def compute_multiple_bounds(m, N, risk, KLQP, disagreement=None, delta=0.05):
""" Compute bounds on the full sample and print their values.
m: Training set size (labeled examples)
N: Full sample size (labeled + unlabeled examples)
risk : Gibbs risk observed on the training set
KLQP : Kullback-Leibler divergence between prior and posterior
disagreement : Expected disagreement on the full sample
delta : confidence parameter (default=0.05)
"""
print('*** Parameters ***')
print('m = %d\nN = %d\nrisk = %f\nKLQP = %f\ndisagreement = %f\ndelta = %f\n'
% (m, N, risk, KLQP, disagreement, delta) )
print('*** Bounds on the risk of the Gibbs Classifier ***')
thm5_KL = bounds.compute_general_transductive_gibbs_bound(d_functions.kl_divergence,risk, m, N, KLQP, delta)
print('Theorem 5-KL : %f' % thm5_KL)
thm5_Dstar = bounds.compute_general_transductive_gibbs_bound(d_functions.new_transductive_divergence, risk, m, N, KLQP, delta)
print('Theorem 5-D* : %f' % thm5_Dstar)
cor7a = bounds.compute_corollary_7a_gibbs_bound(risk, m, N, KLQP, delta)
print('Corollary 7(a): %f' % cor7a)
cor7b = bounds.compute_corollary_7b_gibbs_bound(risk, m, N, KLQP, delta)
print('Corollary 7(b): %f' % cor7b)
derbeko = bounds.compute_derbeko_2007_gibbs_bound(risk, m, N, KLQP, delta)
print('Derbeko (2007): %f' % derbeko)
print('\n*** Bounds on the risk of the Gibbs Classifier (Based on Theorem 5-D*) ***')
twice = 2 * thm5_Dstar
print('Twice the Gibbs: %f' % twice)
if disagreement is None:
print('Via the C-Bound: [disagreement required]')
else:
c_bound = compute_c_bound(thm5_Dstar, disagreement)
print('Via the C-Bound: %f' % c_bound)
def generate_bound_figures(N_list, ratios_list, risk, KLQP, delta=0.05):
""" Illustrate of the bound calculations
N_list : List of full sample size
ratios_list : List of m/N rations ( where m is the number of labeled examples)
risk : Gibbs risk observed on the training set
KLQP : Kullback-Leibler divergence between prior and posterior
delta : confidence parameter (default=0.05)
"""
divergences_dict = OrderedDict()
divergences_dict["Kullback-Leibler"] = d_functions.kl_divergence
divergences_dict["D*-function"] = d_functions.new_transductive_divergence
divergences_dict["Quadratic Distance"] = d_functions.quadratic_distance
divergences_dict["Variation Distance"] = d_functions.variation_distance
divergences_dict["Triangular Discrimination"] = d_functions.triangular_discrimination
n_rows = len(ratios_list)
n_cols = len(divergences_dict)
x_values = np.arange(0., 1.0, .005)
pyplot.subplots_adjust(wspace=0.1, hspace=0.1)
STATS_dict = dict()
for i, divergence_name in enumerate(divergences_dict.keys()):
print('*** D-function: ' + divergence_name + ' ***')
for j, ratio in enumerate(ratios_list):
ax = pyplot.subplot(n_rows, n_cols, j*n_cols + i + 1)
# Compute and draw d-function values (blue curves)
divergence = divergences_dict[divergence_name]
divergence_values = [divergence(risk, x, ratio) for x in x_values]
pyplot.plot(x_values, divergence_values, linewidth=2)
# Compute and draw bound values (horizontal lines) for each value of N
for N in N_list:
m = N * ratio
complexity_term = compute_transductive_complexity_term(divergence, m, N)
bound = compute_general_transductive_gibbs_bound(divergence, risk, m, N, KLQP, delta=delta, complexity_term=complexity_term)
rhs = (KLQP + log(complexity_term / delta)) / m
print('m=%d N=%d bound=%0.3f' % (m,N,bound) )
handle = pyplot.plot([-1., bound, 2.], 3*[rhs], 'o--', label='%0.3f' % bound)[0]
STATS_dict[(i, N, ratio)] = (bound, rhs, handle)
# Compute and draw risk limits (vertical dashed lines)
risk_sup = 1. - ratio * (1.-risk)
risk_inf = ratio * risk
pyplot.plot(2*[risk_sup], [0., 1.], 'k:')
pyplot.plot(2*[risk_inf], [0., 1.], 'k:')
# Set plot properties
pyplot.legend(loc=2)
pyplot.xlim(0., 1.)
pyplot.ylim(0., .5 if ratio > .4 else 1.)
if j == n_rows-1:
pyplot.xlabel(divergence_name)
for tick in ax.xaxis.get_major_ticks():
tick.label.set_fontsize(13)
else:
pyplot.setp(ax.get_xticklabels(), visible=False)
if i == 0:
pyplot.ylabel("m/N = %0.1f" % ratio)
for tick in ax.yaxis.get_major_ticks():
tick.label.set_fontsize(13)
else:
pyplot.setp(ax.get_yticklabels(), visible=False)
# Highlight lower bounds for each (m,N) pairs
for N in N_list:
for j, ratio in enumerate(ratios_list):
best_bound = 1e6
best_i = -1
for i, _ in enumerate(divergences_dict.keys()):
bound, rhs, handle = STATS_dict[(i, N, ratio)]
if bound < best_bound:
best_bound, best_handle, best_i = bound, handle, i
best_handle.set_marker('*')
best_handle.set_markersize(14.)
best_handle.set_markeredgewidth(0.)
pyplot.subplot(n_rows, n_cols, j * n_cols + best_i + 1)
pyplot.legend(loc=2)
pyplot.show()
