Application Of Gaussian Processes Research Articles

Genetic association mapping leveraging Gaussian processes.

Gaussian processes (GPs) are a powerful and useful approach for modelling nonlinear phenomena in various scientific fields, including genomics and genetics. This review focuses on the application of GPs in genetic association mapping. The aim is to identify genetic variants that alter gene regulation along continuous cellular states at the molecular level, as well as disease susceptibility over time and space at the population level. The challenges and opportunities in this field are also addressed.

Inversion in an uncertain ocean using Gaussian processes.

Gaussian processes (GPs) can capture correlation of the acoustic field at different depths in the ocean. This feature is exploited in this work for pre-processing acoustic data before these are employed for source localization and environmental inversion using matched field inversion (MFI) in an underwater waveguide. Via the application of GPs, the data are denoised and interpolated, generating densely populated acoustic fields at virtual arrays, which are then used as data in MFI. Replicas are also computed at the virtual receivers at which field predictions are made. The correlations among field measurements at distinct spatial points are manifested through the selection of kernel functions. These rely on hyperparameters, that are estimated through a maximum likelihood process for optimal denoising and interpolation. The approach, employing Gaussian and Matérn kernels, is tested on synthetic and real data with both an exhaustive search and genetic algorithms and is found to be superior to conventional beamformer MFI. It is also shown that the Matérn kernel, providing more degrees of freedom because of an increased number of hyperparameters, is preferable over the frequently used Gaussian kernel.

Application of Gaussian processes and transfer learning to prediction and analysis of polymer properties

Machine learning has shown superior performance in polymer properties prediction research. However, due to the complex experimental process or simulation process of polymers, it is not practical to obtain a large amount of data for fitting machine learning hyperparameters. This study aims to construct an effective performance prediction model using a small amount of data on polymers and the interaction between properties. In this paper we apply Gaussian Process Regression (GPR) and transfer learning for the establishment of polymer properties prediction models with few samples. Experiments show that when the algorithm is used to predict important properties such as diffusion coefficient and mechanical properties of polymers, the predicted value of the established model is close to the real value of the simulation, which verifies the validity of the model. Transfer learning can build a Gaussian model that describes the relationship between two performances, which not only improves the prediction accuracy of the prediction model, but also visualizes the relationship between performances and provides guidance for further experiments or simulations.

A smart simulation-optimization framework for solar-powered desalination systems

Energy crises caused some secondary challenges in the field of water and food as well its inherent catastrophes. In the nexuses of water and energy, supplying the power for desalination and water treatment process is assumed as an important subject in scientific communities. While, in sunny arid and semi-arid climates (Zahedan, Iran), the application of solar irradiances can convert threats into opportunities. In the present research, in the first step, all operational features in photovoltaic facilities are optimized by Central Composition Design (CCD) as a Response Surface Methodology (RSM) method. In the second step, harvested renewable energy values, carbon emission prevention, initial cost, and maintenance for each year are predicted as per operational factors of the photovoltaic system, which are utilized in the desalination process and with the application of Gaussian Processes, Multilayer Perceptron, Support Vector Machine for Regression (SMOreg) and Polynomial Trees (M5P) algorithms. Finally, in the managerial insight section of the research, an integrated Reverse Osmosis-Photovoltaic system is presented as a green facility of water providing in arid and semi-arid climates. Based on RSM system the main effective factors for energy production, prevention carbon emission (25 year), initial and maintenance costs are Pitch degree (P) (P-value < 0.0001), Pitch degree (P-value < 0.0001), Cross Distance (CD) (P-value < 0.0001), and Panel Capacity (PC) (P-value = 0.0002), respectively. Finally, an SDGS assessment is performed in this investigation, and some managerial insights are proposed. In the different steps of this study, both carbon emission values and cost functions are optimized. While, to the prediction of available solar energy, Gaussian process with more than 0.98 has the most efficiency.

Scalable multi-task Gaussian processes with neural embedding of coregionalization

Multi-task regression attempts to exploit the task similarity in order to achieve knowledge transfer across related tasks for improving the quality of prediction and alleviating the demand of big data. The application of Gaussian process (GP) in this scenario yields the non-parametric yet informative Bayesian multi-task regression paradigm. Multi-task GP (MTGP) provides not only the prediction mean but also the associated prediction variance to quantify uncertainty, thus gaining popularity in various scenarios. The linear model of coregionalization (LMC) is a well-known MTGP paradigm which exploits the dependency of tasks through linear combination of several independent and diverse GPs. The LMC however suffers from high model complexity and limited model capability when handling complicated multi-task cases. To this end, we develop the neural embedding of coregionalization that transforms the latent GPs into a high-dimensional latent space to induce rich yet diverse behaviors. Furthermore, we use advanced variational inference as well as sparse approximation to devise a tight and compact evidence lower bound (ELBO) for higher quality of scalable model inference. Extensive numerical experiments have been conducted to verify the higher prediction quality and better generalization of our model, named NSVLMC, on various real-world multi-task datasets and the cross-fluid modeling of unsteady fluidized bed.

Gaussian Process for Radiance Functions on the Sphere

AbstractEfficient approximation of incident radiance functions from a set of samples is still an open problem in physically based rendering. Indeed, most of the computing power required to synthesize a photo‐realistic image is devoted to collecting samples of the incident radiance function, which are necessary to provide an estimate of the rendering equation solution. Due to the large number of samples required to reach a high‐quality estimate, this process is usually tedious and can take up to several days. In this paper, we focus on the problem of approximation of incident radiance functions on the sphere. To this end, we resort to a Gaussian Process (GP), a highly flexible function modelling tool, which has received little attention in rendering. We make an extensive analysis of the application of GPs to incident radiance functions, addressing crucial issues such as robust hyperparameter learning, or selecting the covariance function which better suits incident radiance functions. Our analysis is both theoretical and experimental. Furthermore, it provides a seamless connection between the original spherical domain and the spectral domain, on which we build to derive a method for fast computation and rotation of spherical harmonics coefficients.

Uncertainty reduction in matched field inversion using Gaussian Processes

Gaussian Processes have been shown to be an effective tool for predicting an acoustic field in the ocean at a densely populated virtual array. This property is employed in this work for pre-processing acoustic data before these are used for source localization and geoacoustic parameter estimation using matched-field inversion (MFI). The process increases the accuracy of MFI as uncertainty in the estimation process is reduced. Via the application of Gaussian Processes, the data are denoised and interpolated and the new, enhanced fields are used as input to MFI along with replicas calculated at the virtual receivers at which field predictions are made. Kernel functions, implicit in the implementation of Gaussian Processes, quantify the correlation among field values at neighboring spatial points. Employing different kernels, the approach is tested on synthetic and real data with both an exhaustive search and genetic algorithms and is found to be superior to conventional Bartlett MFI in source localization and geoacoustic inversion. [Work supported by ONR.]

Data-Driven Electricity Price Risk Assessment for Spot Market

Electricity price risk assessment (EPRA) is essential for spot market analysis and operation. The statistical moments (i.e., the mean and standard deviation) of the price need to be assessed to support market risk control. This paper proposes a data-driven approach for EPRA based on the Gaussian process (GP) framework. Compared with the deep learning algorithms, GP has two merits: (1) the scale of training sample required is small and (2) the time-consuming hyperparameter tuning process is avoided. However, the direct application of GP for EPRA is not tractable due to the complicated discrete relationship between the system operating status and the electricity price. To deal with that, a data-driven EPRA framework is developed that contains a GP surrogate model for the direct current optimal power flow (DC-OPF) problem and a hybrid model-data-based hybrid electricity price calculation method. To guarantee the accuracy of EPRA, an adaptability criterion and a second verification process based on the Karush–Kuhn–Tucker (KKT) condition are developed to distinguish the samples with GP learning errors. Numerical results carried out on IEEE benchmark systems demonstrate that the proposed method can achieve exactly the same EPRA results as Monte Carlo (MC) simulation, which significantly improved the computational efficiency.

A Fast, Two-dimensional Gaussian Process Method Based on Celerite: Applications to Transiting Exoplanet Discovery and Characterization

Abstract Gaussian processes (GPs) are commonly used as a model of stochastic variability in astrophysical time series. In particular, GPs are frequently employed to account for correlated stellar variability in planetary transit light curves. The efficient application of GPs to light curves containing thousands to tens of thousands of data points has been made possible by recent advances in GP methods, including the celerite method. Here we present an extension of the celerite method to two input dimensions where, typically, the second dimension is small. This method scales linearly with the total number of data points when the noise in each large dimension is proportional to the same celerite kernel and only the amplitude of the correlated noise varies in the second dimension. We demonstrate the application of this method to the problem of measuring precise transit parameters from multiwavelength light curves and show that it has the potential to improve transit parameters measurements by orders of magnitude. Applications of this method include transit spectroscopy and exomoon detection, as well a broader set of astronomical problems.

Application of SVM, ANN, GRNN, RF, GP and RT models for predicting discharge coefficients of oblique sluice gates using experimental data

AbstractGates are commonly used to adjust water flow in open channels. By using an oblique/inclined gate, the water transferring capacity of open irrigation canals can be increased. Investigation of free and submerged discharge coefficients for inclined sluice gates is the focus of the present study. First an experimental apparatus incorporating an inclined gate was created. The inclined angle (β) and gate opening (a) were experiment variables, and the five inclination angles include: 0° (vertical gate), 15°, 30°, 45° and 60°. Experimental results showed a greater convergence of flow lines under the gate and increasing the gate angle causes the discharge coefficient to increase. Also experiments showed that increasing the submergence rate (yt/a), decreases the inclined gate discharge coefficient. Performance metrics were created for the experimental results. The metrics utilized Gaussian process (GP) regression, support vector machine (SVM), artificial neural networks (ANN), generalized regression neural network (GRNN), random forest (RF) regression and random tree (RT) based models which were used to predict discharge coefficients (Cd) in both submerged and free flow conditions. The model input parameters were the ratio of the upstream water depth to gate opening (y/a) and the inclined angle (β) for free flow and also the submergence rate (yt/a) for submerged flow. The prediction models show that the ANN model in free flow conditions has the following performance metrics: Coefficient of determination, R2= 0.9957, Root Mean Square Error (RMSE) = 0.0044, and Mean Absolute Error (MAE) = 0.0017. The performance metrics for submerged flow conditions were R2 = 0.9922, RMSE = 0.0079 and MAE = 0.0054. The ANN approach is the most accurate model compared to the others.

Error-Controlled Exploration of Chemical Reaction Networks with Gaussian Processes.

For a theoretical understanding of the reactivity of complex chemical systems, relative energies of stationary points on potential energy hypersurfaces need to be calculated to high accuracy. Due to the large number of intermediates present in all but the simplest chemical processes, approximate quantum chemical methods are required that allow for fast evaluations of the relative energies but at the expense of accuracy. Despite the plethora of benchmark studies, the accuracy of a quantum chemical method is often difficult to assess. Moreover, a significant improvement of a method's accuracy (e.g., through reparameterization or systematic model extension) is rarely possible. Here, we present a new approach that allows for the systematic, problem-oriented, and rolling improvement of quantum chemical results through the application of Gaussian processes. Due to its Bayesian nature, reliable error estimates are provided for each prediction. A reference method of high accuracy can be employed if the uncertainty associated with a particular calculation is above a given threshold. The new data point is then added to a growing data set in order to continuously improve the model and, as a result, all subsequent predictions. Previous predictions are validated by the updated model to ensure that uncertainties remain within the given confidence bound, which we call backtracking. We demonstrate our approach with the example of a complex chemical reaction network.

Physics-aware Gaussian processes in remote sensing

Earth observation from satellite sensory data poses challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression has excelled in biophysical parameter estimation tasks from airborne and satellite observations. GP regression is based on solid Bayesian statistics, and generally yields efficient and accurate parameter estimates. However, GPs are typically used for inverse modeling based on concurrent observations and in situ measurements only. Very often a forward model encoding the well-understood physical relations between the state vector and the radiance observations is available though and could be useful to improve predictions and understanding. In this work, we review three GP models that respect and learn the physics of the underlying processes in the context of both forward and inverse modeling. After reviewing the traditional application of GPs for parameter retrieval, we introduce a Joint GP (JGP) model that combines in situ measurements and simulated data in a single GP model. Then, we present a latent force model (LFM) for GP modeling that encodes ordinary differential equations to blend data-driven modeling and physical constraints of the system governing equations. The LFM performs multi-output regression, adapts to the signal characteristics, is able to cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. Finally, we present an Automatic Gaussian Process Emulator (AGAPE) that approximates the forward physical model using concepts from Bayesian optimization and at the same time builds an optimally compact look-up-table for inversion. We give empirical evidence of the performance of these models through illustrative examples of vegetation monitoring and atmospheric modeling.

Optimizing combustion of coal fired boilers for reducing NOx emission using Gaussian Process

Since the mechanism of boiler combustion is extremely complicated and difficult to apply to model and optimize the combustion process directly, data-driven models attract increasingly attention from industry. This paper focuses on the application of Gaussian Process (GP) in optimizing combustion process for reducing NOx emission of a 330 MW boiler. GP is used to model the relationship between the NOx emission characteristic and boiler operation parameters. The hyperparameters of the GP model are optimized via Genetic Algorithm (GA). Based on 670 sets of production data from the 330 MW tangentially fired boiler, two GP models with 13 and 21-inputs are developed, respectively. The experimental result shows that the 21-inputs model provides better prediction performance than 13-inputs model does. The comparison between Support Vector Machines (SVM) and GP is also given under the 21-inputs circumstance. The influences of some inputs are investigated separately. Then, the predicted NOx emission is used as the objective of searching the optimal parameters for the boiler combustion. Under a given production combustion condition, the NOx decreases from 345 ppm to 238 ppm via optimizing the boiler operational parameters using the 21-inputs GP model, which is a reasonable achievement for the coal fired combustion process.

A Unifying Framework for Gaussian Process Pseudo-Point Approximations using Power Expectation Propagation

Gaussian processes (GPs) are flexible distributions over functions that enable high-level assumptions about unknown functions to be encoded in a parsimonious, flexible and general way. Although elegant, the application of GPs is limited by computational and analytical intractabilities that arise when data are sufficiently numerous or when employing non-Gaussian models. Consequently, a wealth of GP approximation schemes have been developed over the last 15 years to address these key limitations. Many of these schemes employ a small set of pseudo data points to summarise the actual data. In this paper, we develop a new pseudo-point approximation framework using Power Expectation Propagation (Power EP) that unifies a large number of these pseudo-point approximations. Unlike much of the previous venerable work in this area, the new framework is built on standard methods for approximate inference (variational free-energy, EP and Power EP methods) rather than employing approximations to the probabilistic generative model itself. In this way, all of approximation is performed at `inference time' rather than at `modelling time' resolving awkward philosophical and empirical questions that trouble previous approaches. Crucially, we demonstrate that the new framework includes new pseudo-point approximation methods that outperform current approaches on regression and classification tasks.

An application of Gaussian processes on ocular artifact removal from EEG.

Consequences of eye movements are one of the main interferences that distort the brain EEG recordings. In this paper, a multi-modal approach is used to estimate the ocular artifacts in the EEG: both vertical and horizontal eye movement signals recorded by an eye tracker are used as a reference to denoise the EEG. A Gaussian process, i.e. a second order statistics method, is assumed to model the link between the eye tracker signals and the EEG signals. The proposed method is thus a non-linear extension of the well-known adaptive filtering and can be applied with a single EEG signal contrary to independent component analysis (ICA) which is extensively used. The results show the applicability and the efficiency of this model on the ocular artifact removal.

Towards a Service-Based Framework for Environmental Data Processing

Scientists are confronted with significant data management problems due to the huge volume and high complexity of environmental data. An important aspect of environmental data management is that data, needed for a process, are not always in the adequate format. In this contribution, we analyze environmental data structure, and model this data using a semantic-based method. Using this model, we design and implement a framework based on Web services for transformation between massive environmental text-based data and relational databases. We present a mapping model for environmental data transformation to be used in the scenario devoted to the methodology for development of stochastic models for prediction of environmental parameters by application of Gaussian processes.

The application of Gaussian processes in the predictions of permeability across mammalian and polydimethylsiloxane membranes

The problem of predicting the rate of percutaneous absorption of a drug is an important issue, particular with the increasing use of the skin as a means of moderating and controlling drug delivery. One key feature of this problem domain is that human skin permeability to penetrants (often characterised by Kp, the permeability coefficient) has been shown to be inherently non-linear when mathematically related to the key physicochemical parameters of penetrants. The aims of the current study were to apply and validate Gaussian process regression methods to datasets for membranes other than human skin, and to explore how the nature of the dataset may influence its analysis. Permeability data for absorption across rodent and pig skin, and polydimethylsiloxane Silastic® membranes was collected from the literature. Two QSPR methods were applied to compare to the Gaussian process models. The results demonstrated that Gaussian process models with different covariance functions outperform the QSPR model for human, pig and rodent datasets, but in general are not good for Silastic® membranes. These results suggest that the physicochemical parameters employed in this study might not be appropriate for developing models that represent this membrane. In addition, the results show the size of the datasets, in both absolute and comparative senses, appears to influence model quality.

The application of Gaussian processes in the prediction of percutaneous absorption

Abstract Objectives The aim was to assess mathematically the nature of a skin permeability dataset and to determine the utility of Gaussian processes in developing a predictive model for skin permeability, comparing it with existing methods for deriving predictive models. Methods Principal component analysis was carried out in order to determine the nature of the dataset. MatLab software was used to assess the performance of Gaussian process, single linear networks (SLN) and quantitative structure-permeability relationships (QSPRs) using a range of statistical measures. Key findings Principal component analysis showed that the dataset is inherently nonlinear. The Gaussian process model yielded a predictive model that provides a significantly more accurate estimate of skin absorption than previous models, particularly QSPRs (which were consistently worse than Gaussian process or SLN models), and does so across a wider range of molecular properties. Gaussian process models appear particularly capable of providing excellent predictions where previous studies have shown QSPRs to fail, such as where penetrants have high log P and high molecular weight. Conclusions A non-linear approach was more appropriate than QSPRs or SLNs for the analysis of the dataset employed herein, as the prediction and confidence values in the prediction given by the Gaussian process are better than with other methods examined. Gaussian process provides a novel way of analysing skin absorption data that is substantially more accurate, statistically robust and reflective of our empirical understanding of skin absorption than the QSPR methods so far applied to skin absorption.

The application of Gaussian processes in the prediction of percutaneous absorption

The aim was to assess mathematically the nature of a skin permeability dataset and to determine the utility of Gaussian processes in developing a predictive model for skin permeability, comparing it with existing methods for deriving predictive models. Principal component analysis was carried out in order to determine the nature of the dataset. MatLab software was used to assess the performance of Gaussian process, single linear networks (SLN) and quantitative structure-permeability relationships (QSPRs) using a range of statistical measures. Principal component analysis showed that the dataset is inherently non-linear. The Gaussian process model yielded a predictive model that provides a significantly more accurate estimate of skin absorption than previous models, particularly QSPRs (which were consistently worse than Gaussian process or SLN models), and does so across a wider range of molecular properties. Gaussian process models appear particularly capable of providing excellent predictions where previous studies have shown QSPRs to fail, such as where penetrants have high log P and high molecular weight. A non-linear approach was more appropriate than QSPRs or SLNs for the analysis of the dataset employed herein, as the prediction and confidence values in the prediction given by the Gaussian process are better than with other methods examined. Gaussian process provides a novel way of analysing skin absorption data that is substantially more accurate, statistically robust and reflective of our empirical understanding of skin absorption than the QSPR methods so far applied to skin absorption.

Gaussian process: an alternative approach for QSAM modeling of peptides

Different statistical modeling methods (SMMs) are used for nonlinear system classification and regression. On the basis of Bayesian probabilistic inference, Gaussian process (GP) is preliminarily used in the field of quantitative structure-activity relationship (QSAR) but has not yet been applied to quantitative sequence-activity model (QSAM) of biosystems. This paper proposes the application of GP as an alternative tool for the QSAM modeling of peptides. To investigate the modeling performance of GP, three classical peptide panels were used: Angiotensin-I converting enzyme inhibitory dipeptides, bradykinin-potentiating pentapeptides and cationic antimicrobial pentadecapeptides. On this basis, we made a comprehensive comparison between the GP and some widely used SMMs such as PLS, artificial neural network (ANN) and support vector machine (SVM), and gave the conclusions as follow: (1) for those of structurally complicated peptides, particularly the polypeptides, linear PLS was incapable of capturing all dependences hidden in the peptide systems, (2) even in assistance with the monitoring technique, ANN was inclined to be overtrained in the cases of insufficient number of peptide samples, (3) SVM and GP performed best for the three peptide panels. Moreover, since GP was able to correlate the linear and nonlinear-hybrid relationship, it was slightly superior to SVM at most peptide sets.