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This paper revisits building machine learning algorithms that involveinteractions between entities, such as those between financial assets in anactively managed portfolio, or interactions between users in a social network.Our goal is to forecast the future evolution of ensembles of multivariate timeseries in such applications (e.g., the future return of a financial asset orthe future popularity of a Twitter account). Designing ML algorithms for suchsystems requires addressing the challenges of high-dimensional interactions andnon-linearity. Existing approaches usually adopt an ad-hoc approach tointegrating high-dimensional techniques into non-linear models and recentstudies have shown these approaches have questionable efficacy in time-evolvinginteracting systems.  To this end, we propose a novel framework, which we dub as the additiveinfluence model. Under our modeling assumption, we show that it is possible todecouple the learning of high-dimensional interactions from the learning ofnon-linear feature interactions. To learn the high-dimensional interactions, weleverage kernel-based techniques, with provable guarantees, to embed theentities in a low-dimensional latent space. To learn the non-linearfeature-response interactions, we generalize prominent machine learningtechniques, including designing a new statistically sound non-parametric methodand an ensemble learning algorithm optimized for vector regressions. Extensiveexperiments on two common applications demonstrate that our new algorithmsdeliver significantly stronger forecasting power compared to standard andrecently proposed methods.

Symphony in the Latent Space: Provably Integrating High-dimensional Techniques with Non-linear Machine Learning Models