Prediction of COVID-19 Confirmed Cases Using Gradient Boosting Regression Method

The fast spread of coronavirus disease (COVID-19) caused by SARSCoV-2 has become a pandemic and a serious threat to the world. As of May 30, 2020, this disease had infected more than 6 million people globally, with hundreds of thousands of deaths. Therefore, there is an urgent need to predict confirmed cases so as to analyze the impact of COVID-19 and practice readiness in healthcare systems. This study uses gradient boosting regression (GBR) to build a trained model to predict the daily total confirmed cases of COVID-19. The GBR method can minimize the loss function of the training process and create a single strong learner from weak learners. Experiments are conducted on a dataset of daily confirmed COVID-19 cases from January 22, 2020, to May 30, 2020. The results are evaluated on a set of evaluation performance measures using 10-fold cross-validation to demonstrate the effectiveness of the GBR method. The results reveal that the GBR model achieves 0.00686 root mean square error, the lowest among several comparative models.


Introduction
At the end of December 2019, patients with clinical symptoms similar to those of the common cold and pneumonia were reported in Wuhan city, China. Chinese scientists detected that the cause of this pneumonia was a novel coronavirus [1]. The most common clinical features of the disease are cough, fever, and difficulty in breathing. More severe symptoms in some cases can include lung damage, severe acute respiratory syndrome (SARS), breathing failure, and kidney failure, possibly causing death [2]. Coronavirus disease 2019  was named by the World Health Organization (WHO) on February 11, 2020 [3]. The International Committee on Taxonomy of Viruses (ICTV) refers to COVID-19 as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) [3].
Published studies have shown that MERS-CoV and SARS-CoV infections, respectively, spread from dromedary camels and civet cats to humans. CoVs can be transmitted between humans and several animals, such as cattle, cats, camels, and bats [5]. Animal CoVs, such as MERS-CoV, it is noted that it can hardly to be transmitted to humans and then spread between humans [6]. Compared to SARS-CoV and MERS-CoV, SARS-CoV-2 spreads easily and has a low mortality rate [7].
On May 30, 2020, the WHO reported that COVID-19 had infected more than 6 million people in 213 countries and territories, with 369,126 fatalities since the cases were officially registered in January [6]. COVID-19 has become a serious worldwide problem, especially in the United States, Brazil, Russia, Spain, the United Kingdom, India, and Italy [8]. Since the disease has no specific treatment and it spreads rapidly, it is crucial to prepare healthcare services for future cases [9].
Machine learning and approximation algorithms have been used to solve problems in areas such as healthcare [10], industry [11], cloud computing [12,13], human activity recognition [14], and brain tumor classification [15]. Machine learning models are certainly useful to forecast future cases to take control of this global pandemic [16][17][18].
Few studies have used statistical models and artificial intelligence (AI) methods to predict coronavirus cases. The autoregressive integrated moving average (ARIMA) was used to forecast the spread of SARS-CoV-2 [18]. An AI framework to predict the clinical severity of coronavirus was proposed in [19]. A simple and powerful method was proposed to predict the continuation of COVID-19 [20]. However, to develop an effective model to predict future confirmed cases of COVID-19 in the world in different time periods is a challenging issue that needs a solution.
We aim to develop an effective model using a gradient boosting regression (GBR) algorithm to predict daily total confirmed cases and enhance the readiness of healthcare systems.
The rest of the paper is organized as follows. Section 2 explains the materials and methods, including a COVID-19 data sample, the GBR method, and performance evaluation measures. Section 3 describes our experiments and their results. Section 4 provides our conclusions and suggestions for future work.

Materials and Methods
We describe the dataset used to evaluate the work, our computational method, and performance evaluation measures.

COVID-19 Data Sample
The data sample used in this study includes the total daily confirmed cases of COVID-19, collected from the official website (https://gisanddata.maps.arcgis.com/apps/opsdashboard/index.html) of Johns Hopkins University, in the period from January 22, 2020, to May 30, 2020, all over the world. It contains 130 time-series instances from which to build our model, which we compare to other predictive models. Tab. 1 shows some example instances from the collected COVID-19 data sample Fig. 1.
The time-series instances of the dataset were processed for supervised learning methods using the timeseries data of the previous days as input to predict the next day. We used a sliding window technique to create three public benchmark datasets based on different time-intervals (5, 10, and 15 days), respectively, called COVID-19_DataSet1, 1 COVID-19_DataSet2, 2 and COVID-19_DataSet3. 3 Tabs. 2-4 demonstrate the first five instances of these datasets, where TS1; TS2; …; TS15 are features variables of the previous days, and Y is the predicted variable of the next day.    TS1  TS2  TS3  TS4  TS5  Y   555  654  941  1434  2118  2927  654  941  1434  2118  2927  5578  941  1434  2118  2927  5578  6166  1434  2118  2927  5578  6166  8234  1434  2118  2927  5578  6166  8234 To make the values of independent feature variables suitable to ML methods and in a specific range, we transformed them to values between zero and one using a min-max normalization technique: where f i;j is the feature variable in row i and column j of a COVID-19 dataset.
Algorithm 1 lists the steps to train the GBR method to build a trained model with training set We train the GBR method on COVID-19 confirmed case datasets containing feature variables (x i ) that represent total confirmed cases for previous days, and target labels (y i ) that are confirmed cases of the following days. The trained GBR model predicts the total confirmed cases for the next day based on those of previous days.
. . . ; n: 2.2. Fitting a base learner (e.g., tree) h m x i ð Þ to pseudo-residuals, i.e., training it using the training set x i ; r im ð Þ f g n i¼1 . 2.3 Computing a multiplier q m by solving the one-dimensional optimization problem: 2.4. Updating the model:

Performance Evaluation Measures
To evaluate the experimental results of the study, a set of performance measures is utilized to evaluate the differences between the predicted and actual numbers of COVID-19 confirmed cases. These are the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R-squared). RMSE and MAE evaluate the errors between predicted and actual values, which should be small. In contrast, higher values of R-squared give a good indication that the model can correctly predict data instances. These measures are calculated as whereŷ i and y i , respectively, are vectors of the ith predicted and actual values, and y is the mean value of y i .

Experiments and Discussion
We conducted a set of experiments to compare the GBR model to other predictive models in terms of the above performance evaluation measures. We describe and discuss the experimental results for the three COVID-19 datasets. All models were trained based on 10-fold cross-validation, a robust technique, used to train and evaluate ML models. It divides the dataset into 10 folds. The validation process is executed ten times, each time using one fold for testing and the others for training. The final evaluation result is the average over the 10 folds. Tabs. 5-7 show the RMSE, MAE, R-squared, average, and standard deviation using this technique on the three datasets.  Figs. 2-4, we visualize the averaged results of RSME, MAE, and R-squared for the GBR method on the three datasets. From the results, it is clear that the best evaluation results are on COVID-19_DataSet3, which is for a time interval of 15 days. This means that to train the model using a long period of total confirmed cases can produce more accurate predictions.  We compared the performance of the GBR method to that of the popular ML regression methods of extreme gradient boosting regression (XGBR), support vector regression (SVR), and decision tree regression (DTR). Figs. 5-7 show the actual and predicted total confirmed cases of fold 6 test instances for each dataset using GBR, XGBR, SVR, and DTR. From the figures, we can see that the actual and predicted total confirmed cases are better fitted by GBR than by the other methods, and SVR has the worst fitting among the compared methods.   For the 10-fold cross-validation test, we report the average results of RMSE, MAE, and R-squared on the three datasets in Tabs. 8-10. We can notice that GBR achieves the lowest average MAE and the highest average R-squared among the four methods. Figs. 8-10 show the difference in RMSE results between GBR and the other methods on all three datasets.
From the reported results, we find that GBR can effectively predict the total confirmed COVID-19 cases for the next day based on those of previous days. We also conclude that GBR performs better than popular predictive methods in terms of RSME, MAE, and R-squared.

Conclusion and Future Work
The SARS-CoV-2 pandemic has become a serious worldwide problem. Prediction of future confirmed cases of COVID-19 disease using ML methods is important to provide medical services and have readiness in healthcare systems. We proposed the GBR method to predict the daily total confirmed cases of COVID-19 based on the totals of previous days. We selected GBR because it can minimize the loss function in the training process and create a single strong learner from weak learners. We conducted experiments using 10-fold cross-validation on the daily confirmed cases of COVID-19 collected from January 22, 2020, to May 30, 2020. Experimental results were evaluated using RMSE, MAE, and R-squared. The results revealed that GBR is an effective ML tool to predict the daily confirmed cases of COVID-19. The results showed that GBR achieves 0.00686 RMSE, which is the lowest among GBR and the comparison XGBR, SVR, and DTR models on the same datasets. In future work, we plan to conduct a comprehensive study of ML methods to predict the total deaths and recovered cases as well as the total confirmed cases of COVID-19, so as to analyze their performance in more detail.