scholarly journals Time-Series Causality with Missing Data

2021 ◽  
Vol 6 (1) ◽  
pp. 1-4
Author(s):  
Bo Yuan Chang ◽  
Mohamed A. Naiel ◽  
Steven Wardell ◽  
Stan Kleinikkink ◽  
John S. Zelek
Keyword(s):  
Time Series ◽  
Missing Data ◽  
Missing Values ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Gaussian Process Regression ◽  
Series Data ◽  
Causal Relationships ◽  
Sampled Data ◽  
The Past

Over the past years, researchers have proposed various methods to discover causal relationships among time-series data as well as algorithms to fill in missing entries in time-series data. Little to no work has been done in combining the two strategies for the purpose of learning causal relationships using unevenly sampled multivariate time-series data. In this paper, we examine how the causal parameters learnt from unevenly sampled data (with missing entries) deviates from the parameters learnt using the evenly sampled data (without missing entries). However, to obtain the causal relationship from a given time-series requires evenly sampled data, which suggests filling the missing data values before obtaining the causal parameters. Therefore, the proposed method is based on applying a Gaussian Process Regression (GPR) model for missing data recovery, followed by several pairwise Granger causality equations in Vector Autoregssive form to fit the recovered data and obtain the causal parameters. Experimental results show that the causal parameters generated by using GPR data filling offers much lower RMSE than the dummy model (fill with last seen entry) under all missing values percentage, suggesting that GPR data filling can better preserve the causal relationships when compared with dummy data filling, thus should be considered when dealing with unevenly sampled time-series causality learning.

scholarly journals E²GAN: End-to-End Generative Adversarial Network for Multivariate Time Series Imputation

2019 ◽  
Author(s):  
Yonghong Luo ◽  
Ying Zhang ◽  
Xiangrui Cai ◽  
Xiaojie Yuan
Keyword(s):  
Time Series ◽  
Missing Values ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Imputation Accuracy ◽  
Series Data ◽  
Generative Adversarial Network ◽  
Multi Stage ◽  
Advanced Analysis ◽  
End To End

The missing values, appear in most of multivariate time series, prevent advanced analysis of multivariate time series data. Existing imputation approaches try to deal with missing values by deletion, statistical imputation, machine learning based imputation and generative imputation. However, these methods are either incapable of dealing with temporal information or multi-stage. This paper proposes an end-to-end generative model E²GAN to impute missing values in multivariate time series. With the help of the discriminative loss and the squared error loss, E²GAN can impute the incomplete time series by the nearest generated complete time series at one stage. Experiments on multiple real-world datasets show that our model outperforms the baselines on the imputation accuracy and achieves state-of-the-art classification/regression results on the downstream applications. Additionally, our method also gains better time efficiency than multi-stage method on the training of neural networks.

scholarly journals A Missing Data Compensation Method Using LSTM Estimates and Weights in AMI System

Information ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 341
Author(s):  
Hyuk-Rok Kwon ◽  
Pan-Koo Kim
Keyword(s):  
Time Series ◽  
Missing Data ◽  
Missing Values ◽  
Time Series Data ◽  
Short Term Memory ◽  
Interpolation Method ◽  
Estimation Method ◽  
Compensation Method ◽  
Communication Process ◽  
Series Data

With the expansion of advanced metering infrastructure (AMI) installations, various additional services using AMI data have emerged. However, some data is lost in the communication process of data collection. Hence, to address this challenge, the estimation of the missing data is required. To estimate the missing values in the time-series data generated from smart meters, we investigated four methods, ranging from a conventional method to an estimation method applying long short-term memory (LSTM), which exhibits excellent performance in the time-series field, and provided the performance comparison data. Furthermore, because power usages represent estimates of data that are missing some values in the middle, rather than regular time-series estimation data, the simple estimation may lead to an error where the estimated accumulated power usage in the missing data is larger than the real accumulated power usage appearing in the data after the end of the missing data interval. Therefore, this study proposes a hybrid method that combines the advantages of the linear interpolation method and the LSTM estimation-based compensation method, rather than those of conventional methods adopted in the time-series field. The performance of the proposed method is more stable and better than that of other methods.

scholarly journals Large-scale nonlinear Granger causality for inferring directed dependence from short multivariate time-series data

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Axel Wismüller ◽  
Adora M. Dsouza ◽  
M. Ali Vosoughi ◽  
Anas Abidin
Keyword(s):  
Time Series ◽  
Granger Causality ◽  
Observational Data ◽  
Large Scale ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Mathematical Formulation ◽  
Series Data ◽  
Causal Relationships ◽  
Series Systems

AbstractA key challenge to gaining insight into complex systems is inferring nonlinear causal directional relations from observational time-series data. Specifically, estimating causal relationships between interacting components in large systems with only short recordings over few temporal observations remains an important, yet unresolved problem. Here, we introduce large-scale nonlinear Granger causality (lsNGC) which facilitates conditional Granger causality between two multivariate time series conditioned on a large number of confounding time series with a small number of observations. By modeling interactions with nonlinear state-space transformations from limited observational data, lsNGC identifies casual relations with no explicit a priori assumptions on functional interdependence between component time series in a computationally efficient manner. Additionally, our method provides a mathematical formulation revealing statistical significance of inferred causal relations. We extensively study the ability of lsNGC in inferring directed relations from two-node to thirty-four node chaotic time-series systems. Our results suggest that lsNGC captures meaningful interactions from limited observational data, where it performs favorably when compared to traditionally used methods. Finally, we demonstrate the applicability of lsNGC to estimating causality in large, real-world systems by inferring directional nonlinear, causal relationships among a large number of relatively short time series acquired from functional Magnetic Resonance Imaging (fMRI) data of the human brain.

An easy way to create duration variables in binary cross-sectional time-series data

2020 ◽  
Vol 20 (4) ◽  
pp. 916-930
Author(s):  
Andrew Q. Philips
Keyword(s):  
Time Series ◽  
Missing Data ◽  
Time Series Data ◽  
Series Data ◽  
Duration Dependence ◽  
Cross Sectional ◽  
Common Solution ◽  
The Common

In cross-sectional time-series data with a dichotomous dependent variable, failing to account for duration dependence when it exists can lead to faulty inferences. A common solution is to include duration dummies, polynomials, or splines to proxy for duration dependence. Because creating these is not easy for the common practitioner, I introduce a new command, mkduration, that is a straightforward way to generate a duration variable for binary cross-sectional time-series data in Stata. mkduration can handle various forms of missing data and allows the duration variable to easily be turned into common parametric and nonparametric approximations.

scholarly journals Change Point Enhanced Anomaly Detection for IoT Time Series Data

Water ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 1633
Author(s):  
Elena-Simona Apostol ◽  
Ciprian-Octavian Truică ◽  
Florin Pop ◽  
Christian Esposito
Keyword(s):  
Time Series ◽  
Anomaly Detection ◽  
Change Point ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Change Point Detection ◽  
Change Points ◽  
Series Data ◽  
Prediction And Forecasting ◽  
Point Detection

Due to the exponential growth of the Internet of Things networks and the massive amount of time series data collected from these networks, it is essential to apply efficient methods for Big Data analysis in order to extract meaningful information and statistics. Anomaly detection is an important part of time series analysis, improving the quality of further analysis, such as prediction and forecasting. Thus, detecting sudden change points with normal behavior and using them to discriminate between abnormal behavior, i.e., outliers, is a crucial step used to minimize the false positive rate and to build accurate machine learning models for prediction and forecasting. In this paper, we propose a rule-based decision system that enhances anomaly detection in multivariate time series using change point detection. Our architecture uses a pipeline that automatically manages to detect real anomalies and remove the false positives introduced by change points. We employ both traditional and deep learning unsupervised algorithms, in total, five anomaly detection and five change point detection algorithms. Additionally, we propose a new confidence metric based on the support for a time series point to be an anomaly and the support for the same point to be a change point. In our experiments, we use a large real-world dataset containing multivariate time series about water consumption collected from smart meters. As an evaluation metric, we use Mean Absolute Error (MAE). The low MAE values show that the algorithms accurately determine anomalies and change points. The experimental results strengthen our assumption that anomaly detection can be improved by determining and removing change points as well as validates the correctness of our proposed rules in real-world scenarios. Furthermore, the proposed rule-based decision support systems enable users to make informed decisions regarding the status of the water distribution network and perform effectively predictive and proactive maintenance.

scholarly journals Implementation of IoT Framework with Data Analysis Using Deep Learning Methods for Occupancy Prediction in a Building

2021 ◽  
Vol 13 (3) ◽  
pp. 67
Author(s):  
Eric Hitimana ◽  
Gaurav Bajpai ◽  
Richard Musabe ◽  
Louis Sibomana ◽  
Jayavel Kayalvizhi
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Deep Learning ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Machine Learning Algorithms ◽  
Series Data ◽  
Support Vector ◽  
Human Beings ◽  
Feed Forward Network

Many countries worldwide face challenges in controlling building incidence prevention measures for fire disasters. The most critical issues are the localization, identification, detection of the room occupant. Internet of Things (IoT) along with machine learning proved the increase of the smartness of the building by providing real-time data acquisition using sensors and actuators for prediction mechanisms. This paper proposes the implementation of an IoT framework to capture indoor environmental parameters for occupancy multivariate time-series data. The application of the Long Short Term Memory (LSTM) Deep Learning algorithm is used to infer the knowledge of the presence of human beings. An experiment is conducted in an office room using multivariate time-series as predictors in the regression forecasting problem. The results obtained demonstrate that with the developed system it is possible to obtain, process, and store environmental information. The information collected was applied to the LSTM algorithm and compared with other machine learning algorithms. The compared algorithms are Support Vector Machine, Naïve Bayes Network, and Multilayer Perceptron Feed-Forward Network. The outcomes based on the parametric calibrations demonstrate that LSTM performs better in the context of the proposed application.

scholarly journals Uncertainty quantification of the effects of biotic interactions on community dynamics from nonlinear time-series data

2018 ◽  
Vol 15 (147) ◽  
pp. 20180695 ◽  
Author(s):  
Simone Cenci ◽  
Serguei Saavedra
Keyword(s):  
Time Series ◽  
Community Dynamics ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Model Averaging ◽  
Biotic Interactions ◽  
Series Data ◽  
Time Intervals ◽  
Novel Approach ◽  
Data Generating Process

Biotic interactions are expected to play a major role in shaping the dynamics of ecological systems. Yet, quantifying the effects of biotic interactions has been challenging due to a lack of appropriate methods to extract accurate measurements of interaction parameters from experimental data. One of the main limitations of existing methods is that the parameters inferred from noisy, sparsely sampled, nonlinear data are seldom uniquely identifiable. That is, many different parameters can be compatible with the same dataset and can generalize to independent data equally well. Hence, it is difficult to justify conclusive assertions about the effect of biotic interactions without information about their associated uncertainty. Here, we develop an ensemble method based on model averaging to quantify the uncertainty associated with the effect of biotic interactions on community dynamics from non-equilibrium ecological time-series data. Our method is able to detect the most informative time intervals for each biotic interaction within a multivariate time series and can be easily adapted to different regression schemes. Overall, this novel approach can be used to associate a time-dependent uncertainty with the effect of biotic interactions. Moreover, because we quantify uncertainty with minimal assumptions about the data-generating process, our approach can be applied to any data for which interactions among variables strongly affect the overall dynamics of the system.

scholarly journals An Empirical Mode-Spatial Model for Environmental Data Imputation

Hydrology ◽  
2018 ◽  
Vol 5 (4) ◽  
pp. 63 ◽  
Author(s):  
Benjamin Nelsen ◽  
D. Williams ◽  
Gustavious Williams ◽  
Candace Berrett
Keyword(s):  
Time Series ◽  
Spatial Data ◽  
Missing Values ◽  
Time Series Data ◽  
Environmental Data ◽  
Series Data ◽  
Data Imputation ◽  
Accurate Data ◽  
Target Station ◽  
Periodic Components

Complete and accurate data are necessary for analyzing and understanding trends in time-series datasets; however, many of the available time-series datasets have gaps that affect the analysis, especially in the earth sciences. As most available data have missing values, researchers use various interpolation methods or ad hoc approaches to data imputation. Since the analysis based on inaccurate data can lead to inaccurate conclusions, more accurate data imputation methods can provide accurate analysis. We present a spatial-temporal data imputation method using Empirical Mode Decomposition (EMD) based on spatial correlations. We call this method EMD-spatial data imputation or EMD-SDI. Though this method is applicable to other time-series data sets, here we demonstrate the method using temperature data. The EMD algorithm decomposes data into periodic components called intrinsic mode functions (IMF) and exactly reconstructs the original signal by summing these IMFs. EMD-SDI initially decomposes the data from the target station and other stations in the region into IMFs. EMD-SDI evaluates each IMF from the target station in turn and selects the IMF from other stations in the region with periodic behavior most correlated to target IMF. EMD-SDI then replaces a section of missing data in the target station IMF with the section from the most closely correlated IMF from the regional stations. We found that EMD-SDI selects the IMFs used for reconstruction from different stations throughout the region, not necessarily the station closest in the geographic sense. EMD-SDI accurately filled data gaps from 3 months to 5 years in length in our tests and favorably compares to a simple temporal method. EMD-SDI leverages regional correlation and the fact that different stations can be subject to different periodic behaviors. In addition to data imputation, the EMD-SDI method provides IMFs that can be used to better understand regional correlations and processes.

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