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

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.

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Constructing the Microbial Association Network from Large-Scale Time Series Data Using Granger Causality

Genes ◽

10.3390/genes10030216 ◽

2019 ◽

Vol 10 (3) ◽

pp. 216 ◽

Cited By ~ 3

Author(s):

Dongmei Ai ◽

Xiaoxin Li ◽

Gang Liu ◽

Xiaoyi Liang ◽

Li Xia

Keyword(s):

Time Series ◽

Microbial Community ◽

Granger Causality ◽

Large Scale ◽

Community Dynamics ◽

Time Series Data ◽

Series Data ◽

Association Network ◽

Causal Relationships ◽

Network Analyses

The increasing availability of large-scale time series data allows the inference of microbial community dynamics by association network analysis. However, correlation-based association network analyses are noninformative of causal, mediating and time-dependent relationships between microbial community functional factors. To address this insufficiency, we introduced the Granger causality model to the analysis of a recent marine microbial time series dataset. We systematically constructed a directed acyclic network, representing both internal and external causal relationships among the microbial and environmental factors. We further optimized the network by removing false causal associations using the conditional Granger causality. The final network was visualized as a Granger graph, which was analyzed to identify causal relationships driven by key functional operators in the environment, such as Gammaproteobacteria, which was Granger caused by total organic nitrogen and primary production (p < 0.05 and Q < 0.05).

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Time-Series Causality with Missing Data

Journal of Computational Vision and Imaging Systems ◽

10.15353/jcvis.v6i1.3552 ◽

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.

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Convex Hull Convolutive Non-Negative Matrix Factorization for Uncovering Temporal Patterns in Multivariate Time-Series Data

10.21437/interspeech.2016-571 ◽

2016 ◽

Cited By ~ 5

Author(s):

Colin Vaz ◽

Asterios Toutios ◽

Shrikanth S. Narayanan

Keyword(s):

Time Series ◽

Convex Hull ◽

Matrix Factorization ◽

Time Series Data ◽

Multivariate Time Series ◽

Temporal Patterns ◽

Series Data ◽

Non Negative Matrix Factorization

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Modeling Low-risk Actions from Multivariate Time Series Data Using Distributional Reinforcement Learning

2020 11th International Conference on Awareness Science and Technology (iCAST) ◽

10.1109/icast51195.2020.9319476 ◽

2020 ◽

Author(s):

Yosuke Sato ◽

Jianwei Zhang

Keyword(s):

Time Series ◽

Reinforcement Learning ◽

Time Series Data ◽

Multivariate Time Series ◽

Low Risk ◽

Series Data

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Change Point Enhanced Anomaly Detection for IoT Time Series Data

Water ◽

10.3390/w13121633 ◽

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.

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

Future Internet ◽

10.3390/fi13030067 ◽

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.

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

Journal of The Royal Society Interface ◽

10.1098/rsif.2018.0695 ◽

2018 ◽

Vol 15 (147) ◽

pp. 20180695 ◽

Cited By ~ 7

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.

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