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Ensemble Methods: One obvious approach
to making more reliable decisions is to
combine the output of several different
models. In this chapter we explore the use
of methods for combining models (called
ensemble methods) generated by machine
learning. In particular, we have explored
voting, stacking, bagging and boosting. In
many cases they have proved to increase
predictive performance over a single model.
In voting a set of n different learning algo-
rithms (in this chapter we applied decision
trees, SVM, ANN, and 1-NN) are trained
on the same training data, and prediction
is performed by allowing all n classifiers to
'vote' on class prediction, final prediction is
the class that gets the most votes. Stacking
train n learning algorithms (here we applied
decision trees, SVM, ANN, and 1-NN) in the
same training data and train another learning
algorithm, the “meta-learner”, (we applied
decision trees) to learn to predict the class
from the predictions of the base learners.
Bagging draws n bootstrap samples from
the training data, trains a given learning
algorithm (here we consider decision trees)
on each of these n samples (producing n
classifiers) and predicts by simple voting
of all n classifiers. Boosting generates a
series of classifiers using the same learning
algorithm (here we applied decision trees)
but differently weighted examples from the
same training set, and predicts by weighted
majority vote (weighted by accuracy) of all
n classifiers.
notes with similar timbre). By building a classi-
fier based on the contextual features of the notes
of an interpreter, we intend to obtain a classifier
which predicts what type of notes an interpreter
performs in a particular musical context.
evaluation
We evaluated the induced classifiers by per-
forming the standard 10-fold cross validation in
which 10% of the training set is held out in turn
as test data while the remaining 90% is used
as training data. When performing the 10-fold
cross validation, we leave out the same number
of examples per class (i.e., the same number of
notes per performer). In the data sets, the number
of examples is the same for each class (i.e., each
interpreter) considered, thus by leaving out the
same number of examples per class we maintain
a balanced training set. In order to avoid opti-
mistic estimates of the classifier performance, we
explicitly remove from the training set all melody
fragment repetitions of the hold out fragment. This
is motivated by the fact that musicians are likely
to perform a melody fragment and its repetition
in a similar way. Thus, the applied 10-fold cross
validation procedure, in addition to holding out a
test example from the training set, also removes
repetitions of the example.
a case study
We have applied our algorithm to a set of mono-
phonic recordings obtained from professional
saxophonists in a controlled studio environment.
The musicians were instructed to interpret sev-
eral Jazz standards by following the score of the
piece.
The motivation for inducing the classifiers as
described above is that we would like to devise a
mechanism to capture which (perceptual) type of
notes are played in a particular musical context
by an interpreter. By clustering the notes of all
the interpreters based on the notes' perceptual
features, we intend to obtain a number of sets,
each containing perceptually similar notes (e.g.,
Training Data
The training data used in this case study are
monophonic recordings of four Jazz standards
( Body and Soul, Once I Loved, Like Someone in
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