Nonstationary Gaussian Process Discriminant Analysis With Variable Selection for High-Dimensional Functional Data

High-dimensional classification and feature selection tasks are ubiquitous with the recent advancement in data acquisition technology. In several application areas such as biology, genomics, and proteomics, the data are often functional in their nature and exhibit a degree of roughness and nonstationarity. These structures pose additional challenges to commonly used methods that rely mainly on a two-stage approach performing variable selection and classification separately. We propose in this work a novel Gaussian process discriminant analysis (GPDA) that combines these steps in a unified framework. Our model is a two-layer nonstationary Gaussian process coupled with an Ising prior to identify differentially-distributed locations. Scalable inference is achieved via developing a variational scheme that exploits advances in the use of sparse inverse covariance matrices. We demonstrate the performance of our methodology on simulated datasets and two proteomics datasets: breast cancer and SARS-CoV-2. Our approach distinguishes itself by offering explainability as well as uncertainty quantification in addition to low computational cost, which are crucial to increase trust and social acceptance of data-driven tools. Supplementary materials for this article are available online.

Probabilistic Forecasting of Electricity Demand Incorporating Mobility Data

Due to extreme weather conditions and anomalous events such as the COVID-19 pandemic, utilities and grid operators worldwide face unprecedented challenges. These unanticipated changes in trends introduce new uncertainties in conventional short-term electricity demand forecasting (EDF) since its result depends on recent usage as an input variable. In order to quantify the uncertainty of EDF effectively, this paper proposes a comprehensive probabilistic EFD method based on Gaussian process regression (GPR) and kernel density estimation (KDE). GPR is a non-parametric method based on Bayesian theory, which can handle the uncertainties in EDF using limited data. Mobility data is incorporated to manage uncertainty and pattern changes and increase forecasting model scalability. This study first performs a correlation study for feature selection that comprises weather, renewable and non-renewable energy, and mobility data. Then, different kernel functions of GPR are compared, and the optimal function is recommended for real applications. Finally, real data are used to validate the effectiveness of the proposed model and are elaborated with three scenarios. Comparison results with other conventional adopted methods show that the proposed method can achieve high forecasting accuracy with a minimum quantity of data while addressing forecasting uncertainty, thus improving decision-making.

Estimation of Covid-19 Prevalence Dynamics from Pooled Data

Estimating the prevalence of a disease, such as COVID-19, is necessary for evaluating and mitigating risks of its transmission. Estimates that consider how prevalence changes with time provide more information about these risks but are difficult to obtain due to the necessary survey intensity and commensurate testing costs. Motivated by a dataset on COVID-19, from the University of Notre Dame, we propose pooling and jointly testing multiple samples to reduce testing costs. A nonparametric, hierarchical Bayesian model is used to infer population prevalence from the pooled test results without needing to retest individuals from pools that test positive. This approach is shown to reduce uncertainty compared to individual testing at the same budget and to produce similar estimates compared to individual testing at a much higher budget through simulation studies and an analysis of COVID-19 infections at Notre Dame.

Gaussian Process-aided Transfer Learning for Probabilistic Load Forecasting against Anomalous Events

A probabilistic load forecasting method that can deal with sudden load pattern changes caused by abnormal events such as COVID-19 is proposed in this paper. The deep residual network (ResNet) is first applied to extract the load pattern for the normal period from historical data. When an abnormal event occurs, a Gaussian Process (GP) with a composite kernel is utilized to adapt to the changes on load pattern by estimating the forecasting residual of the ResNet. The designed kernel enables the proposed method to adapt rapidly to changes in the load pattern and effectively quantify the uncertainties caused by the abnormal event using a few training samples. Comparative tests with state-of-the-art point and probabilistic forecasting methods demonstrate the effectiveness of the proposed method. IEEE

EPIDEMICS FROM THE EYE OF THE PATHOGEN

While a common trend in disease modeling is to develop models of increasing complexity, it was recently pointed out that outbreaks appear remarkably simple when viewed in the incidence vs. cumulative cases (ICC) plane. This article details the theory behind this phenomenon by analyzing the stochastic Susceptible, Infected, Recovered (SIR) model in the cumulative cases domain. We prove that the Markov chain associated with this model reduces, in the ICC plane, to a pure birth chain for the cumulative number of cases, whose limit leads to an independent increments Gaussian process that fluctuates about a deterministic ICC curve. We calculate the associated variance and quantify the additional variability due to estimating incidence over a finite period of time. We also illustrate the universality brought forth by the ICC concept on real-world data for Influenza A and for the COVID-19 outbreak in Arizona. © 2022 SIAM.Published by SIAM.

Impact of Upsurge in Covid-19 Cases on Indian Stock Market: A Machine Learning Approach

In the present study, the influence of the surge in pandemic cases and fatalities due to pandemics on the stock performance of NIFTY 50 have been analyzed by employing a regression analysis algorithm using Python Software. The data have been collected for 27 months starting from 1st Jan 2020 to 31st March 2022 and for the application of machine learning tools the data connected to the stock market and COVID 19 have been integrated into the first phase and thereafter preprocessing has been carried out on the data to bring uniformity to data in the second phase. After preprocessing in the third phase data has been evaluated using five leading regression algorithms. The findings of the study reflected that COVID 19 figures and fatalities have severally impacted the stock market returns of the leading index i.e., NIFTY 50. Further, it was gathered from the study that REPTree regression would be a better fit to the model and Gaussian Process would be least fitted to the model as REPTree the lower values of MAE, RMSE, RAE, and R2 error in case of performance evaluation of upsurge in COVID 19 fatalities and surge in stock market returns. © 2022 IEEE.

Backcasting COVID-19: a physics-informed estimate for early case incidence.

It is widely accepted that the number of reported cases during the first stages of the COVID-19 pandemic severely underestimates the number of actual cases. We leverage delay embedding theorems of Whitney and Takens and use Gaussian process regression to estimate the number of cases during the first 2020 wave based on the second wave of the epidemic in several European countries, South Korea and Brazil. We assume that the second wave was more accurately monitored, even though we acknowledge that behavioural changes occurred during the pandemic and region- (or country-) specific monitoring protocols evolved. We then construct a manifold diffeomorphic to that of the implied original dynamical system, using fatalities or hospitalizations only. Finally, we restrict the diffeomorphism to the reported cases coordinate of the dynamical system. Our main finding is that in the European countries studied, the actual cases are under-reported by as much as 50%. On the other hand, in South Korea-which had a proactive mitigation approach-a far smaller discrepancy between the actual and reported cases is predicted, with an approximately 18% predicted underestimation. We believe that our backcasting framework is applicable to other epidemic outbreaks where (due to limited or poor quality data) there is uncertainty around the actual cases.

Bayesian inference

Bayesian statistical methods have become more popular in different applications of scientific research over the past several decades. This is mainly due to the computing capacity of modern machines and the recent advances in Bayesian computational methodologies. In this chapter, we give a brief introduction to Bayesian analysis and discuss the difference between Bayesian and classical frequentist statistics. To illustrate Bayesian methodologies, a diagnostic COVID-19 test is used to present the basic principles of the Bayesian approach, prior distribution, likelihood function, and posterior distribution. As an application of the Bayesian methodologies, we introduce Bayesian linear regression and Gaussian process regression and their Bayesian inference framework. © 2023 Elsevier Inc. All rights reserved.

Machine learning for optimizing daily COVID-19 vaccine dissemination to combat the pandemic.

Introduction: Vaccines are the most important instrument for bringing the pandemic to a close and saving lives and helping to reduce the risks of infection. It is important that everyone has equal access to immunizations that are both safe and effective. There is no one who is safe until everyone gets vaccinated. COVID-19 vaccinations are a game-changer in the fight against diseases. In addition to examining attitudes toward these vaccines in Africa, Asia, Oceania, Europe, North America, and South America, the purpose of this paper is to predict the acceptability of COVID-19 vaccines and study their predictors. Materials and methods: Kaggle datasets are used to estimate the prediction outcomes of the daily COVID-19 vaccination to prevent a pandemic. The Kaggle data sets are classified into training and testing datasets. The training dataset is comprised of COVID-19 daily data from the 13th of December 2020 to the 13th of June 2021, while the testing dataset is comprised of COVID-19 daily data from the 14th of June 2021 to the 14th of October 2021. For the prediction of daily COVID-19 vaccination, four well-known machine learning algorithms were described and used in this study: CUBIST, Gaussian Process (GAUSS), Elastic Net (ENET), Spikes, and Slab (SPIKES). Results: Among the models considered in this paper, CUBIST has the best prediction accuracy in terms of Mean Absolute Scaled Error (MASE) of 9.7368 for Asia, 2.8901 for America, 13.2169 for Oceania, and 3.9510 for South America respectively. Conclusion: This research shows that machine learning can be of great benefit for optimizing daily immunization of citizens across the globe. And if used properly, it can help decision makers and health administrators to comprehend immunization rates and create strategies to enhance them.

Nonstationary Gaussian Process Discriminant Analysis With Variable Selection for High-Dimensional Functional Data

High-dimensional classification and feature selection tasks are ubiquitous with the recent advancement in data acquisition technology. In several application areas such as biology, genomics, and proteomics, the data are often functional in their nature and exhibit a degree of roughness and nonstationarity. These structures pose additional challenges to commonly used methods that rely mainly on a two-stage approach performing variable selection and classification separately. We propose in this work a novel Gaussian process discriminant analysis (GPDA) that combines these steps in a unified framework. Our model is a two-layer nonstationary Gaussian process coupled with an lsing prior to identify differentially-distributed locations. Scalable inference is achieved via developing a variational scheme that exploits advances in the use of sparse inverse covariance matrices. We demonstrate the performance of our methodology on simulated datasets and two proteomics datasets: breast cancer and SARS-CoV-2. Our approach distinguishes itself by offering explainability as well as uncertainty quantification in addition to low computational cost, which are crucial to increase trust and social acceptance of data-driven tools. Supplementary materials for this article are available online.

Bayesian inference

Bayesian statistical methods have become more popular in different applications of scientific research over the past several decades. This is mainly due to the computing capacity of modern machines and the recent advances in Bayesian computational methodologies. In this chapter, we give a brief introduction to Bayesian analysis and discuss the difference between Bayesian and classical frequentist statistics. To illustrate Bayesian methodologies, a diagnostic COVID-19 test is used to present the basic principles of the Bayesian approach, prior distribution, likelihood function, and posterior distribution. As an application of the Bayesian methodologies, we introduce Bayesian linear regression and Gaussian process regression and their Bayesian inference framework.

Multi-outputs Gaussian process for predicting Burkina Faso COVID-19 spread using correlations from the weather parameters.

The novel coronavirus has affected all regions of the world, but each country has experienced different rates of infection. In West Africa, in particular, infection rates remain low as compared to other parts of the world. This heterogeneity in the spread of COVID-19 raises a lot of questions that are still unanswered. However, some studies point out that people's mobility, size of gatherings, rate of testing, and weather have a great impact on the COVID-19 spread. In this work, we first evaluate the correlation between meteorological parameters and COVID-19 cases using Spearman's rank correlation. Secondly, multi-output Gaussian processes (MOGP) are used to predict the daily confirmed COVID-19 cases by exploring its relationships with meteorological parameters. The number of daily reported COVID-19 cases, as well as, weather variables collected from March 9, 2020, to October 18, 2021, were used in the analysis. The weather variables considered in the analysis are the mean temperature, relative humidity, wind direction, insolation, precipitation, and wind speed. The predicting model was constructed exploiting the correlation between the data of the daily confirmed COVID-19 cases and data of the weather variables. The results show that a significant correlation between the daily confirmed COVID-19 cases was found with humidity, wind direction, wind speed, and insolation. These parameters are used to construct the predictive model using the Multi-Output Gaussian process (MOGP). Different combinations of the data of meteorological parameters together with the data of daily reported COVID-19 cases were used to derive different models. We found that the best predictor is obtained using the combination of Humidity and insolation. This model is then used to predict the daily confirmed COVID-19 cases knowing the humidity and Insolation.

Forecasting Crude Oil Prices with Major S&P 500 Stock Prices: Deep Learning, Gaussian Process, and Vine Copula

This paper introduces methodologies in forecasting oil prices (Brent and WTI) with multivariate time series of major S&P 500 stock prices using Gaussian process modeling, deep learning, and vine copula regression. We also apply Bayesian variable selection and nonlinear principal component analysis (NLPCA) for data dimension reduction. With a reduced number of important covariates, we also forecast oil prices (Brent and WTI) with multivariate time series of major S&P 500 stock prices using Gaussian process modeling, deep learning, and vine copula regression. To apply real data to the proposed methods, we select monthly log returns of 2 oil prices and 74 large-cap, major S&P 500 stock prices across the period of February 2001–October 2019. We conclude that vine copula regression with NLPCA is superior overall to other proposed methods in terms of the measures of prediction errors.

Energy Consumption Prediction for Fused Deposition Modelling 3D Printing Using Machine Learning

Additive manufacturing (AM) technologies are growing more and more in the manufacturing industry;the increase in world energy consumption encourages the quantification and optimization of energy use in additive manufacturing processes. Orientation of the part to be printed is very important for reducing energy consumption. Our work focuses on defining the most appropriate direction for minimizing energy consumption. In this paper, twelve machine learning (ML) algorithms are applied to model energy consumption in the fused deposition modelling (FDM) process using a database of the FDM 3D printing of isovolumetric mechanical components. The adequate predicted model was selected using four performance criteria: mean absolute error (MAE), root mean squared error (RMSE), R-squared (R2), and explained variance score (EVS). It was clearly seen that the Gaussian process regressor (GPR) model estimates the energy consumption in FDM process with high accuracy: R2 > 99%, EVS > 99%, MAE < 3.89, and RMSE < 5.8.

Multi-Output Gaussian Process-Based Data Augmentation for Multi-Building and Multi-Floor Indoor Localization

Location fingerprinting based on Received Signal Strength Indicator (RSSI) has become a mainstream indoor localization technique due to its advantage of not requiring the installation of new infrastructure and the modification of existing devices, especially given the prevalence of Wi-Fi-enabled devices and the ubiquitous Wi-Fi access in modern buildings. The use of Artificial Intelligence (AI)/Machine Learning (ML) technologies like Deep Neural Networks (DNNs) makes location fingerprinting more accurate and reliable, especially for large-scale multi-building and multi-floor indoor localization. The application of DNNs for indoor localization, however, depends on a large amount of preprocessed and deliberately-labeled data for their training. Considering the difficulty of the data collection in an indoor environment, especially under the current epidemic situation of COVID-19, we investigate three different methods of RSSI data augmentation based on Multi-Output Gaussian Process (MOGP), i.e., by a single floor, by neighboring floors, and by a single building;unlike Single-Output Gaussian Process (SOGP), MOGP can take into account the correlation among RSSI observations from multiple Access Points (APs) deployed closely to each other (e.g., APs on the same floor of a building) by collectively handling them. The feasibility of the MOGP-based RSSI data augmentation is demonstrated through experiments using a recently-published work based on Recurrent Neural Network (RNN) indoor localization model and the UJIIndoorLoc, i.e., the most popular publicly-available multi-building and multi-floor indoor localization database;the RNN model trained with the UJIIndoorLoc database, augmented by using the whole RSSI data of a building in fitting an MOGP model (i.e., by a single building), outperforms the other two augmentation methods and reduces the mean three-dimensional positioning error from 8.62 m to 8.42 m in comparison to the RNN model trained with the original UJIIndoorLoc database. © 2022 IEEE.

Effect of increased number of COVID-19 tests using supervised machine learning models

Machine learning is widely being used in medical field for disease diagnostics and research.The area of machine learning is mainly classified into 3 parts: supervised, unsupervised and reinforcement learning.Supervised machine learning (ML) algorithms are used in this paper for modeling and showing the impact of increased testing on the number of daily confirmed cases of COVID-19. The algorithms used to carry out this study are decision tree regression and random forest regression. Machine learning for modeling has proven to be significant for forecasting and hence decision making over the future course of actions. In this paper, Gaussian process regression has been used for modeling as well as forecasting the daily confirmed cases in South Korea. The results obtained show that if the number of tests conducted is increased to the population of South Korea, approximately equal to 51, 286, 183, the peak in the daily cases is obtained earlier and hence the overall number of daily cases is less compared to current cases.

A hierarchical Bayesian approach for modeling the evolution of the 7-day moving average of the number of deaths by COVID-19.

In this paper, we propose a hierarchical Bayesian approach for modeling the evolution of the 7-day moving average for the number of deaths due to COVID-19 in a country, state or city. The proposed approach is based on a Gaussian process regression model. The main advantage of this model is that it assumes that a nonlinear function f used for modeling the observed data is an unknown random parameter in opposite to usual approaches that set up f as being a known mathematical function. This assumption allows the development of a Bayesian approach with a Gaussian process prior over f. In order to estimate the parameters of interest, we develop an MCMC algorithm based on the Metropolis-within-Gibbs sampling algorithm. We also present a procedure for making predictions. The proposed method is illustrated in a case study, in which, we model the 7-day moving average for the number of deaths recorded in the state of São Paulo, Brazil. Results obtained show that the proposed method is very effective in modeling and predicting the values of the 7-day moving average.

Framework for enhancing the estimation of model parameters for data with a high level of uncertainty.

Reliable data are essential to obtain adequate simulations for forecasting the dynamics of epidemics. In this context, several political, economic, and social factors may cause inconsistencies in the reported data, which reflect the capacity for realistic simulations and predictions. In the case of COVID-19, for example, such uncertainties are mainly motivated by large-scale underreporting of cases due to reduced testing capacity in some locations. In order to mitigate the effects of noise in the data used to estimate parameters of models, we propose strategies capable of improving the ability to predict the spread of the diseases. Using a compartmental model in a COVID-19 study case, we show that the regularization of data by means of Gaussian process regression can reduce the variability of successive forecasts, improving predictive ability. We also present the advantages of adopting parameters of compartmental models that vary over time, in detriment to the usual approach with constant values.

Data Analysis Using a Coupled System of Ornstein–Uhlenbeck Equations Driven by Lévy Processes

In this work, we have analyzed data sets from various fields using a coupled Ornstein–Uhlenbeck (OU) system of equations driven by Lévy processes. The Ornstein–Uhlenbeck model is well known for its ability to capture stochastic behaviors when used as a predictive model. There’s empirical evidence showing that there exist dependencies or correlations between events;thus, we may be able to model them together. Here we show such correlation between data from finance, geophysics and health as well as show the predictive performance when they are modeled with a coupled Ornstein–Uhlenbeck system of equations. The results show that the solution to the stochastic system provides a good fit to the data sets analyzed. In addition by comparing the results obtained when the BDLP is a Γ(a,b) process or an IG(a,b) process, we are able to deduce the best choice out of the two to model our data sets.

A multi-task Gaussian process self-attention neural network for real-time prediction of the need for mechanical ventilators in COVID-19 patients.

OBJECTIVE: The Coronavirus Disease 2019 (COVID-19) pandemic has overwhelmed the capacity of healthcare resources and posed a challenge for worldwide hospitals. The ability to distinguish potentially deteriorating patients from the rest helps facilitate reasonable allocation of medical resources, such as ventilators, hospital beds, and human resources. The real-time accurate prediction of a patient's risk scores could also help physicians to provide earlier respiratory support for the patient and reduce the risk of mortality. METHODS: We propose a robust real-time prediction model for the in-hospital COVID-19 patients' probability of requiring mechanical ventilation (MV). The end-to-end neural network model incorporates the Multi-task Gaussian Process to handle the irregular sampling rate in observational data together with a self-attention neural network for the prediction task. RESULTS: We evaluate our model on a large database with 9,532 nationwide in-hospital patients with COVID-19. The model demonstrates significant robustness and consistency improvements compared to conventional machine learning models. The proposed prediction model also shows performance improvements in terms of area under the receiver operating characteristic curve (AUROC) and area under the precision-recall curve (AUPRC) compared to various deep learning models, especially at early times after a patient's hospital admission. CONCLUSION: The availability of large and real-time clinical data calls for new methods to make the best use of them for real-time patient risk prediction. It is not ideal for simplifying the data for traditional methods or for making unrealistic assumptions that deviate from observation's true dynamics. We demonstrate a pilot effort to harmonize cross-sectional and longitudinal information for mechanical ventilation needing prediction.