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# Robust Inference for Multiclass Classification

*Proceedings of Algorithmic Learning Theory*, PMLR 83:368-386, 2018.

#### Abstract

We consider the problem of robust inference in which inputs may be
maliciously corrupted by a powerful adversary, and the learner’s
goal is to accurately predict the original, uncorrupted input’s true
label given only the adversarially corrupted version of the input.
We specifically focus on the multiclass version of this problem in
which more than two labels are possible. We substantially extend and
generalize previous work which had only considered the binary case,
thus uncovering stark differences between the two cases. We show how
robust inference can be modeled as a zero-sum game between a learner
who maximizes the expected accuracy, and an adversary. The value of
this game is the best-attainable accuracy rate of any algorithm. We
then show how the optimal policy for both the learner and adversary
can be exactly characterized in terms of a particular hypergraph,
specifically, as the hypergraph’s maximum fractional independent set
and minimum fractional set cover, respectively. This
characterization yields efficient algorithms in the size of the
domain (number of possible inputs). For the typical setting that the
domain is huge, we also design efficient local computation
algorithms for approximating maximum fractional independent set in
hypergraphs. This leads to a near optimal algorithm for the learner
whose complexity is independent of the domain size, instead
depending only on the rank and maximum degree of the underlying
hypergraph, and on the desired approximation ratio.