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キーワード:
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要旨:
We investigate algebraic, logical, and geometric
properties of concepts recognized by various classes
of probabilistic classifiers. For this we introduce a
natural hierarchy of probabilistic classifiers, the
lowest level of which comprises the naive Bayesian
classifiers. We show that the expressivity of classifiers on the
different levels in the hierarchy is characterized
algebraically by separability with polynomials of
different degrees. A consequence of this result is that
every linearly separable concept can be recognized by a
naive Bayesian classifier. We contrast this result with
negative results about the naive Bayesian classifier
previously reported in the literature, and point out that
these results only pertain to specific learning
scenarios for naive Bayesian classifiers. We also present
some logical and geometric characterizations of linearly
separable concepts, thus providing additional intuitive
insight into what concepts are recognizable by naive
Bayesian classifiers.
