Deep Distribution Regression

In recent years, a variety of machine learning methods, such as random forest, gradient boosting trees and neural networks have gained popularity and been widely adopted. These methods are often flexible enough to uncover complex relationships in high-dimensional data without strong assumptions on the underlying data structure. Off-the-shelf software is available to put these algorithms into production [Pedregosa et al. (2011), Abadi et al. (2016) and Paszke et al. (2017)]. However, in regression and forecasting tasks, many of the machine learning methods only provide a point estimate, without any additional information regarding the uncertainty of the target quantity. Understanding uncertainties are often crucial in fields such as financial markets and risk analysis [Diebold et al. (1997), Timmermann (2000)], population and demographic studies [Wilson and Bell (2007)], transportation and traffic analysis [Zhu and Laptev (2017), Rodrigues and Pereira (2018)] and energy forecasting [Hong et al. (2016)].