Scalable variable selection for two-view learning tasks with projection operators

Vector-valued, or more generally structured output learning tasks arising from various domains have attracted much research attention in recent years [Micchelli and Pontil, 2005, Deshwal et al., 2019, Brogat-Motte et al., 2022]. For both supervised but also unsupervised learning approaches, multi-view data has been of interest [Hotelling, 1936, Xu et al., 2013, Minh et al., 2016a]. Despite many successful approaches for various multi-view and vector-valued learning settings, including interpretability to these models has received less attention. While there are various feature selection and dimensionality reduction methods either for scalar-valued learning tasks, or unsupervised methods for data represented in a single view [Zebari et al., 2020, Li et al., 2017, Anette and Nokto, 2018, Bommert et al., 2020], there is scarcity of methods suitable for when data is represented in two views, or arises from a vector-valued learning task. From the point of view of interpretability, especially feature selection methods are advantageous over dimensionality reduction since the relevant features are directly obtained as a result and not given only in (linear) combinations. Recently, some feature selection methods have been proposed for structured output learning tasks.