## Cost-Sensitive Learning with Noisy Labels

*Nagarajan Natarajan, Inderjit S. Dhillon, Pradeep Ravikumar, Ambuj Tewari*; 18(155):1−33, 2018.

### Abstract

We study binary classification in the presence of \emph{class-
conditional} random noise, where the learner gets to see labels
that are flipped independently with some probability, and where
the flip probability depends on the class. Our goal is to devise
learning algorithms that are efficient and statistically
consistent with respect to commonly used utility measures. In
particular, we look at a family of measures motivated by their
application in domains where cost-sensitive learning is
necessary (for example, when there is class imbalance). In
contrast to most of the existing literature on consistent
classification that are limited to the classical 0-1 loss, our
analysis includes more general utility measures such as the AM
measure (arithmetic mean of True Positive Rate and True Negative
Rate). For this problem of cost-sensitive learning under class-
conditional random noise, we develop two approaches that are
based on suitably modifying surrogate losses. First, we provide
a simple unbiased estimator of any loss, and obtain performance
bounds for empirical utility maximization in the presence of
i.i.d. data with noisy labels. If the loss function satisfies a
simple symmetry condition, we show that using unbiased estimator
leads to an efficient algorithm for empirical maximization.
Second, by leveraging a reduction of risk minimization under
noisy labels to classification with weighted 0-1 loss, we
suggest the use of a simple weighted surrogate loss, for which
we are able to obtain strong utility bounds. This approach
implies that methods already used in practice, such as biased
SVM and weighted logistic regression, are provably noise-
tolerant. For two practically important measures in our family,
we show that the proposed methods are competitive with respect
to recently proposed methods for dealing with label noise in
several benchmark data sets.

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