VAEneu: A New Avenue for VAE Application on Probabilistic Forecasting

Probabilistic forecasting is essential in decision-making, particularly in fields where accurately assessing risk is critical, such as healthcare [1, 2, 3], weather forecasting [4, 5], flood risk assessment [6], seismic hazard prediction [7, 8], renewable energy sector [9], and economic and financial risk management [10, 11]. These models provide insights into possible future outcomes and their likelihoods, aiding decision-makers in resource allocation, policy formulation, and strategic planning. The importance of these forecasts lies in their ability to model uncertainty about the future in the form of predictive distribution. The ultimate goal of a probabilistic forecaster is to output a predictive distribution with good calibration and sharpness. Calibration is concerned with the statistical consistency between predictive distribution and observation, while sharpness governs the confidence in the forecast itself. A sharp probabilistic forecaster outputs a narrow predictive distribution, which represents high confidence in the forecast. However, sharpness is desirable in conjunction with calibration to employ high confidence aligned with the true distribution.