Gradient tree boosting with random output projections for multi-label classification and multi-output regression

Multi-output supervised learning aims to model input-output relationships from observations of inputoutput pairs whenever the output space is a vector of random variables. Multi-output classification and regression tasks have numerous applications in domains ranging from biology to multimedia, and recent applications in this area correspond to very high dimensional output spaces (Agrawal et al, 2013; Dekel and Shamir, 2010). Classification and regression trees (Breiman et al, 1984) are popular supervised learning methods that provide state-of-the-art performance when exploited in the context of ensemble methods, namely Random forests (Breiman, 2001; Geurts et al, 2006) and Boosting (Freund and Schapire, 1997; Friedman, 2001). Classification and regression trees can obviously be exploited to handle multi-output problems. The most straightforward way to address multi-output tasks is to apply standard single output methods separately and independently on each output. Although simple, this method, called binary relevance (Tsoumakas et al, 2009) in multi-label classification or single target (Spyromitros-Xioufis et al, 2012) in multi-output regression is often suboptimal as it does not exploit potential correlations that might exist between the outputs. Tree ensemble methods have however been explicitely extended by several authors to the joint prediction of multiple outputs (e.g., Segal, 1992; Blockeel et al, 2000). These extensions build a single tree to predict all outputs at once. They adapt the score measure used to assess splits during the tree growth to take into account all outputs and label each tree leaf with a vector of values, one for each output.