the contributions of different variables on the model outputs. We propose a novel deep learning architecture, called spatiotemporal attention mechanism (STAM) for simultaneous learning of the most important time steps and variables. STAM is a causal (i.e., only depends on past inputs and does not use future inputs) and scalable (i.e., scales well with an increase in the number of variables) approach that is comparable to the state-of-the-art models in terms of computational tractability. We demonstrate our models' performance on two popular public datasets and a domain-specific dataset. When compared with the baseline models, the results show that STAM maintains state-of-the-art prediction accuracy while offering the benefit of accurate spatiotemporal interpretability. The learned attention weights are validated from a domain knowledge perspective for these real-world datasets.
University of Virginia（弗吉尼亚大学）；IBM Research（IBM研究院）；UT Austin（德克萨斯大学奥斯汀分校）
Multivariate time series forecasting focuses on predicting future values based on historical context. State-of-the-art sequence-to-sequence models rely on neural attention between timesteps, which allows for temporal learning but fails to consider distinct spatial relationships between variables. In contrast, methods based on graph neural networks explicitly model variable relationships. However, these methods often rely on predefined graphs that cannot change over time and perform separate spatial and temporal updates without establishing direct connections between each variable at every time…
Deep learning has become a one-size-fits-all solution for technical and business domains thanks to its flexibility and adaptability. It is implemented using opaque models, which unfortunately undermines the outcome trustworthiness. In order to have a better understanding of the behavior of a system, particularly one driven by time series, a look inside a deep learning model so-called posthoc eXplainable Artificial Intelligence (XAI) approaches, is important. There are two major types of XAI for time series data, namely model-agnostic and model-specific. Model-specific approach is considered in…
There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recoverin…
This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects in the conditional variance, as they are usually present in spatial econometric applications. Furthermore, spatial and temporal cross-variable effects are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and diffe…
Optimal decision-making in social settings is often based on forecasts from time series (TS) data. Recently, several approaches using deep neural networks (DNNs) such as recurrent neural networks (RNNs) have been introduced for TS forecasting and have shown promising results. However, the applicability of these approaches is being questioned for TS settings where there is a lack of quality training data and where the TS to forecast exhibit complex behaviors. Examples of such settings include financial TS forecasting, where producing accurate and consistent long-term forecasts is notoriously di…
Technion - Israel Institute of Technology（以色列理工学院）；Duke University（杜克大学）
Multivariate time-series have become abundant in recent years, as many data-acquisition systems record information through multiple sensors simultaneously. In this paper, we assume the variables pertain to some geometry and present an operator-based approach for spatiotemporal analysis. Our approach combines three components that are often considered separately: (i) manifold learning for building operators representing the geometry of the variables, (ii) Riemannian geometry of symmetric positive-definite matrices for multiscale composition of operators corresponding to different time samples, …
The dependencies of the lagged (Pearson) correlation function on the coefficients of multivariate autoregressive models are interpreted in the framework of time series graphs. Time series graphs are related to the concept of Granger causality and encode the conditional independence structure of a multivariate process. The authors show that the complex dependencies of the Pearson correlation coefficient complicate an interpretation and propose a novel partial correlation measure with a straightforward graph-theoretical interpretation. The novel measure has the additional advantage that its samp…
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Criteo AI Lab（Criteo人工智能实验室）
A recent line of work in the machine learning community addresses the problem of predicting high-dimensional spatiotemporal phenomena by leveraging specific tools from the differential equations theory. Following this direction, we propose in this article a novel and general paradigm for this task based on a resolution method for partial differential equations: the separation of variables. This inspiration allows us to introduce a dynamical interpretation of spatiotemporal disentanglement. It induces a principled model based on learning disentangled spatial and temporal representations of a ph…
A Critical Audit of Spatiotemporal Forecasting Benchmark Datasets and Models
Imperial College London（帝国理工学院）；Ruhr University Bochum（鲁尔大学波鸿分校）；Queen Mary University of London（伦敦玛丽女王大学）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）
Geographic patterns in stroke mortality have been studied as far back as the 1960s, when a region of the southeastern United States became known as the "stroke belt" due to its unusually high rates of stroke mortality. While stroke mortality rates are known to increase exponentially with age, an investigation of spatiotemporal trends by age group at the county-level is daunting due to the preponderance of small population sizes and/or few stroke events by age group. Here, we harness the power of a complex, nonseparable multivariate space-time model which borrows strength across space, time, an…
Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regress…
University College London（伦敦大学学院）；University of Oxford（牛津大学）；The Alan Turing Institute（艾伦·图灵研究所）
As a relatively new field, network neuroscience has tended to focus on aggregate behaviours of the brain averaged over many successive experiments or over long recordings in order to construct robust brain models. These models are limited in their ability to explain dynamic state changes in the brain which occurs spontaneously as a result of normal brain function. Hidden Markov Models (HMMs) trained on neuroimaging time series data have since arisen as a method to produce dynamical models that are easy to train but can be difficult to fully parametrise or analyse. We propose an interpretation …
UQGNN: Uncertainty Quantification of Graph Neural Networks for Multivariate Spatiotemporal Prediction
Florida State University（佛罗里达州立大学）；Massachusetts Institute of Technology（麻省理工学院）；University of Alabama, Tuscaloosa（阿拉巴马大学塔斯卡洛osa分校）；University of Florida（佛罗里达大学）
Periodic monitoring of groundwater quality at industrial and commercial sites generates large volumes of spatiotemporal concentration data. Data modelling is typically restricted to either the analysis of monotonic trends in individual wells, or independent fitting of spatial concentration distributions (e.g. Kriging) to separate monitoring time periods. Neither of these techniques satisfactorily elucidate the interaction between spatial and temporal components of the data. Potential negative consequences include an incomplete understanding of groundwater plume dynamics, which can lead to the …
With increasing computing capabilities of modern supercomputers, the size of the data generated from the scientific simulations is growing rapidly. As a result, application scientists need effective data summarization techniques that can reduce large-scale multivariate spatiotemporal data sets while preserving the important data properties so that the reduced data can answer domain-specific queries involving multiple variables with sufficient accuracy. While analyzing complex scientific events, domain experts often analyze and visualize two or more variables together to obtain a better underst…
A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the framework, including the negative binomial, gamma and Gaussian distributions. We develop an iterative algorithm to obtain unconditional means, variances and auto-/cross-covariances for models with higher order lags. Analytical solutions are given for the univariate model with lag one and multivariate models with linear mean-variance relationship. A special case of t…
The literature on Gaussian graphical models (GGMs) contains two equally rich and equally significant domains of research efforts and interests. The first research domain relates to the problem of graph determination. That is, the underlying graph is unknown and needs to be inferred from the data. The second research domain dominates the applications in spatial epidemiology. In this context GGMs are typically referred to as Gaussian Markov random fields (GMRFs). Here the underlying graph is assumed to be known: the vertices correspond to geographical areas, while the edges are associated with a…
Fine particulate matter (PM2.5) is a mixture of air pollutants that has adverse effects on human health. Understanding the health effects of PM2.5 mixture and its individual species has been a research priority over the past two decades. However, the limited availability of speciated PM2.5 measurements continues to be a major challenge in exposure assessment for conducting large-scale population-based epidemiology studies. The PM2.5 species have complex spatial-temporal and cross dependence structures that should be accounted for in estimating the spatiotemporal distribution of each component.…
Davis and Mikosch [7] introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series. There we showed some standard statistical properties of the sample extremogram. A major difficulty was the construction of credible confidence bands for the extremogram. In this paper, we employ the stationary bootstrap to overcome this problem. Moreover, we introduce the cross extremogram as a measure of extremal serial dependence between two or more time series. We also study the extremogram for return times between extremal events. …
This paper presents a novel dynamic network autoregressive conditional heteroscedasticity (ARCH) model based on spatiotemporal ARCH models to forecast volatility in the US stock market. To improve the forecasting accuracy, the model integrates temporally lagged volatility information and information from adjacent nodes, which may instantaneously spill across the entire network. The model is also suitable for high-dimensional cases where multivariate ARCH models are typically no longer applicable. We adopt the theoretical foundations from spatiotemporal statistics and transfer the dynamic ARCH …
We consider the application of KronPCA spatio-temporal modeling techniques [Greenewald et al 2013, Tsiligkaridis et al 2013] to the extraction of spatiotemporal features for video dismount classification. KronPCA performs a low-rank type of dimensionality reduction that is adapted to spatio-temporal data and is characterized by the T frame multiframe mean and covariance of p spatial features. For further regularization and improved inverse estimation, we also use the diagonally corrected KronPCA shrinkage methods we presented in [Greenewald et al 2013]. We apply this very general method to the…
The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance function plays a key role in modeling, inference, and prediction. For multivariate space-time data, understanding the spatio-temporal variability, within and across variables, is essential in employing a realistic covariance model. Meanwhile, the complexity of generic covariances often makes model fitting very challenging, and simplified covariance structures, inc…
DARTs: A Dual-Path Robust Framework for Anomaly Detection in High-Dimensional Multivariate Time Series
Xi’an Jiaotong University, School of Computer Science and Technology（西安交通大学计算机科学与技术学院）；Fudan University, College of Intelligent Robotics and Advanced Manufacturing（复旦大学智能机器人与先进制造学院）
Spatiotemporal traffic data (e.g., link speed/flow) collected from sensor networks can be organized as multivariate time series with additional spatial attributes. A crucial task in analyzing such data is to identify and detect anomalous observations and events from the data with complex spatial and temporal dependencies. Robust Principal Component Analysis (RPCA) is a widely used tool for anomaly detection. However, the traditional RPCA purely relies on the global low-rank assumption while ignoring the local temporal correlations. In light of this, this study proposes a Hankel-structured tens…
Bakar Computational Health Sciences Institute, University of California, San Francisco（加州大学旧金山分校巴卡尔计算健康科学研究所）
Clinical data for ambulatory care, which accounts for 90% of the nations healthcare spending, is characterized by relatively small sample sizes of longitudinal data, unequal spacing between visits for each patient, with unequal numbers of data points collected across patients. While deep learning has become state-of-the-art for sequence modeling, it is unknown which methods of time aggregation may be best suited for these challenging temporal use cases. Additionally, deep models are often considered uninterpretable by physicians which may prevent the clinical adoption, even of well performing …
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…
