  Consider a general machine learning setting where the output is a set of
labels or sequences. This output set is unordered and its size varies with the
input. Whereas multi-label classification methods seem a natural first resort,
they are not readily applicable to set-valued outputs because of the growth
rate of the output space; and because conventional sequence generation doesn't
reflect sets' order-free nature. In this paper, we propose a unified
framework--sequential set generation (SSG)--that can handle output sets of
labels and sequences. SSG is a meta-algorithm that leverages any probabilistic
learning method for label or sequence prediction, but employs a proper
regularization such that a new label or sequence is generated repeatedly until
the full set is produced. Though SSG is sequential in nature, it does not
penalize the ordering of the appearance of the set elements and can be applied
to a variety of set output problems, such as a set of classification labels or
sequences. We perform experiments with both benchmark and synthetic data sets
and demonstrate SSG's strong performance over baseline methods.
