  In recent years, quadratic weighted kappa has been growing in popularity in
the machine learning community as an evaluation metric in domains where the
target labels to be predicted are drawn from integer ratings, usually obtained
from human experts. For example, it was the metric of choice in several recent,
high profile machine learning contests hosted on Kaggle :
https://www.kaggle.com/c/asap-aes , https://www.kaggle.com/c/asap-sas ,
https://www.kaggle.com/c/diabetic-retinopathy-detection . Yet, little is
understood about the nature of this metric, its underlying mathematical
properties, where it fits among other common evaluation metrics such as mean
squared error (MSE) and correlation, or if it can be optimized analytically,
and if so, how. Much of this is due to the cumbersome way that this metric is
commonly defined. In this paper we first derive an equivalent but much simpler,
and more useful, definition for quadratic weighted kappa, and then employ this
alternate form to address the above issues.
