Probabilistic Prediction of Extreme Events in Time Series with Deep Learning Methods

Time series forecasting is a very active field of research due to the many applications in which it can be involved. One such application regards predicting the occurrences of extreme events, which refers to rare and potentially dangerous situation, like meteorological hazards or financial crises. Many models have been proposed through the years to tackle this challenge. Along them, Deep Learning models have proven to be very effective and are becoming increasingly popular thanks to their capability to learn and generalize from historical data. We review the fundamental basics behind Deep Learning Networks, focusing on Long-Short Term Memory (LSTM), a Recurrent Neural Network architecture able to efficiently learn time-dependencies within sequential data. We introduce the concept of Normalizing Flows, a recently developed Deep Learning approach to estimate, with high flexibility, the probability distribution of the data. We present a real-life problem in the field of hydrology, regarding the prediction of extreme flood events in river basins. We discussed two LSTM-based models which, have been proven to be effective in rainfallrunoff prediction, as well as a new approach involving a normalizing flow conditioned to an LSTM. In this thesis, we investigate the potential of these models with experimental results, compared against established baseline models found in the literature.