Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting time series. However, modeling statistical dependencies can improve accuracy and enable analysis of interaction effects. Deep learning methods are well suited for this problem, but multi-variate models often assume a simple parametric distribution and do not scale to high dimensions. In this work we model the multi-variate temporal dynamics of time series via an autoregressive deep learning model, where the data distribution is represented by a conditioned normalizing flow. This combination retains the power of autoregressive models, such as good performance in extrapolation into the future, with the flexibility of flows as a general purpose high-dimensional distribution model, while remaining computationally tractable. We show that it improves over the state-of-the-art for standard metrics on many real-world data sets with several thousand interacting time-series.
Heterogeneity and irregularity of multi-source data sets present a significant challenge to time-series analysis. In the literature, the fusion of multi-source time-series has been achieved either by using ensemble learning models which ignore temporal patterns and correlation within features or by defining a fixed-size window to select specific parts of the data sets. On the other hand, many studies have shown major improvement to handle the irregularity of time-series, yet none of these studies has been applied to multi-source data. In this work, we design a novel architecture, PIETS, to model heterogeneous time-series. PIETS has the following characteristics: (1) irregularity encoders for multi-source samples that can leverage all available information and accelerate the convergence of the model; (2) parallelised neural networks to enable flexibility and avoid information overwhelming; and (3) attention mechanism that highlights different information and gives high importance to the most related data. Through extensive experiments on real-world data sets related to COVID-19, we show that the proposed architecture is able to effectively model heterogeneous temporal data and outperforms other state-of-the-art approaches in the prediction task.
Modern time series datasets are often high-dimensional, incomplete/sparse, and nonstationary. These properties hinder the development of scalable and efficient solutions for time series forecasting and analysis. To address these challenges, we propose a Nonstationary Temporal Matrix Factorization (NoTMF) model, in which matrix factorization is used to reconstruct the whole time series matrix and vector autoregressive (VAR) process is imposed on a properly differenced copy of the temporal factor matrix. This approach not only preserves the low-rank property of the data but also offers consistent temporal dynamics. The learning process of NoTMF involves the optimization of two factor matrices and a collection of VAR coefficient matrices. To efficiently solve the optimization problem, we derive an alternating minimization framework, in which subproblems are solved using conjugate gradient and least squares methods. In particular, the use of conjugate gradient method offers an efficient routine and allows us to apply NoTMF on large-scale problems. Through extensive experiments on Uber movement speed dataset, we demonstrate the superior accuracy and effectiveness of NoTMF over other baseline models. Our results also confirm the importance of addressing the nonstationarity of real-world time series data such as spatiotemporal traffic flow/speed.
Estimating causal relations is vital in understanding the complex interactions in multivariate time series. Non-linear coupling of variables is one of the major challenges inaccurate estimation of cause-effect relations. In this paper, we propose to use deep autoregressive networks (DeepAR) in tandem with counterfactual analysis to infer nonlinear causal relations in multivariate time series. We extend the concept of Granger causality using probabilistic forecasting with DeepAR. Since deep networks can neither handle missing input nor out-of-distribution intervention, we propose to use the Knockoffs framework (Barberand Cand`es, 2015) for generating intervention variables and consequently counterfactual probabilistic forecasting. Knockoff samples are independent of their output given the observed variables and exchangeable with their counterpart variables without changing the underlying distribution of the data. We test our method on synthetic as well as real-world time series datasets. Overall our method outperforms the widely used vector autoregressive Granger causality and PCMCI in detecting nonlinear causal dependency in multivariate time series.
Wireless Sensor Networks (WSNs) have recently attracted greater attention worldwide due to their practicality in monitoring, communicating, and reporting specific physical phenomena. The data collected by WSNs is often inaccurate as a result of unavoidable environmental factors, which may include noise, signal weakness, or intrusion attacks depending on the specific situation. Sending high-noise data has negative effects not just on data accuracy and network reliability, but also regarding the decision-making processes in the base station. Anomaly detection, or outlier detection, is the process of detecting noisy data amidst the contexts thus described. The literature contains relatively few noise detection techniques in the context of WSNs, particularly for outlier-detection algorithms applying time series analysis, which considers the effective neighbors to ensure a global-collaborative detection. Hence, the research presented in this paper is intended to design and implement a global outlier-detection approach, which allows us to find and select appropriate neighbors to ensure an adaptive collaborative detection based on time-series analysis and entropy techniques. The proposed approach applies a random forest algorithm for identifying the best results. To measure the effectiveness and efficiency of the proposed approach, a comprehensive and real scenario provided by the Intel Berkeley Research lab has been simulated. Noisy data have been injected into the collected data randomly. The results obtained from the experiment then conducted experimentation demonstrate that our approach can detect anomalies with up to 99% accuracy.
Recognizing subtle historical patterns is central to modeling and forecasting problems in time series analysis. Here we introduce and develop a new approach to quantify deviations in the underlying hidden generators of observed data streams, resulting in a new efficiently computable universal metric for time series. The proposed metric is in the sense that we can compare and contrast data streams regardless of where and how they are generated and without any feature engineering step. The approach proposed in this paper is conceptually distinct from our previous work on data smashing, and vastly improves discrimination performance and computing speed. The core idea here is the generalization of the notion of KL divergence often used to compare probability distributions to a notion of divergence in time series. We call this the sequence likelihood (SL) divergence, which may be used to measure deviations within a well-defined class of discrete-valued stochastic processes. We devise efficient estimators of SL divergence from finite sample paths and subsequently formulate a universal metric useful for computing distance between time series produced by hidden stochastic generators.
A new variational mode decomposition (VMD) based deep learning approach is proposed in this paper for time series forecasting problem. Firstly, VMD is adopted to decompose the original time series into several sub-signals. Then, a convolutional neural network (CNN) is applied to learn the reconstruction patterns on the decomposed sub-signals to obtain several reconstructed sub-signals. Finally, a long short term memory (LSTM) network is employed to forecast the time series with the decomposed sub-signals and the reconstructed sub-signals as inputs. The proposed VMD-CNN-LSTM approach is originated from the decomposition-reconstruction-ensemble framework, and innovated by embedding the reconstruction, single forecasting, and ensemble steps in a unified deep learning approach. To verify the forecasting performance of the proposed approach, four typical time series datasets are introduced for empirical analysis. The empirical results demonstrate that the proposed approach outperforms consistently the benchmark approaches in terms of forecasting accuracy, and also indicate that the reconstructed sub-signals obtained by CNN is of importance for further improving the forecasting performance.
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