Probability-theoretic Definition of Category Utility
The probability-theoretic definition of category utility given in Fisher (1987) and Witten & Frank (2005) is as follows:
where is a size- set of -ary features, and is a set of categories. The term designates the marginal probability that feature takes on value, and the term designates the category-conditional probability that feature takes on value given that the object in question belongs to category .
The motivation and development of this expression for category utility, and the role of the multiplicand as a crude overfitting control, is given in the above sources. Loosely (Fisher 1987), the term is the expected number of attribute values that can be correctly guessed by an observer using a probability-matching strategy together with knowledge of the category labels, while is the expected number of attribute values that can be correctly guessed by an observer the same strategy but without any knowledge of the category labels. Their difference therefore reflects the relative advantage accruing to the observer by having knowledge of the category structure.
Read more about this topic: Category Utility
Famous quotes containing the words definition, category and/or utility:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“The truth is, no matter how trying they become, babies two and under don’t have the ability to make moral choices, so they can’t be “bad.” That category only exists in the adult mind.”
—Anne Cassidy (20th century)
“Moral sensibilities are nowadays at such cross-purposes that to one man a morality is proved by its utility, while to another its utility refutes it.”
—Friedrich Nietzsche (1844–1900)