scholarly journals Probabilistic Graphical Model for Continuous Variables

2022 ◽  
pp. 251-265
Author(s):  
Jing Wang ◽  
Jinglin Zhou ◽  
Xiaolu Chen
Keyword(s):  
Time Series ◽  
Graphical Model ◽  
Continuous Process ◽  
Probabilistic Graphical Model ◽  
Learning Method ◽  
Continuous Variables ◽  
Sampled Data ◽  
Process Variables ◽  
Learning Mechanisms ◽  
Gaussian Distributions

AbstractMost of the sampled data in complex industrial processes are sequential in time. Therefore, the traditional BN learning mechanisms have limitations on the value of probability and cannot be applied to the time series. The model established in Chap. 10.1007/978-981-16-8044-1_13 is a graphical model similar to a Bayesian network, but its parameter learning method can only handle the discrete variables. This chapter aims at the probabilistic graphical model directly for the continuous process variables, which avoids the assumption of discrete or Gaussian distributions.

A Probabilistic-Graphical-Model Based Approach for Representing Lineages in Uncertain Data

2011 ◽  
Vol 34 (10) ◽  
pp. 1897-1906 ◽  
Author(s):  
Kun YUE ◽  
Wei-Yi LIU ◽  
Yun-Lei ZHU ◽  
Wei ZHANG
Keyword(s):  
Graphical Model ◽  
Uncertain Data ◽  
Probabilistic Graphical Model ◽  
Model Based

A deep multi-task representation learning method for time series classification and retrieval

2021 ◽  
Vol 555 ◽  
pp. 17-32
Author(s):  
Ling Chen ◽  
Donghui Chen ◽  
Fan Yang ◽  
Jianling Sun
Keyword(s):  
Time Series ◽  
Representation Learning ◽  
Learning Method ◽  
Time Series Classification ◽  
Task Representation

A Probabilistic Graphical Model-based Approach for Minimizing Energy Under Performance Constraints

2015 ◽  
Vol 43 (1) ◽  
pp. 267-281 ◽  
Author(s):  
Nikita Mishra ◽  
Huazhe Zhang ◽  
John D. Lafferty ◽  
Henry Hoffmann
Keyword(s):  
Graphical Model ◽  
Probabilistic Graphical Model ◽  
Performance Constraints ◽  
Model Based

scholarly journals Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

2018 ◽  
Vol 22 (2) ◽  
pp. 1175-1192 ◽  
Author(s):  
Qian Zhang ◽  
Ciaran J. Harman ◽  
James W. Kirchner
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Irregular Sampling ◽  
Quality Data ◽  
Sampled Data ◽  
Spectral Slope ◽  
Water Quality Data ◽  
Fractal Scaling ◽  
Wide Range ◽  
Irregularly Sampled Data

Abstract. River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling – in the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) – are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β  =  0) to Brown noise (β  =  2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb–Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of prescribed β values and gap distributions. The aliasing method, however, does not itself account for sampling irregularity, and this introduces some bias in the result. Nonetheless, the wavelet method is recommended for estimating β in irregular time series until improved methods are developed. Finally, all methods' performances depend strongly on the sampling irregularity, highlighting that the accuracy and precision of each method are data specific. Accurately quantifying the strength of fractal scaling in irregular water-quality time series remains an unresolved challenge for the hydrologic community and for other disciplines that must grapple with irregular sampling.

Sign in / Sign up

Export Citation Format

Share Document