Hypothesis Testing for Class-Conditional Noise Using Local Maximum
  Likelihood
Weisong Yang Rafael Poyiadzi Niall Twomey Raul Santos Rodriguez
In supervised learning, automatically assessing the quality of the labels
before any learning takes place remains an open research question. In certain
particular cases, hypothesis testing procedures have been proposed to assess
whether a given instance-label dataset is contaminated with class-conditional
label noise, as opposed to uniform label noise. The existing theory builds on
the asymptotic properties of the Maximum Likelihood Estimate for parametric
logistic regression. However, the parametric assumptions on top of which these
approaches are constructed are often too strong and unrealistic in practice. To
alleviate this problem, in this paper we propose an alternative path by showing
how similar procedures can be followed when the underlying model is a product
of Local Maximum Likelihood Estimation that leads to more flexible
nonparametric logistic regression models, which in turn are less susceptible to
model misspecification. This different view allows for wider applicability of
the tests by offering users access to a richer model class. Similarly to
existing works, we assume we have access to anchor points which are provided by
the users. We introduce the necessary ingredients for the adaptation of the
hypothesis tests to the case of nonparametric logistic regression and
empirically compare against the parametric approach presenting both synthetic
and real-world case studies and discussing the advantages and limitations of
the proposed approach.