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A density estimator can be turned into a classifier in two ways, both
of them being essentially *likelihood ratio* methods. Denote the
class variable by and the set of input variables by . In the
first method, adopted in our classification experiments under the name
of *MT classifier*, an MT model is trained on the domain
, treating the class variable like any other variable
and pooling all the training data together. In the testing phase, a
new instance
is classified by picking the most
likely value of the class variable given the settings of the other
variables:

Similarly, for the MF classifier (termed ``D-SIDE'' by [Kontkanen, Myllymaki, Tirri
1996]),
above is an MF trained on
.
The second method calls for partitioning the training set according to
the values of the class variable and for training a tree density estimator
on each partition. This is equivalent to training a mixture of trees
with observed choice variable, the choice variable being the class
[Chow, Liu 1968,Friedman, Geiger, Goldszmidt
1997]. In particular,
if the trees are forced to have the same structure we obtain the
Tree Augmented Naive Bayes (TANB) classifier of [Friedman, Geiger, Goldszmidt
1997].
In either case one turns to Bayes formula:

to classify a new instance . The analog of the MF classifier in
this setting is the naive Bayes classifier.

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Journal of Machine Learning Research
2000-10-19