scholarly journals Exploitation of Kronecker Structure in Gaussian Process Regression for Efficient Biomedical Signal Processing

2021 ◽  
Vol 7 (2) ◽  
pp. 287-290
Author(s):  
Jannik Prüßmann ◽  
Jan Graßhoff ◽  
Philipp Rostalski
Keyword(s):  
Gaussian Process ◽  
Source Separation ◽  
Gaussian Process Regression ◽  
Efficient Solutions ◽  
Biomedical Signal Processing ◽  
Hyperparameter Optimization ◽  
Performance Loss ◽  
Versatile Tool ◽  
Data Points ◽  
Spatio Temporal

Abstract Gaussian processes are a versatile tool for data processing. Unfortunately, due to storage and runtime requirements, standard Gaussian process (GP) methods are limited to a few thousand data points. Thus, they are infeasible in most biomedical, spatio-temporal problems. The methods treated in this work cover GP inference and hyperparameter optimization, exploiting the Kronecker structure of covariance matrices. To solve regression and source separation problems, two different approaches are presented. The first approach uses efficient matrix-vector-products, whilst the second approach is based on efficient solutions to the eigendecomposition. The latter also enables efficient hyperparameter optimization. In comparison to standard GP methods, the proposed methods can be applied to very large biomedical datasets without any further performance loss and perform substantially faster. The performance is demonstrated on esophageal manometry data, where the cardiac and respiratory signal components are to be inferred by source separation.

Validation of Adaptive Gaussian Process Regression Model Used for SIF Prediction

2018 ◽  
Author(s):  
Arvind Keprate ◽  
R. M. Chandima Ratnayake ◽  
Shankar Sankararaman
Keyword(s):  
Regression Model ◽  
Gaussian Process ◽  
Prediction Accuracy ◽  
Experimental Validation ◽  
Gaussian Process Regression ◽  
Absolute Error ◽  
Coefficient Of Determination ◽  
Data Sets ◽  
Maximum Absolute Error ◽  
Data Points

The main aim of this paper is to perform the validation of the adaptive Gaussian process regression model (AGPRM) developed by the authors for the Stress Intensity Factor (SIF) prediction of a crack propagating in topside piping. For validation purposes, the values of SIF obtained from experiments available in the literature are used. Sixty-six data points (consisting of L, a, c and SIF values obtained by experiments) are used to train the AGPRM, while four independent data sets are used for validation purposes. The experimental validation of the AGPRM also consists of the comparison of the prediction accuracy of AGPRM and Finite Element Method (FEM) relative to the experimentally derived SIF values. Four metrics, namely, Root Mean Square Error (RMSE), Average Absolute Error (AAE), Maximum Absolute Error (MAE), and Coefficient of Determination (R2), are used to compare the accuracy. A case study illustrating the development and experimental validation of the AGPRM is presented. Results indicate that the prediction accuracy of the AGPRM is comparable with and even higher than that of the FEM, provided the training points of the AGPRM are aptly chosen.

Prediction of Abdominal Aortic Aneurysms Using Sparse Gaussian Process Regression

2013 ◽  
Author(s):  
A. Ijaz ◽  
J. Choi ◽  
W. Lee ◽  
S. Baek
Keyword(s):  
Gaussian Process ◽  
Morphological Changes ◽  
Gaussian Process Regression ◽  
Abdominal Aortic Aneurysms ◽  
Aortic Aneurysms ◽  
Abdominal Aortic ◽  
Risk Of Rupture ◽  
Spatial Estimates ◽  
Spatio Temporal ◽  
Small Aneurysms

Abdominal Aortic Aneurysms (AAA) is a form of vascular disease causing focal enlargement of abdominal aorta. It affects a large part of population and has up to 90% mortality rate. Since risks from open surgery or endovascular repair outweighs the risk of AAA rupture, surgical treatments are not recommended with AAA less than 5.5cm in diameter. Recent clinical recommendations suggest that people with small aneurysms should be examined 3∼36 months depending on size to get information about morphological changes. While advances in biomechanics provide state-of-the-art spatial estimates of stress distributions of AAA, there are still limitations in modeling its time evolution. Thus, there is no biomechanical framework to utilize such information from a series of medical images that would aid physicians in detecting small aneurysms with high risk of rupture. For the present study, we use series of CT images of small AAAs taken at different times to model and predict the spatio-temporal evolution of AAA. This is achieved using sparse local Gaussian process regression.

scholarly journals Linking Gaussian process regression with data-driven manifold embeddings for nonlinear data fusion

2019 ◽  
Vol 9 (3) ◽  
pp. 20180083 ◽  
Author(s):  
Seungjoon Lee ◽  
Felix Dietrich ◽  
George E. Karniadakis ◽  
Ioannis G. Kevrekidis
Keyword(s):  
Gaussian Process ◽  
Information Fusion ◽  
Gaussian Process Regression ◽  
Statistical Modelling ◽  
Training Data ◽  
High Fidelity ◽  
Several Variables ◽  
Mathematical Algorithms ◽  
Data Points ◽  
Fidelity Model

In statistical modelling with Gaussian process regression, it has been shown that combining (few) high-fidelity data with (many) low-fidelity data can enhance prediction accuracy, compared to prediction based on the few high-fidelity data only. Such information fusion techniques for multi-fidelity data commonly approach the high-fidelity model f h ( t ) as a function of two variables ( t , s ), and then use f l ( t ) as the s data. More generally, the high-fidelity model can be written as a function of several variables ( t , s 1 , s 2 ….); the low-fidelity model f l and, say, some of its derivatives can then be substituted for these variables. In this paper, we will explore mathematical algorithms for multi-fidelity information fusion that use such an approach towards improving the representation of the high-fidelity function with only a few training data points. Given that f h may not be a simple function—and sometimes not even a function—of f l , we demonstrate that using additional functions of t , such as derivatives or shifts of f l , can drastically improve the approximation of f h through Gaussian processes. We also point out a connection with ‘embedology’ techniques from topology and dynamical systems. Our illustrative examples range from instructive caricatures to computational biology models, such as Hodgkin–Huxley neural oscillations.

Characterization of Structural Dynamics With Uncertainty by Using Gaussian Processes

2011 ◽  
Author(s):  
Z. Xia ◽  
J. Tang
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Regression Models ◽  
Structural Response ◽  
Gaussian Process Regression ◽  
Monte Carlo Sampling ◽  
Structural Systems ◽  
Data Points ◽  
Small Set

An efficient way to capture the dynamic characteristics of structural systems with uncertainties has been an important and challenging subject. While such characterization is valuable for structural response predictions, it could be impractical in many application situations where a sufficiently large sample is expensive or unavailable. In this paper, Gaussian process regression models are employed to capture structural dynamical responses, especially responses with uncertainties. When Gaussian processes are used to make predictions for responses with uncertainties, the sampling costs can be significantly reduced because only a relatively small set of data points is needed. With no loss of generality, applications of Gaussian process regression models are introduced in conjunction with Monte Carlo sampling. This approach can be easily generalized to situations where data points are obtained by other sampling techniques.

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