  Choosing a suitable loss function is essential when learning by empirical
risk minimisation. In many practical cases, the datasets used for training a
classifier may contain incorrect labels, which prompts the interest for using
loss functions that are inherently robust to label noise. In this paper, we
study the Fisher-Rao loss function, which emerges from the Fisher-Rao distance
in the statistical manifold of discrete distributions. We derive an upper bound
for the performance degradation in the presence of label noise, and analyse the
learning speed of this loss. Comparing with other commonly used losses, we
argue that the Fisher-Rao loss provides a natural trade-off between robustness
and training dynamics. Numerical experiments with synthetic and MNIST datasets
illustrate this performance.
