Beyond Gaussian Processes: Pearson Type VII Processes for Robust Bayesian Regression

A stock price index measures the change in several share prices, which can describe the market and assist investors in deciding on a specific investment. Thus, foreseeing the stock price index benefits investors in creating a better investment strategy. However, forecasting the stock price index can be challenging due to its non-linearity, non-stationary and high uncertainty. Gaussian process regression (GPR) is an attractive and powerful approach for prediction, especially when the data fluctuates over time with fewer restrictions. Besides, the GPR gains advantages over other forecasting techniques as it can offer predictions with uncertainty to provide margin errors. In this study, we evaluate the use of GPR to predict the stock price of Thailand (SET). The SET data are divided into 2 datasets; the data in the year 2015 - 2020 and the data in the year 2020 due to the massive change during the COVID-19 pandemic. The prediction results from the GPR are then compared to the machine learning approaches, artificial neural network (ANN) and recurrent neural network (RNN) using evaluation scores; the root mean square error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE) and the Nash-Sutcliffe efficiency (NSE). The results indicate that the GPR is superior to the ANN and RNN for both datasets as it provides a high prediction accuracy. Moreover, the results suggest that the GPR is less sensitive to the number of input lags in the model. Therefore, the GPR is more favorable for the prediction of SET than the ANN and RNN.
 HIGHLIGHTS
 
 The Gaussian process regression (GPR) was applied to predict the stock price index of Thailand (SET)
 The predictive performance of the GPR was compared to artificial neural networks (ANNs) and recurrent neural networks (RNNs)
 The results indicate that GPR outperformed the other methods as it provided a high prediction accuracy along with prediction intervals
 
 GRAPHICAL ABSTRACT

The wind power industry has experienced a significant increase and popularity in recent times, and the latest statistics indicate that this sector is still thriving. However, one of the essential steps in developing wind energy projects is finding suitable sites for wind farms, which involves understanding the nature of wind speed, wind direction, terrain, and environmental impacts. To predict the wind energy production over the expected lifespan of a wind farm, vertical wind speed extrapolation to the hub height of the wind turbine is necessary. Therefore, this study presents a comprehensive evaluation of seven statistical approaches for vertical wind speed extrapolation, including Generalized Linear Models (GLM), Linear Regression (LR), Support Vector Machines (SVM), Generalized Additive Models (GAM), Gaussian Process Regression (GPR), Regression Tree (RT), and Ensemble Regression (ER). The accuracy of these methods is assessed using performance metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Normalized RMSE (NRMSE), Normalized MSE (NMSE), Mean Bias Error (MBE), Mean Absolute Error (MAE), Mean Percentage Error (MPE), Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE), and R-squared (R2). The study concludes that, on average, GLM performs the best out of all seven statistical methods.

Accurate ultra-short-term wind speed forecasting is great significance to ensure large scale integration of wind power into the power grid, but the randomness, instability, and non-linear nature of wind speed make it very difficult to be predicted accurately. To solve this problem, shifted window stationary attention transformer (SWSA transformer) is proposed based on a global attention mechanism for ultra-short-term forecasting of wind speed. SWSA transformer can sufficiently extract these complicated features of wind speed to improve the prediction accuracy of wind speed. First, positional embedding and temporal embedding are added at the bottom of the proposed method structure to mark wind speed series, which enables complicated global features of wind speed to be more effectively extracted by attention. Second, a shifted window is utilized to enhance the ability of attention to capture features from the edge sequences. Third, a stationary attention mechanism is applied to not only extract features of wind speed but also optimize the encoder-decoder network for smoothing wind speed sequences. Finally, the predicted values of wind speed are obtained using the calculation in the decoder network. To verify the proposed method, tests are performed utilizing data from an real offshore wind farm. The results show that the proposed method outperforms many popular models evaluated by many indexes including gated recurrent unit, Gaussian process regression, long-short term memory, shared weight long short-term memory network, and shared weight long short-term memory network -Gaussian process regression, in terms of mean absolute error, mean square error (MSE), root mean square error, mean absolute percentage error, mean square percentage error, and coefficient of determination (R2).

Evaluation of artificial neurocomputing algorithms and their metacognitive robustness in predictive modeling of fuel consumption rates during tillage

Student academic performance serves as a key indicator in higher education assessment. For students in Informatics Engineering, foundational computing skills are critical to their academic progression, and these are primarily acquired through first-semester courses. This study proposes a predictive model for Cumulative Grade Point Average (GPA) using the Support Vector Regression (SVR) method with a Radial Basis Function (RBF) kernel. The courses "Introduction to Algorithms," "Computation I," "Computation II," and "Data Structures" were selected as independent variables, as they provide essential computing foundations for subsequent coursework. The dataset comprised 270 records, each containing grades from the aforementioned courses and the corresponding GPA achieved by students in their fourth semester. To ensure data quality, outlier detection was performed using the Z-score method, resulting in a refined dataset of 200 entries. This dataset was then split into 75% for training and 25% for testing. A grid search optimization identified the best hyperparameter combination: C = 100, γ = 0.05, and ε = 0.05. Model evaluation yielded promising results, with a Mean Absolute Error (MAE) of 0.0742, a Mean Absolute Percentage Error (MAPE) of 2.19%, a Mean Squared Error (MSE) of 0.012, and an R² score of 0.8695—indicating strong predictive accuracy. Furthermore, the F-test produced a value of 74.9440, which exceeds the critical F-value of 2.5787, confirming the statistical significance of the independent variables in predicting GPA. This model has the potential to support academic monitoring and enhancement efforts by delivering actionable predictions and insights for the Informatics Engineering program.

Accurate estimation of crop parameters, such as Leaf Area Index (LAI) and biomass over large areas using remote sensing techniques, is crucial for monitoring crop growth and yield prediction. In this study, a Gaussian Process Regression (GPR) method was developed to estimate LAI and biomass values of sugarcane during growth season using optical and synthetic-Aperture Radar (SAR) data fusion. Predicting LAI on an independent test data set using the GPR and the combined optical and SAR indices provided better prediction accuracies of LAI; with the GPR based on radial basis function (Root Mean Square Error [RMSE] = 0.34, Mean Absolute Error [MAE] = 0.28 and Mean Absolute Percentage Error [MAPE] = 10.5%) and polynomial function (RMSE = 0.42, MAE = 0.31 and MAPE = 12.58%), respectively. The test results of sugarcane biomass also showed that the GPR (poly) produced the highest statistical results (RMSE = 2.45 kg/m2, MAE = 1.72 kg/m2, MAPE = 8.1%) using the combined indices. The results suggest that the crop biophysical retrieval based on optical and SAR data fusion and GPR proposed in this study could improve LAI and biomass estimation that could help for effective crop growth monitoring and mapping applications.

Earth observation from satellite sensory data pose challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression and other kernel methods have excelled in biophysical parameter estimation tasks from space. GP regression is based on solid Bayesian statistics, and generally yield 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 is available though. In this work, we review three GP models that respect and learn the physics of the underlying processes in the context of inverse modeling. First, we will introduce a Joint GP (JGP) model that combines in situ measurements and simulated data in a single GP model. Second, we present a latent force model (LFM) for GP modeling that encodes ordinary differential equations to blend data-driven modeling and physical models of the system. 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 via interpolation, reducing the number of necessary nodes. Empirical evidence of the performance of these models will be presented through illustrative examples of vegetation monitoring and atmospheric modeling.

Mechanical property prediction plays a crucial role in the steel industry, enabling better materials selection and enhancing production efficiency. In this study, we propose a novel framework that facilitates optimal materials selection for steel’s alloying elements, based on accurate predictions of the Jominy hardness curve. Leveraging Gaussian Process (GP) regression, we provide probabilistic predictions of steel hardenability characteristics from alloy element composition. Taking it a step further, our framework incorporates these accurate predictions into a constrained optimization process, yielding optimal compositions that reduce overall spending while meeting performance specifications. Through data obtained from 1080 steel samples, our GP regression model exhibits high accuracy, achieving an RMSE of 1.37 and showcasing significant improvements in the field. Moreover, our constrained optimization utilizing the GP model and historical market data reveals an average cost reduction of 18% on alloying element expenses, highlighting the tangible cost-saving potential of this approach. By leveraging Gaussian Process (GP) regression, we not only achieve accurate predictions of the Jominy hardness curve based on alloy element composition, but we also introduce a crucial element of uncertainty quantification. This empowers us to place trust in the results of our optimization process, ensuring robust and reliable materials selection. The integration of GP regression and optimization provides a powerful tool for achieving cost-effective materials selection and marks a significant advancement compared to existing studies. This research underscores the promise of machine learning in the steel industry, demonstrating its ability to yield substantial cost savings and enhance decision-making in materials selection.

This paper describes a real-time data collection framework and an adaptive machining learning method for constructing a real-time energy prediction model for a machine tool. To effectively establish the energy consumption pattern of a machine tool over time, the energy prediction model is continuously updated with new measurement data to account for time-varying effects of the machine tool, such as tool wear and machine tool deterioration. In this work, a real-time data collection and processing framework is developed to retrieve raw data from a milling machine tool and its sensors and convert them into relevant input features. The extracted input features are then used to construct the energy prediction model using Gaussian Process (GP) regression. To update the GP regression model with real-time streaming data, we investigate the use of sparse representation of the covariance matrix to reduce the computational and storage demands of the GP regression. We compare computational efficiency of sparse GP to that of full GP regression model and show the effectiveness of the sparse GP regression model for tracking the variation in the energy consumption pattern of the target machine.

Stock price prediction is a crucial, yet highly challenging task due to the nonlinear, volatile, and complex nature of financial markets. Traditional forecasting methods often struggle to capture intricate patterns in real-world data. This study proposes a machine learning-based approach using Gaussian Process Regression (GPR) to predict short-term stock prices, specifically targeting the Open, High, and Low values of stocks listed under the NIFTY 500 index. The model incorporates a rich set of financial indicators including previous close price, trading volume, 52-week highs/lows, and the percentage increase or decrease in value over the past 30 days and past 1 year. The dataset is cleaned, log-transformed to reduce skewness in highly varying financial attributes, scaled and evaluated using k-fold cross-validation to ensure robust performance estimation. The GPR model is trained with a composite kernel combining Radial Basis Function (RBF), WhiteKernel, and ConstantKernel. The model outputs not only point predictions but also provides uncertainty estimations, making it highly suitable for real-world financial decision-making. Evaluation metrics such as Mean Squared Error (MSE), <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{R}^{2}$</tex> score, Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) are computed, and the predictions are visualized for interpretability. Experimental results demonstrate that the proposed model is both accurate and interpretable, with the ability to support investor decisions through data-driven insights. The system achieves a MAPE of 0.748567% and an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{R}^{2}$</tex> score of 0.997453, indicating promising performance in forecasting key stock indicators.

In the hot strip rolling (HSR) process, accurate prediction of bending force can improve the control accuracy of the strip crown and flatness, and further improve the strip shape quality. In this paper, six machine learning models, including Artificial Neural Network (ANN), Support Vector Machine (SVR), Classification and Regression Tree (CART), Bagging Regression Tree (BRT), Least Absolute Shrinkage and Selection operator (LASSO), and Gaussian Process Regression (GPR), were applied to predict the bending force in the HSR process. A comparative experiment was carried out based on a real-life dataset, and the prediction performance of the six models was analyzed from prediction accuracy, stability, and computational cost. The prediction performance of the six models was assessed using three evaluation metrics of root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R2). The results show that the GPR model is considered as the optimal model for bending force prediction with the best prediction accuracy, better stability, and acceptable computational cost. The prediction accuracy and stability of CART and ANN are slightly lower than that of GPR. Although BRT also shows a good combination of prediction accuracy and computational cost, the stability of BRT is the worst in the six models. SVM not only has poor prediction accuracy, but also has the highest computational cost while LASSO showed the worst prediction accuracy.

Accurate prognostication of carbon allowance valuation movements is essential for informing environmental policy formulation and enhancing the efficacy of market-driven regulatory instruments. Sophisticated predictive methodologies enable policymakers to calibrate carbon tax structures more effectively, optimize Emissions Trading Scheme (ETS) functionality, and channel capital toward sustainable, low-emission projects with increased confidence. This research focuses on the Tianjin Emissions Trading Scheme (TJTS) — an early provincial-level carbon exchange established as a component of China’s comprehensive national decarbonization agenda. We introduce a novel prediction framework utilizing Gaussian process regression (GPR), wherein model hyperparameters are determined via Bayesian optimization. This approach facilitates the estimator’s dynamic adaptation to unobserved market dynamics and latent trading patterns. Our empirical analysis employs daily settlement prices for Tianjin Emission Allowances (TJEA) spanning December 26, 2013, to March 23, 2021. This period encompasses significant regulatory reforms, distinct phases of market maturation, and evolving participant behavior within China’s progressively integrated national carbon pricing system. Model performance was rigorously evaluated using an out-of-sample testing window from June 8, 2020, to March 23, 2021. The results demonstrate exceptional predictive accuracy, quantified by a relative root-mean-square error (RRMSE) of 0.3818%, root-mean-square error (RMSE) of 0.0971, mean absolute error (MAE) of 0.0628, and a correlation coefficient (CC) reaching 99.838%. To our knowledge, this constitutes the inaugural application of Gaussian process regression within the context of China’s carbon trading exchanges. Beyond advancing theoretical insights into price discovery mechanisms within nascent emissions markets, the developed methodology offers a versatile analytical template readily transferable to comparable cap-and-trade systems globally.

River stream estimation is a subject matter that needs constant research and development since it is all-important in the management of water resources, meeting the water demand, irrigation and agricultural activities, and providing distant signal in unwanted situations such as floods. Unfortunately, a universal technique has been impossible to talk about yet although many techniques have been used for estimation and modeling. This has made it necessary to develop different techniques and / or to make comparisons between techniques and to determine the most accurate method for the parameters used. In this context, in this study, the distribution graphs of the flow data fourteen stations located in the Euphrates-Tigris Basin for the years 1981-2010 were created and their conformity to the normal distribution was investigated Evaluation has been made with Adaptive Neural Fuzzy Logic System (ANFIS), Support Vector Regression (SVR) techniques and the newly introduced Gaussian Process Regression (GPR), Extreme Learning Machine (ELM) and Emotional Neural Networks (ENN) artificial intelligence techniques. Root Mean Square Error (RMSE), Mean Square Error (MSE), Mean Absolute Error (MAE) and correlation coefficient (r), which are frequently used, were used to determine the model performance. In addition, it is aimed to find out which technique gives better results with rank analysis. Although all models work well, the sequence with regards to the comparison outcomes of the techniques obtained from rank analysis was observed to be ELM, GPR, ENN, SVR, ANFIS respectively. In order to better interpret the results, Taylor diagrams and time series graphics of the model outputs were created.

Accurately estimating the amount of evaporation loss is necessary for scheduling and calculating irrigation water requirements. In this study, four machine learning (ML) modeling approaches, extreme learning machine (ELM), gradient boosting machine (GBM), quantile random forest (QRF), and Gaussian process regression (GPR), have been developed to estimate the monthly evaporation loss over two stations located in Iraq. Monthly climatical parameters have been used as an input variable for simulating the evaporation rate. Several statistical measures (e.g., mean absolute error (MAE), correlation coefficient (R), mean absolute percentage error (MAPE), and modified index of agreement (Md)), as well as graphical inspection, were used to compare the performances of the applied models. The results showed that the GBM model has much better performance in predicting monthly evaporation over two stations compared to other applied models. For the first case study which was in Diyala, the results showed a prediction enhancement in terms of MAE and RMSE by 7.17%, 21.01%; 16.51%, 15.74%; and 23.14%, 26.64%; using GBM compared to ELM, GPR, and QRF, respectively. However, for the second case study (in Erbil), the prediction enhancement was improved in terms of reduction of MAE and RMSE by 10.88%, 9.24%; 15.24%, 5%; and 16.06%, 15.76%; respectively, compared to ELM, GPR, and QRF models. The results of the proposed GMBM model can therefore assist local stakeholders in the management of water resources.

Development of machine learning-based standalone GUI application for predicting hydraulic conductivity and compaction parameters of lateritic soils