  In Bayesian classification, it is important to establish a probabilistic
model for each class for likelihood estimation. Most of the previous methods
modeled the probability distribution in the whole sample space. However,
real-world problems are usually too complex to model in the whole sample space;
some fundamental assumptions are required to simplify the global model, for
example, the class conditional independence assumption for naive Bayesian
classification. In this paper, with the insight that the distribution in a
local sample space should be simpler than that in the whole sample space, a
local probabilistic model established for a local region is expected much
simpler and can relax the fundamental assumptions that may not be true in the
whole sample space. Based on these advantages we propose establishing local
probabilistic models for Bayesian classification. In addition, a Bayesian
classifier adopting a local probabilistic model can even be viewed as a
generalized local classification model; by tuning the size of the local region
and the corresponding local model assumption, a fitting model can be
established for a particular classification problem. The experimental results
on several real-world datasets demonstrate the effectiveness of local
probabilistic models for Bayesian classification.
