Causation Entropy Identifies Sparsity Structure for Parameter Estimation of Dynamic Systems

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Pileun Kim ◽  
Jonathan Rogers ◽  
Jie Sun ◽  
Erik Bollt
Keyword(s):  
Parameter Estimation ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Measurement Data ◽  
Relative Magnitude ◽  
Initial Guess ◽  
Series Data ◽  
System Parameters ◽  
Estimation Problems ◽  
System States

Parameter estimation is an important topic in the field of system identification. This paper explores the role of a new information theory measure of data dependency in parameter estimation problems. Causation entropy is a recently proposed information-theoretic measure of influence between components of multivariate time series data. Because causation entropy measures the influence of one dataset upon another, it is naturally related to the parameters of a dynamical system. In this paper, it is shown that by numerically estimating causation entropy from the outputs of a dynamic system, it is possible to uncover the internal parametric structure of the system and thus establish the relative magnitude of system parameters. In the simple case of linear systems subject to Gaussian uncertainty, it is first shown that causation entropy can be represented in closed form as the logarithm of a rational function of system parameters. For more general systems, a causation entropy estimator is proposed, which allows causation entropy to be numerically estimated from measurement data. Results are provided for discrete linear and nonlinear systems, thus showing that numerical estimates of causation entropy can be used to identify the dependencies between system states directly from output data. Causation entropy estimates can therefore be used to inform parameter estimation by reducing the size of the parameter set or to generate a more accurate initial guess for subsequent parameter optimization.

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.

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