  We show when maximizing a properly defined $f$-divergence measure with
respect to a classifier's predictions and the supervised labels is robust with
label noise. Leveraging its variational form, we derive a nice decoupling
property for a family of $f$-divergence measures when label noise presents,
where the divergence is shown to be a linear combination of the variational
difference defined on the clean distribution and a bias term introduced due to
the noise. The above derivation helps us analyze the robustness of different
$f$-divergence functions. With established robustness, this family of
$f$-divergence functions arises as useful metrics for the problem of learning
with noisy labels, which do not require the specification of the labels' noise
rate. When they are possibly not robust, we propose fixes to make them so. In
addition to the analytical results, we present thorough experimental evidence.
Our code is available at
https://github.com/UCSC-REAL/Robust-f-divergence-measures.
