Using discrete wavelet transform for optimizing COVID-19 new cases and deaths prediction worldwide with deep neural networks

Abstract

This work aims to compare deep learning models designed to predict daily number of cases and deaths caused by COVID-19 for 183 countries, using a daily basis time series, in addition to a feature augmentation strategy based on Discrete Wavelet Transform (DWT). The following deep learning architectures were compared using two different feature sets with and without DWT: (1) a homogeneous architecture containing multiple LSTM (Long-Short Term Memory) layers and (2) a hybrid architecture combining multiple CNN (Convolutional Neural Network) layers and multiple LSTM layers. Therefore, four deep learning models were evaluated: (1) LSTM, (2) CNN + LSTM, (3) DWT + LSTM and (4) DWT + CNN + LSTM. Their performances were quantitatively assessed using the metrics: Mean Absolute Error (MAE), Normalized Mean Squared Error (NMSE), Pearson R, and Factor of 2. The models were designed to predict the daily evolution of the two main epidemic variables up to 30 days ahead. After a fine-tuning procedure for hyperparameters optimization of each model, the results show a statistically significant difference between the models’ performances both for the prediction of deaths and confirmed cases (p-value<0.001). Based on NMSE values, significant differences were observed between LSTM and CNN+LSTM, indicating that convolutional layers added to LSTM networks made the model more accurate. The use of wavelet coefficients as additional features (DWT+CNN+LSTM) achieved equivalent results to CNN+LSTM model, which demonstrates the potential of wavelets application for optimizing models, since this allows training with a smaller time series data.