Uncertainty quantification is not an easy task. Its difficulty depends on various factors related to the available data, the application domain, and also the learned task. Having multiple outputs to predict simultaneously can be even more demanding, principally when these outputs are correlated. This research work focuses on producing confidence regions for multi-target regression, where the objective is to predict many real-valued outputs at once, by using conformal prediction: a theoretically proven method that can be added to any Machine Learning model to generate set predictions whose size and statistical guarantee depend on a user-defined error rate. First, a simple extension of single-target regression conformal methods is proposed by following a naïve approach that treats these targets as independent. Second, copulas are exploited to take into account the existing correlations between outputs when giving conformal regions. Third, ellipsoids are considered in order to produce more flexible conformal regions according to the possible relationships between targets while maintaining the desired error rate.
