Summary: | This paper revisits building machine learning algorithms that
involve interactions between entities, such as those between
financial assets in an actively managed portfolio, or interactions between users in a social network. Our goal is to forecast
the future evolution of ensembles of multivariate time series
in such applications (e.g., the future return of a financial asset
or the future popularity of a Twitter account). Designing ML
algorithms for such systems requires addressing the challenges
of high-dimensional interactions and non-linearity. Existing
approaches usually adopt an ad-hoc approach to integrating
high-dimensional techniques into non-linear models and recent studies have shown these approaches have questionable
efficacy in time-evolving interacting systems.<br>
To this end, we propose a novel framework, which we dub as
the additive influence model. Under our modeling assumption, we show that it is possible to decouple the learning of
high-dimensional interactions from the learning of non-linear
feature interactions. To learn the high-dimensional interactions, we leverage kernel-based techniques, with provable
guarantees, to embed the entities in a low-dimensional latent
space. To learn the non-linear feature-response interactions,
we generalize prominent machine learning techniques, including designing a new statistically sound non-parametric method
and an ensemble learning algorithm optimized for vector regressions. Extensive experiments on two common applica-
tions demonstrate that our new algorithms deliver significantly
stronger forecasting power compared to standard and recently
proposed methods.
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