This software calculates confidence intervals on binomials given
independently drawn examples.  It is primarily intended to be useful
for classifier evaluation, but may have wider uses.

files: 

occams_razor_bound - Compute an upper bound on the confidence interval.
	Usage:
	./occams_razor_bound <bound_error_rate> <number_of_examples> <number_of_errors> <bit_description_length>


	Where: 	<bound_error_rate> is the error rate of the bound (0.05 is 
			popular for unknown reasons)
		<number_of_examples> is the number of examples that you are \
			testing.
		<number_of_errors> is the number of errors on the examples.

	Example usage:
		# ./occams_razor_bound 0.1 100 12 23
		0.372256

lower_orb - Exactly the same as upper_bound, except that it
calculates the lower end of a confidence interval.

	Example usage:
	 	#  ./lower_orb 0.1 100 12 23
	 	0.01353

pac-mdl_bound - compute a pac-mdl bound in the transductive setting.
The output is a bound on the number of errors in the test set.
	Usage:
	./pac-mdl_bound <bound_error_rate> <number_of_train_examples> <number_of_train_errors> <bit_description_length> <number_of_test_examples>

	Where: 	<bound_error_rate> is the error rate of the bound (0.05 is 
			popular for unknown reasons)
		<number_of_train_examples> is the number of train set examples. 		<number_of_train_errors> is the number of errors in the train set.
		<bit_description_length> is the description length of the transductive classifier
		<number_of_test_examples> is the number of test set examples

	Example usage:
		# ./pac-mdl_bound 0.1 100 2 23 300
		74

ipm_bound - compute an inductive pac-mdl bound.
	Usage:
	./ipm_bound <bound_error_rate> <number_of_train_examples> <number_of_train_errors> <transductive_bit_description_length> <unseen_test_set_size>
	Where: 	<bound_error_rate> is the error rate of the bound (0.05 is popular for unknown reasons)
		<number_of_train_examples> is the number of train set examples. 		<number_of_train_errors> is the number of errors in the train set.
		<bit_description_length> is the largest description length of a transductive classifier consistent with the classifier
		<unseen_test_set_size> the size of the test set corresponding to the transductive classifier.

	Example Usage:
		# ./ipm_bound 0.2 100 1 23 100
		0.28

binomial.cc - core logic.  An approximation (Stirling's Series) is
	used to compute the binomial coefficients.  The approximation is 
	good to about 6 decimal places.   The execution time is dependent 
	upon the input but is generally sublinear in n (the number of 
	coin flips/examples).

binomial.h - the header file for binomial.cc

hypergeometric.cc - core logic.  An approximation (Stirling's Series) is
	used to compute the coefficients.  The approximation is 
	good to about 6 decimal places.   The execution time is dependent 
	upon the input but is generally sublinear in n (the number of 
	coin flips/examples).

hypergeometric.h - the header file for hypergeometric.cc

occams_razor_bound.cc - An interface which calculates the occam's razor bound

lower_orb.cc - An interface which calculates a lower bound

