We have seen that under a decomposable distribution over TANs it is possible to
efficiently determine the MAP undirected TAN structure and the set of k MAP
TAN structures and their relative probability weights. We used these results to
construct two new classifiers: maptan and maptan+bma. We have provided
empirical results showing that both classifiers improve over established TAN
based classifiers with equivalent complexity. From a practical point of view, selecting
when to use sstbmatan,maptan+bma,maptan depends mainly on two
factors: the amount of uncertainty a posteriori in the models we expect to have
and the ratio between the value of accuracy and the value of efficiency for the
user. We can see a qualitative sketch of when to choose each classifier in figure 2.
For any value of the ratio, we will choose maptan when uncertainty a posteriori
in models is low, sstbmatan when it is high and maptan+bmainbetween. If
learning takes place in an environment where accuracy is much more important
than efficiency, then our threshold in uncertainty to use maptan+bma and
sstbmatan will be lower. If learning takes place in an environment where effi-
ciency is much more important than accuracy, then maptan will be our choice
most of the times unless uncertainty in models is very high.
We have seen that under a decomposable distribution over TANs it is possible toefficiently determine the MAP undirected TAN structure and the set of k MAPTAN structures and their relative probability weights. We used these results toconstruct two new classifiers: maptan and maptan+bma. We have providedempirical results showing that both classifiers improve over established TANbased classifiers with equivalent complexity. From a practical point of view, selectingwhen to use sstbmatan,maptan+bma,maptan depends mainly on twofactors: the amount of uncertainty a posteriori in the models we expect to haveand the ratio between the value of accuracy and the value of efficiency for theuser. We can see a qualitative sketch of when to choose each classifier in figure 2.For any value of the ratio, we will choose maptan when uncertainty a posterioriin models is low, sstbmatan when it is high and maptan+bmainbetween. Iflearning takes place in an environment where accuracy is much more importantthan efficiency, then our threshold in uncertainty to use maptan+bma andsstbmatan will be lower. If learning takes place in an environment where effi-ciency is much more important than accuracy, then maptan will be our choicemost of the times unless uncertainty in models is very high.
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