An Interpretable Probabilistic Autoregressive Neural Network Model for Time Series Forecasting

Forecasting time series data presents an emerging field of data science that has its application ranging from stock price and exchange rate prediction to the early prediction of epidemics. Numerous statistical and machine learning methods have been proposed in the last five decades with the demand for generating high-quality and reliable forecasts. However, in real-life prediction problems, situations exist in which a model based on one of the above paradigms is preferable, and therefore, hybrid solutions are needed to bridge the gap between classical forecasting methods and scalable neural network models. We introduce an interpretable probabilistic autoregressive neural network model for an explainable, scalable, and "white box-like" framework that can handle a wide variety of irregular time series data (e.g., nonlinearity and nonstationarity). Sufficient conditions for asymptotic stationarity and geometric ergodicity are obtained by considering the asymptotic behavior of the associated Markov chain. During computational experiments, PARNN outperforms standard statistical, machine learning, and deep learning models on a diverse collection of real-world datasets coming from economics, finance, and epidemiology, to mention a few. Furthermore, the proposed PARNN model improves forecast accuracy significantly for 10 out of 12 datasets compared to state-of-the-art models for short to long-term forecasts

Epicasting: An Ensemble Wavelet Neural Network (EWNet) for Forecasting Epidemics

Infectious diseases remain among the top contributors to human illness and death worldwide, among which many diseases produce epidemic waves of infection. The unavailability of specific drugs and ready-to-use vaccines to prevent most of these epidemics makes the situation worse. These force public health officials and policymakers to rely on early warning systems generated by reliable and accurate forecasts of epidemics. Accurate forecasts of epidemics can assist stakeholders in tailoring countermeasures, such as vaccination campaigns, staff scheduling, and resource allocation, to the situation at hand, which could translate to reductions in the impact of a disease. Unfortunately, most of these past epidemics exhibit nonlinear and non-stationary characteristics due to their spreading fluctuations based on seasonal-dependent variability and the nature of these epidemics. We analyse a wide variety of epidemic time series datasets using a maximal overlap discrete wavelet transform (MODWT) based autoregressive neural network and call it EWNet model. MODWT techniques effectively characterize non-stationary behavior and seasonal dependencies in the epidemic time series and improve the nonlinear forecasting scheme of the autoregressive neural network in the proposed ensemble wavelet network framework. From a nonlinear time series viewpoint, we explore the asymptotic stationarity of the proposed EWNet model to show the asymptotic behavior of the associated Markov Chain. We also theoretically investigate the effect of learning stability and the choice of hidden neurons in the proposal. From a practical perspective, we compare our proposed EWNet framework with several statistical, machine learning, and deep learning models. Experimental results show that the proposed EWNet is highly competitive compared to the state-of-the-art epidemic forecasting methods

An ensemble neural network approach to forecast Dengue outbreak based on climatic condition

Dengue fever is a virulent disease spreading over 100 tropical and subtropical countries in Africa, the Americas, and Asia. This arboviral disease affects around 400 million people globally, severely distressing the healthcare systems. The unavailability of a specific drug and ready-to-use vaccine makes the situation worse. Hence, policymakers must rely on early warning systems to control intervention-related decisions. Forecasts routinely provide critical information for dangerous epidemic events. However, the available forecasting models (e.g., weather-driven mechanistic, statistical time series, and machine learning models) lack a clear understanding of different components to improve prediction accuracy and often provide unstable and unreliable forecasts. This study proposes an ensemble wavelet neural network with exogenous factor(s) (XEWNet) model that can produce reliable estimates for dengue outbreak prediction for three geographical regions, namely San Juan, Iquitos, and Ahmedabad. The proposed XEWNet model is flexible and can easily incorporate exogenous climate variable(s) confirmed by statistical causality tests in its scalable framework. The proposed model is an integrated approach that uses wavelet transformation into an ensemble neural network framework that helps in generating more reliable long-term forecasts. The proposed XEWNet allows complex non-linear relationships between the dengue incidence cases and rainfall; however, mathematically interpretable, fast in execution, and easily comprehensible. The proposal’s competitiveness is measured using computational experiments based on various statistical metrics and several statistical comparison tests. In comparison with statistical, machine learning, and deep learning methods, our proposed XEWNet performs better in 75% of the cases for short-term and long-term forecasting of dengue incidence