Gaussian Regression Model Research Articles

Multi-task Learning for Gaussian Graphical Regressions with High Dimensional Covariates

Gaussian graphical regression is a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which permits the response variables and covariates to outnumber the sample size. However, traditional approaches of fitting the model via separate node-wise lasso regressions overlook the network-induced structure among these regressions, leading to high error rates, particularly when the number of nodes is large. To address this issue, we propose a multi-task learning estimator for fitting Gaussian graphical regression models, which incorporates a cross-task group sparsity penalty and a within-task element-wise sparsity penalty to govern the sparsity of active covariates and their effects on the graph, respectively. We also develop an efficient augmented Lagrangian algorithm for computation, which solves subproblems with a semi-smooth Newton method. We further prove that our multi-task learning estimator has considerably lower error rates than the separate node-wise regression estimates, as the cross-task penalty enables borrowing information across tasks. We examine the utility of our method through simulations and an application to a gene co-expression network study with brain cancer patients.

Semi-Supervised Soft Computing for Ammonia Nitrogen Using a Self-Constructing Fuzzy Neural Network with an Active Learning Mechanism

Ammonia nitrogen (NH3-N) is a key water quality variable that is difficult to measure in the water treatment process. Data-driven soft computing is one of the effective approaches to address this issue. Since the detection cost of NH3-N is very expensive, a large number of NH3-N values are missing in the collected water quality dataset, that is, a large number of unlabeled data are obtained. To enhance the prediction accuracy of NH3-N, a semi-supervised soft computing method using a self-constructing fuzzy neural network with an active learning mechanism (SS-SCFNN-ALM) is proposed in this study. In the SS-SCFNN-ALM, firstly, to reduce the computational complexity of active learning, the kernel k-means clustering algorithm is utilized to cluster the labeled and unlabeled data, respectively. Then, the clusters with larger information values are selected from the unlabeled data using a distance metric criterion. Furthermore, to improve the quality of the selected samples, a Gaussian regression model is adopted to eliminate the redundant samples with large similarity from the selected clusters. Finally, the selected unlabeled samples are manually labeled, that is, the NH3-N values are added into the dataset. To realize the semi-supervised soft computing of the NH3-N concentration, the labeled dataset and the manually labeled samples are combined and sent to the developed SCFNN. The experimental results demonstrate that the test root mean square error (RMSE) and test accuracy of the proposed SS-SCFNN-ALM are 0.0638 and 86.31%, respectively, which are better than the SCFNN (without the active learning mechanism), MM, DFNN, SOFNN-HPS, and other comparison algorithms.

Analysis of the degradation in transmission accuracy of RV reducers considering the wear clearance between cycloidal wheels and pinwheels

To accurately determine the transmission accuracy degradation pattern of Rotate Vector (RV) reducers due to wear, a predictive method is proposed that simultaneously considers the initial clearance and wear clearance between the cycloid wheel and the pinwheel. The initial clearance is derived from a comprehensive gear system analysis, considering assembly errors, manufacturing errors and modifications. Building on this, the wear depth of the cycloid wheel tooth profile is numerically simulated using Archard's wear theory, revealing the wear distribution pattern under various operating conditions. A Gaussian regression model is used to predict the maximum wear amount for different operational durations. Based on the predicted wear amount, a multi-body dynamic simulation model incorporating wear clearance was established to analyze the transmission error under varying clearance conditions. Results indicate that the wear depth along the tooth profile initially increases and then decreases. The depth and region of wear along the tooth profile gradually increase with load and output speed, with the impact of load on the wear region being greater than that of output speed. Under the initial clearance condition, the maximum transmission error is 22.91″. As the wear clearance increases, transmission accuracy declines sharply. When the cumulative wear clearance reaches 0.2 mm, the transmission error exceeds the allowable backlash limit. This study provides a theoretical reference for predicting accuracy degradation and guides the manufacturing design of RV reducers.

Gaussian Mixture Regression Model with Sparsity for Clustering of Territory Risk in Auto Insurance

Abstract Insurance rating territory design and accurate estimation of territory risk relativities are fundamental aspects of auto insurance rate regulation. It is crucial to develop methodologies that can facilitate the effective design of rating territories and their risk relativities estimate, as they directly impact the rate filing and the decision support of the rate change review process. This article proposes a Gaussian Mixture Regression model clustering approach for territory design. The proposed method incorporates a linear regression model, taking spatial location as model covariates, which helps estimate the cluster mean more accurately. Also, to further enhance the estimation of territory risk relativities, we impose sparsity through sparse matrix decomposition of the membership coefficient matrix obtained from the Gaussian Mixture Regression model. By transitioning from the current hard clustering method to a soft approach, our methodology could improve the evaluation of territory risk for rate-making purposes. Moreover, using non-negative sparse matrix approximation ensures that the estimation of risk relativities for basic rating units remains smooth, effectively eliminating data noise from the territory risk relativity estimate. Overall, our novel methodology aims to significantly enhance the accuracy and reliability of risk analysis in auto insurance. Furthermore, the proposed method exhibits potential for extension to various other domains that involve spatial clustering of data, thereby broadening its applicability and expanding its usefulness beyond auto insurance rate regulation.

Seismic vulnerability analysis of hospitals and school buildings considering the Gaussian regression algorithm

This study combines the Gaussian regression algorithm to propose a nonlinear regression model that can be used to evaluate the seismic vulnerability of regional hospitals and school buildings. The failure features and disaster mechanisms of hospital and school buildings affected by the Jishishan (JSS) earthquake on December 18, 2023, and the Wenchuan (WC) earthquake on May 12, 2008, were reported. The samples of 252 damaged buildings (37 hospitals and 215 schools) in Dujiangyan city affected by the Wenchuan earthquake for which the author participated in the survey were collected and counted. Hospitals and school buildings were classified according to the types of reinforced concrete (RC) and masonry structures, and earthquake vulnerability probability matrices for hospital and school building clusters were established considering the actual failure probabilities. A total of 2103,213 acceleration records (from the Wenchuan earthquake) monitored by 12 real stations were selected. Using dynamic time history and response spectrum analysis methods, time history and spectrum curves were generated, considering the influence of different seismic directions. Using the developed Gaussian regression model, vulnerability comparison curves and parameter matrices considering multiple regression algorithms were generated. This paper considers the effects of the construction year and number of floors on the seismic vulnerability of hospital and school buildings. Seismic vulnerability curves and failure probability matrices were generated and established on the basis of actual structural failure probabilities. According to regression and vulnerability surface analysis, the evaluation results of the proposed model are highly consistent with actual field observations.

A Copula Discretization of Time Series-Type Model for Examining Climate Data

The study presents a comparative analysis of climate data under two scenarios: a Gaussian copula marginal regression model for count time series data and a copula-based bivariate count time series model. These models, built after comprehensive simulations, offer adaptable autocorrelation structures considering the daily average temperature and humidity data observed at a regional airport in Mobile, AL.

Probabilistic ductile deformation limit state prediction of monolithic exterior shear keys based on quantile regression machine learning techniques

Shear strength and ductile deformation capacity of monolithic exterior shear keys play important roles on the seismic behavior of highway bridges. Improving the ductility of the shear key through reasonable design could effectively restrict superstructure displacement and minimize damage to pier columns. However, most existing studies primarily focus on evaluating the shear strength and damage mechanisms of shear keys, with limited attention given to analytical models for assessing ductile deformation capacity. To this end, this study proposes a method that combines quantile regression and machine learning techniques to predict the ductile deformation limit states of shear keys. The proposed numerical modeling method for shear keys is validated using the experimental data on lateral load-displacement curves. On this basis, Latin hypercubic sampling and joint simulation are utilized to establish the ductile deformation limit state database. The ductile deformation limit states of shear keys are characterized by their lateral displacements in three distinct damage states. The main influencing factors of each limit states are investigated by correlation analysis. Three quantile regression machine learning models are trained and constructed to conduct point and interval prediction for the ductile deformation limit states. All three models, particularly the Gaussian process quantile regression model, are proven to demonstrate exceptional prediction accuracy and uncertainty quantification. Experimental data validation confirms that these models outperform the prediction accuracy of existing simplified models.

Enhanced Environmental Sustainability for the Acoustic Absorption Properties of Cabuya Fiber in Building Construction Using Machine Learning Predictive Model

Sustainability in construction is a growing concern due to the significant polluting waste generated before, during, and after a building’s life cycle. The use of natural materials can significantly reduce the environmental footprint in obtaining, manufacturing, transportation, execution, use, maintenance, and demolition of the building, especially when locally sourced. Natural fibers, in particular, can be used in room acoustics, offering good acoustic absorption while meeting sustainability goals. The objectives of this paper are to evaluate cabuya fiber, grown in Ecuador, as an acoustic absorbing material and to introduce a novel approach using machine learning to simulate the material’s acoustic properties. Eight samples of cabuya fiber, bound with a solution of water and Ca(OH)2, were prepared with thicknesses between 12 and 30.6 mm. The sound absorption coefficients (SACs) were calculated using an impedance tube, following international standards. A Gaussian regression model was built for the predictions. The results showed that the 30.6 mm sample achieved maximum absorption coefficients of 0.91 at 2 kHz and 0.9 at 5 kHz. The model predictions are very accurate, with a mean square error of just 0.0002. These findings offer valuable insights into using cabuya fiber and advanced predictive models to enhance building acoustic performance and reduce environmental impact.

A new ridge type estimator and its performance for the linear regression model: Simulation and application

Ridge regression is employed to address the issue of multicollinearity among independent variables. The shrinkage parameter (k) plays a key role in balancing the bias and variance tradeoff. This paper reviewed several promising existing ride regression estimators designed for estimating the ridge or shrinkage parameter k within the Gaussian linear regression model. In addition, we have proposed a new estimator (CK), which is a function of number of independent variables, sample size and standard error of regression model. The performance of our proposed estimator with OLS and existing shrinkage estimators, is compared using extensive Monte Carlo simulations in terms of minimum mean squared error (MSE). Simulation results demonstrated that the proposed CK estimator outperformed other in the majority of the considered simulation scenarios. A real-life data is analyzed to illustrate the findings of the paper.

Advancing solar PV panel power prediction: A comparative machine learning approach in fluctuating environmental conditions

Solar photovoltaic (PV) panels play a crucial role in sustainable energy generation, yet their power output often faces uncertainties due to dynamic weather conditions. In this study, a comparative machine learning approach is introduced, utilizing multivariate regression (MR), support vector machine regression (SVMR), and Gaussian regression (GR) techniques for precise solar PV panel power prediction. The investigation into the impact of environmental factors—solar radiation, ambient temperature, and relative humidity—on PV panel output reveals the superior predictive capabilities of SVMR models. With a mean squared error (MSE) of 0.038, a mean absolute error (MAE) of 0.17, and an R2 value of 0.99, SVMR outperforms GR and MR models. Conversely, Gaussian regression demonstrates comparatively weaker performance, yielding an R2 of 0.88, an MSE of 0.49, and an MAE of 0.63.This research underscores the reliability and enhanced accuracy of the proposed SVMR model in forecasting solar PV panel output. The outcomes presented herein carry significant implications for promoting the widespread adoption of PV panels in electricity generation, particularly in challenging environmental conditions. The findings offer valuable insights into optimizing solar PV deployment, ultimately contributing to the expansion of solar power generation in the national energy landscape. Moreover, the comparative analysis provides insights into how anticipated PV power generation can adapt to varying weather conditions, encompassing factors such as temperature, humidity, and solar radiation.

A novel mixture model for characterizing human aiming performance data

Fitts’ law is often employed as a predictive model for human movement, especially in the field of human-computer interaction. Models with an assumed Gaussian error structure are usually adequate when applied to data collected from controlled studies. However, observational data (often referred to as data gathered ‘in the wild’) typically display noticeable positive skewness relative to a mean trend as users do not routinely try to minimize their task completion time. As such, the exponentially modified Gaussian (EMG) regression model has been applied to aimed movements data. However, it is also of interest to reasonably characterize those regions where a user likely was not trying to minimize their task completion time. In this article, we propose a novel model with a two-component mixture structure—one Gaussian and one exponential—on the errors to identify such a region. An expectation-conditional-maximization (ECM) algorithm is developed for estimation of such a model and some properties of the algorithm are established. The efficacy of the proposed model, as well as its ability to inform model-based clustering, are addressed in this work through extensive simulations and an insightful analysis of a human aiming performance study.

Relationships among six urban air pollutants and identification of pollution types – A case study of Chinese cities above prefecture level

Urban air pollution is caused by the interplay of urban development and natural conditions, but it's unclear which factor has a greater impact. Studying the link between air pollutants and identifying the types of pollution causes is crucial for understanding the pollution mechanisms and formulating efficient management measures. During the research period from 2015 to 2020, this study analyzed the relationships between six air pollutants, calculated the city capacity (CC) and natural condition (NC) scores of 285 cities with the help of the index system and entropy weight TOPSIS model, and employed Gaussian Mixture Model (GMM) and random forest regression model to identify air pollution types. The results show: During the study period, the concentrations of most pollutants decreased, with SO2 experiencing the largest decline, reflecting the significant effectiveness of China's recent atmospheric pollution control efforts. In terms of spatial distribution, the North China Plain (NCP) and the Loess Plateau (LP) remain focal areas of pollution. The correlation analysis results indicate a significant positive correlation among all air pollutants except O3, underscoring the necessity of coordinated pollution control efforts, but the complexity of O3 pollution should not be overlooked. High-value agglomerations of CC scores calculated by the model are predominantly located in the eastern coastal region, while NC scores exhibit two high-value agglomerations in the north and south. Utilizing the GMM, the 285 cities were classified into three categories, and the random forest regression model was employed to identify them as CC dominate, NC dominate, and intermediate types. This paper proposes a novel approach for categorizing city air pollution types, aiming to tailor prevention measures and foster sustainable urban development.

Prediction Models of Growth Characteristics and Yield for Chinese Winter Wheat Based on Machine Learning

In order to eliminate the limitations of traditional winter wheat yield prediction methods, the prediction models based on machine learning are used to improve the accuracy of winter wheat yield prediction. In this study, by collecting a large amount of domestic literature about wheat growth characteristics, the irrigation amount, fertilization amount, soil nutrient status, planting density, maximum leaf area index (LAImax), maximum aboveground dry matter accumulation (Dmax) and yield (Y) were chosen to develop the learning models. Using the data of the irrigation amount, fertilization amount, soil nutrient status and planting density as the training set, the regression prediction models (Gaussian process regression mode, linear regression model, regression tree mode and support vector machine model) were used to train and learn the data of the LAImax, Dmax and Y, respectively. The results show that the Gaussian regression model has the best precision compared to the other models. The coefficients of determination (R2) of the learning results of the Gaussian regression model for the LAImax, Dmax and Y are 0.9, 0.93 and 0.86, and the root mean square error (RMSE) is 0.57, 1125.1 and 640.41. Based on the data of the irrigation amount, nitrogen application amount, potassium application amount, phosphorus application amount, organic matter content, total nitrogen content, alkali-hydrolyzable nitrogen content, available phosphorus content, available potassium content and planting density, the method proposed in this paper can reliably predict the LAImax, the Dmax and Y of winter wheat. The results also have certain reference significance for the yield prediction of other crops.

Exact selective inference with randomization

Summary We introduce a pivot for exact selective inference with randomization. Not only does our pivot lead to exact inference in Gaussian regression models, but it is also available in closed form. We reduce this problem to inference for a bivariate truncated Gaussian variable. By doing so, we give up some power that is achieved with approximate maximum likelihood estimation in Panigrahi & Taylor (2023). Yet our pivot always produces narrower confidence intervals than a closely related data-splitting procedure. We investigate the trade-off between power and exact selective inference on simulated datasets and an HIV drug resistance dataset.

Improved Gaussian regression model for retrieving ground methane levels by considering vertical profile features

Atmospheric methane is one of the major greenhouse gases and has a great impact on climate change. To obtain the polluted levels of atmospheric methane in the ground-level range, this study used satellite observations and vertical profile features derived by atmospheric chemistry model to estimate the ground methane concentrations in first. Then, the improved daily ground-level atmospheric methane concentration dataset with full spatial coverage (100%) and 5-km resolution in mainland China from 2019 to 2021 were retrieved by station-based observations and gaussian regression model. The overall estimated deviation between the estimated ground methane concentrations and the WDCGG station-based measurements is less than 10 ppbv. The R by ten-fold cross-validation is 0.93, and the R2 is 0.87. The distribution of the ground-level methane concentrations in the Chinese region is characterized by high in the east and south, and low in the west and north. On the time scale, ground-level methane concentration in the Chinese region is higher in winter and lower in summer. Meanwhile, the spatial and temporal distribution and changes of ground-level methane in local areas have been analyzed using Shandong Province as an example. The results have a potential to detect changes in the distribution of methane concentration.

Forecasting Consumer Price Index with Federal Open Market Committee Sentiment Index

AbstractThe Federal Open Market Committee (FOMC) is a component of the Federal Reserve System responsible for overseeing open market operations. The FOMC meets roughly eight or more times per year to assess the economy of the United States. After each meeting, the FOMC releases a statement to the press outlining its assessment of the US economy and its monetary policy stance. The sentiment of these statements may have an influence on the US economy and financial markets. Using sentiment and correlational analyses, this research examines how the sentiment of these statements affects the US economy and financial markets by analyzing how FOMC statement sentiment is correlated with the Consumer Price Index (CPI), the National Financial Conditions Index (NFCI), and the Adjusted National Financial Conditions Index (ANFCI). We find evidence to suggest that there is a moderate negative correlation between an FOMC statement's sentiment and the US City Average CPI value associated with the month before and the month after the statement's release. We also find that there is no evidence to suggest there exists a correlation between an FOMC statement's sentiment and the NFCI value associated with the week before or the week after the statement's release. However, we do find evidence to suggest that there is a moderate negative correlation between an FOMC statement's sentiment and the ANFCI value associated with the week before and the week after the statement's release. We also found that out of the three models we tested (linear regression, vine copula regression, and Gaussian copula regression), the Gaussian copula regression model performs the best when forecasting the CPI and the ANFCI. Additionally, we find that when forecasting CPI values, the models that include FOMC statement sentiment are more accurate than the models that exclude FOMC statement sentiment.

Probabilistic post-processing of short to mediumrange temperature forecasts: Implications for heatwave prediction in India.

Accurate and reliable air temperature forecasts are necessary for predicting and responding to thermal disasters such as heat strokes. Forecasts from Numerical Weather Prediction(NWP) models contain biases which require post-processing. Studies assessing the skill of probabilistic post-processing techniques (PPTs) on temperature forecasts in India are lacking. This study aims to evaluate probabilistic post-processing approaches such as Nonhomogeneous Gaussian Regression (NGR) and Bayesian Model Averaging (BMA) for improving daily temperature forecasts from two NWP models, namely, the European Centre for Medium Range Weather Forecasts (ECMWF) and the Global Ensemble Forecast System (GEFS), across the Indian subcontinent. Apart from that, the effect of probabilistic PPT on heatwave prediction skills across India is also evaluated. Results show that probabilistic PPT comprehensively outperform traditional approaches in forecasting temperatures across India at all lead times. In the Himalayan regions where the forecast skill of raw forecasts is low, the probabilistic techniques are not able to produce skillful forecasts even though they perform much better than traditional techniques. The NGR method is found to be the best performing PPT across the Indian region. Post-processing Tmax forecasts using the NGR approach was found to considerably improve the heatwave prediction skill across highly heatwave prone regions in India. The outcomes of this study will be helpful in setting up improved heatwave prediction and early warning systems in India.

Advances in computer AI-assisted multimodal data fusion techniques

Abstract Through the integration of multimodal data fusion technology and computer AI technology, people’s needs for intelligent life can be better met. This paper introduces the alignment and perception algorithm for multimodal data fusion, which is based on combining the multimodal data fusion model. Taking the air pollutant concentration prediction as an example, the time series of air pollutant concentration is obtained through the LSTM model for concentration prediction, and the attention mechanism is introduced to establish the numerical prediction model of air pollution. Different stations are also selected to acquire weather image data, and the TS-Conv-LSTM multimodal spatio-temporal fusion model of air quality images is constructed by utilizing the Conv-LSTM cell as an encoder, and then the TransConv-LSTM cell, which integrates the anti-convolution and the long-short-term memory network cell, as a decoder. The Gaussian regression model was then used to combine numerical prediction and image prediction models, thus achieving the multimodal synergistic prediction of air pollutant concentrations. The RMSE of the ATT-LSTM model on the dataset was reduced to 8.03 compared to the comparison model, and the predictive fit to the image dataset was above 0.75 for all R² values. The lowest MAE value obtained by the multimodal collaborative prediction model is only 3.815, and the highest R² value is up to 0.985. Introducing deep learning techniques into multimodal data fusion helps to explore the value of massive data more deeply and obtain more comprehensive and reliable information about it.

Performance of Alternative Estimators in the Poisson-Inverse Gaussian Regression Model: Simulation and Application

Abstract The study proposed and compared the biased estimators for the Poisson-Inverse Gaussian regression model to deal with correlated regressors. The limitations of each biased estimator are also discussed. Additionally, some biasing parameters for the Stein estimator are proposed. The performance of estimators is evaluated with the help of a simulation study and a real-life application based on the minimum mean squared error criterion. The simulation and application findings favor the ridge estimator with specific biasing parameters because it provides less variation than others.

A Probabilistic Approach to Turbine Uncertainty

Abstract Efficiency is an essential metric for assessing turbine performance. Modern turbines rely heavily on numerical computational fluid dynamics (CFD) tools for design improvement. With more compact turbines leading to lower aspect ratio airfoils, the influence of secondary flows is significant on performance. Secondary flows and detached flows, in general, remain a challenge for commercial CFD solvers; hence, there is a need for high-fidelity experimental data to tune these solvers used by turbine designers. Efficiency measurements in engine-representative test rigs are challenging for multiple reasons; an inherent problem to any experiment is to remove the effects specific to the turbine rig. This problem is compounded by the narrow uncertainty band required to detect the incremental improvements achieved by turbine designers. Efficiency measurements carried out in engine-representative turbine rigs have traditionally relied upon assumptions such as constant gas properties and neglecting heat loss. This research presents an uncertainty framework that combines inputs from experiments and computational tools. This methodology allows quantifying uncertainty for high-fidelity efficiency data in engine-representative turbine facilities. This paper presents probabilistic sampling techniques to allow for uncertainty propagation. The effect of rig-specific effects, such as heat transfer and gas properties, on efficiency is demonstrated. Sources of uncertainty are identified, and a framework is presented which divides the sources into bias and stochastic. The framework allows the combination of experimental and numerical uncertainty. Gaussian regression models are developed to obtain speed-lines for the turbine map using the uncertainty of the measured efficiency.