Bayes discrimination with mean square error loss

摘要

The Bayes decision strategy for classifying data among distinct classes is considered. A random variable X is assigned to that population for which the expected loss (or Bayes risk) is minimal. A 0–1 cost structure, which penalizes all misassignments with unit loss, is usually employed. This paper considers the behavior of the decision strategy under the influence of a mean square error loss function. It is found that the latter results in fewer misclassifications than the former, in many instances. Furthermore, it is more robust with respect to deviations from the assumed distribution of the data.