Abstract
This paper introduces a novel Robust Regression
(RR) model, named Sinkhorn regression, which
imposes Sinkhorn distances on both loss function
and regularization. Traditional RR methods target
at searching for an element-wise loss function
(e.g., Lp-norm) to characterize the errors such that
outlying data have a relatively smaller influence on
the regression estimator. Due to the neglect of the
geometric information, they often lead to the suboptimal
results in the practical applications. To
address this problem, we use a cross-bin distance
function, i.e., Sinkhorn distances, to capture the geometric
knowledge of real data. Sinkhorn distances
is invariant in movement, rotation and zoom. Thus,
our method is more robust to variations of data
than traditional regression models. Meanwhile, we
leverage Kullback-Leibler divergence to relax the
proposed model with marginal constraints into its
unbalanced formulation to adapt more types of features.
In addition, we propose an efficient algorithm
to solve the relaxed model and establish its
complete statistical guarantees under mild conditions.
Experiments on the five publicly available
microarray data sets and one mass spectrometry
data set demonstrate the effectiveness and robustness
of our method.
Keywords
- Machine Learning: Classification
- Machine Learning Applications: Other
