Bi-convex Optimization to Learn Classifiers from Multiple Biomedical Annotations.

The problem of constructing classifiers from multiple annotators who provide inconsistent training labels is important and occurs in many application domains. Many existing methods focus on the understanding and learning of the crowd behaviors. Several probabilistic algorithms consider the construction of classifiers for specific tasks using consensus of multiple labelers annotations. These methods impose a prior on the consensus and develop an expectation-maximization algorithm based on logistic regression loss. We extend the discussion to the hinge loss commonly used by support vector machines. Our formulations form bi-convex programs that construct classifiers and estimate the reliability of each labeler simultaneously. Each labeler is associated with a reliability parameter, which can be a constant, or class-dependent, or varies for different examples. The hinge loss is modified by replacing the true labels by the weighted combination of labelers' labels with reliabilities as weights. Statistical justification is discussed to motivate the use of linear combination of labels. In parallel to the expectation-maximization algorithm for logistic-based methods, efficient alternating algorithms are developed to solve the proposed bi-convex programs. Experimental results on benchmark datasets and three real-world biomedical problems demonstrate that the proposed methods either outperform or are competitive to the state of the art.