- ...tasks
- The law
is only proved for discrete valued learning tasks, but there
is no reason to believe it does not also apply to continuous valued
tasks
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...only
- To provide an example
of an implausible similarity metric, consider the similarity metric
defined by the root node, that everything is similar. This will
not be plausible as there is too great a level of dissimilarity in classes
with respect to this metric. If it were a relevant similarity metric,
and the distribution of training examples was representative of the
distribution of objects in the domain as a whole, then the similarity
assumption would be violated, as similar objects would have probability of
just 0.58 of belonging to the same class. This probability can be
calculated as follows. The probabilities of an object being + or -
are 0.3 and 0.7 respectively. If an object is + then the
probability of it belonging to the same class as another
object to which it is similar is 0.3. If an object is - then the
probability of it belonging to the same class as another
object to which it is similar is
0.7. Thus, the probability of an object belonging to the same class as
another similar object is 4#4.
The numbers involved in this simple example are, of course, too small
to reach any such conclusion with a high level of confidence-the
example is intended as illustrative only.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Mon Sep 9 12:13:30 EST 1996