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16.2. Training Set Bound Calculation

Many of the training set based bounds effectively reduce the value of δ by some fixed amount. The program ’bound’ will automatically reduce the value of δ with two arguments.

  1. log_prior <float>: the log (base e) of the “prior” (in the sense of theorem 4.6.1) of the hypothesis.
  2. log_hypothesis_size <float>: the log of the number of hypotheses (in the sense of theorem 4.2.1)

Each of these arguments acts independently to reduce the value of δ. The value of δ will only be reduced on training example based bounds. There are two more arguments necessary for application of one of the simple training set based bound:

  1. training_examples <int>: the number of training examples.
  2. training_errors <int>: the number of training errors.

Here is an application of a simple training set based bound:

12:07AM z-26: cat train_error  
train_examples 100  
train_errors 3  
log_prior -50  
delta 0.3  
12:07AM z-27: bound train_error  
Applying varying approximation tail bound  
delta 0.3  
lower_delta 0.5  
train_examples 100  
train_errors 3  
log_hypothesis_size 0  
log_prior -50  
approximation automatic  
true_error = 0.03 0.466502545401 9.31322574615e-10

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