scholarly journals Gaussian Process Modelling for Improved Resolution in Faraday Depth Reconstruction

2021 ◽  
Author(s):  
S W Ndiritu ◽  
A M M Scaife ◽  
D L Tabb ◽  
M Cárcamo ◽  
J Hanson
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Missing Values ◽  
Probabilistic Method ◽  
Process Modelling ◽  
Polarization Data ◽  
Rotation Measure ◽  
Depth Reconstruction ◽  
Novel Method ◽  
Complex Polarization

Abstract The incomplete sampling of data in complex polarization measurements from radio telescopes negatively affects both the rotation measure (RM) transfer function and the Faraday depth spectra derived from these data. Such gaps in polarization data are mostly caused by flagging of radio frequency interference and their effects worsen as the percentage of missing data increases. In this paper we present a novel method for inferring missing polarization data based on Gaussian processes (GPs). Gaussian processes are stochastic processes that enable us to encode prior knowledge in our models. They also provide a comprehensive way of incorporating and quantifying uncertainties in regression modelling. In addition to providing non-parametric model estimates for missing values, we also demonstrate that Gaussian process modelling can be used for recovering rotation measure values directly from complex polarization data, and that inferring missing polarization data using this probabilistic method improves the resolution of reconstructed Faraday depth spectra.

Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes

1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Partial Ordering ◽  
Boundary Crossing ◽  
Conditional Probabilities ◽  
Life Distribution ◽  
Life Distributions ◽  
Bounded Below ◽  
Crossing Probabilities

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

Multi-model multivariate Gaussian process modelling with correlated noises

2017 ◽  
Vol 58 ◽  
pp. 11-22 ◽  
Author(s):  
Xiaodan Hong ◽  
Biao Huang ◽  
Yongsheng Ding ◽  
Fan Guo ◽  
Lei Chen ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Process Modelling ◽  
Multivariate Gaussian ◽  
Multivariate Gaussian Process ◽  
Correlated Noises

scholarly journals Wavelet-based simulation of random processes from certain classes with given accuracy and reliability

2019 ◽  
Vol 25 (3) ◽  
pp. 217-225
Author(s):  
Ievgen Turchyn
Keyword(s):  
Stochastic Processes ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Random Processes

Abstract We consider stochastic processes {Y(t)} which can be represented as {Y(t)=(X(t))^{s}} , {s\in\mathbb{N}} , where {X(t)} is a stationary strictly sub-Gaussian process, and build a wavelet-based model that simulates {Y(t)} with given accuracy and reliability in {L_{p}([0,T])} . A model for simulation with given accuracy and reliability in {L_{p}([0,T])} is also built for processes {Z(t)} which can be represented as {Z(t)=X_{1}(t)X_{2}(t)} , where {X_{1}(t)} and {X_{2}(t)} are independent stationary strictly sub-Gaussian processes.

Approximation to the exit probability of a continuous Gaussian process over a U-shaped boundary of increasing curvature

1995 ◽  
Vol 32 (2) ◽  
pp. 429-442
Author(s):  
A. N. Balabushkin
Keyword(s):  
Brownian Motion ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Simple Approximation ◽  
Minimum Point ◽  
Second Derivative ◽  
Numerical Examples ◽  
Exit Probability ◽  
Continuous Gaussian Process

A simple approximation to the probability of crossing a U-shaped boundary by a Brownian motion is given. The larger the second derivative of the curve at a minimum point, the higher the accuracy of the approximation. The result is also extended to a class of continuous Gaussian processes with definite properties. Numerical examples are given.

Gaussian Process Emulation for Big Data in Data-Driven Metamaterials Design

2019 ◽  
Author(s):  
Ramin Bostanabad ◽  
Yu-Chin Chan ◽  
Liwei Wang ◽  
Ping Zhu ◽  
Wei Chen
Keyword(s):  
Big Data ◽  
Gaussian Process ◽  
Engineering Design ◽  
Training Data ◽  
Data Driven ◽  
Training Dataset ◽  
Massive Datasets ◽  
Unit Cells ◽  
Gaussian Process Emulation ◽  
Novel Method

Abstract Our main contribution is to introduce a novel method for Gaussian process (GP) modeling of massive datasets. The key idea is to build an ensemble of independent GPs that use the same hyperparameters but distribute the entire training dataset among themselves. This is motivated by our observation that estimates of the GP hyperparameters change negligibly as the size of the training data exceeds a certain level, which can be found in a systematic way. For inference, the predictions from all GPs in the ensemble are pooled to efficiently exploit the entire training dataset for prediction. We name our modeling approach globally approximate Gaussian process (GAGP), which, unlike most largescale supervised learners such as neural networks and trees, is easy to fit and can interpret the model behavior. These features make it particularly useful in engineering design with big data. We use analytical examples to demonstrate that GAGP achieves very high predictive power that matches or exceeds that of state-of-the-art machine learning methods. We illustrate the application of GAGP in engineering design with a problem on data-driven metamaterials design where it is used to link reduced-dimension geometrical descriptors of unit cells and their properties. Searching for new unit cell designs with desired properties is then accomplished by employing GAGP in inverse optimization.

scholarly journals An Imbalanced Data Handling Framework for Industrial Big Data Using a Gaussian Process Regression-Based Generative Adversarial Network

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 669 ◽  
Author(s):  
Eunseo Oh ◽  
Hyunsoo Lee
Keyword(s):  
Big Data ◽  
Gaussian Process ◽  
Missing Values ◽  
Gaussian Process Regression ◽  
Estimation Methods ◽  
Data Handling ◽  
Generative Adversarial Network ◽  
Data Set ◽  
Adversarial Network ◽  
Industrial Big Data

The developments in the fields of industrial Internet of Things (IIoT) and big data technologies have made it possible to collect a lot of meaningful industrial process and quality-based data. The gathered data are analyzed using contemporary statistical methods and machine learning techniques. Then, the extracted knowledge can be used for predictive maintenance or prognostic health management. However, it is difficult to gather complete data due to several issues in IIoT, such as devices breaking down, running out of battery, or undergoing scheduled maintenance. Data with missing values are often ignored, as they may contain insufficient information from which to draw conclusions. In order to overcome these issues, we propose a novel, effective missing data handling mechanism for the concepts of symmetry principles. While other existing methods only attempt to estimate missing parts, the proposed method generates a whole set of data set using Gaussian process regression and a generative adversarial network. In order to prove the effectiveness of the proposed framework, we examine a real-world, industrial case involving an air pressure system (APS), where we use the proposed method to make quality predictions and compare the results with existing state-of-the-art estimation methods.

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