  This paper investigates a new online learning problem with doubly-streaming
data, where the data streams are described by feature spaces that constantly
evolve, with new features emerging and old features fading away. The challenges
of this problem are two folds: 1) Data samples ceaselessly flowing in may carry
shifted patterns over time, requiring learners to update hence adapt
on-the-fly. 2) Newly emerging features are described by very few samples,
resulting in weak learners that tend to make error predictions. A plausible
idea to overcome the challenges is to establish relationship between the
pre-and-post evolving feature spaces, so that an online learner can leverage
the knowledge learned from the old features to better the learning performance
on the new features. Unfortunately, this idea does not scale up to
high-dimensional media streams with complex feature interplay, which suffers an
tradeoff between onlineness (biasing shallow learners) and
expressiveness(requiring deep learners). Motivated by this, we propose a novel
OLD^3S paradigm, where a shared latent subspace is discovered to summarize
information from the old and new feature spaces, building intermediate feature
mapping relationship. A key trait of OLD^3S is to treat the model capacity as a
learnable semantics, yields optimal model depth and parameters jointly, in
accordance with the complexity and non-linearity of the input data streams in
an online fashion. Both theoretical analyses and empirical studies substantiate
the viability and effectiveness of our proposal.
