def run_second_feature_boundary_simulations():
hyp_space_type = "boundary"
n_hyp = 4
n_features = 3
n_labels = 2
sampling = "max"
# feature, label pairs
xs = [0, 1, 1, 2]
ys = [1, 0, 1, 0]
figure, ax = plt.subplots()
figure.set_size_inches(10, 10)
for i, (x, y) in enumerate(zip(xs, ys)):
# get predictions from active learning model
al = ConceptActiveLearner(n_features, hyp_space_type, sampling)
active_learning_prob_one = np.array(
[al.expected_information_gain(x) for x in range(n_features)])
# normalize
active_learning_prob_one = active_learning_prob_one / \
np.sum(active_learning_prob_one)
# perform update
al.update(x=x, y=y)
active_learning_prob_two = np.array(
[al.expected_information_gain(x) for x in range(n_features)])
# normalize
denom = np.sum(active_learning_prob_two)
active_learning_prob_two = np.divide(active_learning_prob_two,
denom,
where=denom != 0)
active_learning_prob_two[np.isclose(denom, 0)] = 0
# get predictions from self-teaching model
st = ConceptSelfTeacher(n_features, hyp_space_type, sampling)
st.update_learner_posterior()
st.update_self_teaching_posterior()
self_teacher_prob_one = st.self_teaching_posterior[0, :, 0]
# update learner posterior after a single observation
updated_learner_posterior = st.learner_posterior[:, x, y]
st.learner_posterior = np.repeat(updated_learner_posterior,
n_labels * n_features).reshape(
n_hyp, n_features, n_labels)
# update learner and self-teacher after a single observation
st.update_learner_posterior()
st.update_self_teaching_posterior()
self_teacher_prob_two = st.self_teaching_posterior[0, :, 0]
# plot second feature prob
plt.subplot(2, 2, i + 1)
plt.plot(
np.arange(1, n_features + 1),
active_learning_prob_two,
color='red',
# linestyle=':',
label="Information Gain model")
plt.plot(np.arange(1, n_features + 1),
self_teacher_prob_two,
color='blue',
label="Self-teaching model")
axes = plt.gca()
axes.set_ylim([0, 1])
plt.xlabel("Feature", fontsize=16)
plt.ylabel("Probability of selecting feature", fontsize=16)
plt.title('x = {}, y = {}'.format(x + 1, y), fontsize=18)
plt.xticks([1, 2, 3], fontsize=16)
plt.yticks(fontsize=16)
handles, labels = ax.get_legend_handles_labels()
plt.legend(fontsize=12)
plt.tight_layout()
plt.savefig('figures/concept_learning_boundary_second_feature_prob.png')
def plot_mismatching_example_figures():
# function to check numbers for made up example
hyp_space_type = "boundary"
n_features = 3
# get predictions from self-teaching model
st = ConceptSelfTeacher(n_features, hyp_space_type)
st.learner_posterior = np.array([[[0, 1/4], [0, 1/2], [0, 1/2]],
[[0, 1/4], [0, 1/2], [1/3, 1/6]],
[[0, 1/4], [1/2, 0], [1/3, 1/6]],
[[0, 1/4], [1/2, 0], [1/3, 1/6]]])
learner_posterior_flat = st.learner_posterior.reshape(4, 6).T
plt.figure()
sns.heatmap(learner_posterior_flat, cmap='Greys',
linewidth=0.5, vmin=0, vmax=1)
plt.xticks([1/2, 3/2, 5/2, 7/2], ['h1', 'h2', 'h3', 'h4'])
plt.yticks([1/2, 3/2, 5/2, 7/2, 9/2, 11/2],
['x=1, y=0', 'x=1, y=1',
'x=2, y=0', 'x=2, y=1',
'x=3, y=0', 'x=3, y=1'],
rotation=0)
plt.tick_params(
axis='both',
which='both',
bottom=False,
left=False)
plt.savefig('figures/example/mismatching_learner_posterior_heatmap.pdf')
plt.close()
teaching_posterior = st.learner_posterior * 1/4
denom = np.sum(teaching_posterior, axis=(1, 2))
teaching_posterior = (teaching_posterior.T / denom.T).T
teaching_posterior_flat = teaching_posterior.reshape(4, 6).T
plt.figure()
sns.heatmap(teaching_posterior_flat, cmap='Greys',
linewidth=0.5, vmin=0, vmax=1)
plt.xticks([1/2, 3/2, 5/2, 7/2], ['h1', 'h2', 'h3', 'h4'])
plt.yticks([1/2, 3/2, 5/2, 7/2, 9/2, 11/2],
['x=1, y=0', 'x=1, y=1',
'x=2, y=0', 'x=2, y=1',
'x=3, y=0', 'x=3, y=1'],
rotation=0)
plt.tick_params(
axis='both',
which='both',
bottom=False,
left=False)
plt.savefig('figures/example/mismatching_teaching_posterior_heatmap.pdf')
plt.close()
learner_posterior_colsum = np.sum(learner_posterior_flat, axis=0)
plt.figure()
sns.barplot(np.arange(4), learner_posterior_colsum, palette='Greys')
plt.xticks(np.arange(4), ['h1', 'h2', 'h3', 'h4'])
plt.savefig('figures/example/mismatching_learner_posterior_colsum.pdf')
learner_posterior_rowsum = np.sum(learner_posterior_flat, axis=1)
plt.figure()
sns.barplot(np.arange(6), learner_posterior_rowsum, palette='Greys')
plt.xticks(np.arange(6), ['x=1, y=0', 'x=1, y=1', 'x=2, y=0',
'x=2, y=1', 'x=3, y=0', 'x=3, y=1'])
plt.savefig('figures/example/mismatching_learner_posterior_rowsum.pdf')
teaching_posterior_rowsum = np.sum(teaching_posterior_flat, axis=1)
plt.figure()
sns.barplot(np.arange(6), teaching_posterior_rowsum, palette='Greys')
plt.xticks(np.arange(6), ['x=1, y=0', 'x=1, y=1', 'x=2, y=0',
'x=2, y=1', 'x=3, y=0', 'x=3, y=1'])
plt.savefig('figures/example/mismatching_teaching_posterior_rowsum.pdf')
# calculate 1/Z
Z = np.sum(learner_posterior_flat, axis=0) * 1/6
Z_inv = 1 / Z
plt.figure()
sns.barplot(np.arange(4), Z_inv, palette='Greys')
plt.xticks(np.arange(4), ['h1', 'h2', 'h3', 'h4'])
plt.savefig('figures/example/mismatching_Z_inv.pdf')
self_teaching_posterior = np.sum(teaching_posterior * 1/4, axis=(0, 2))
plt.figure()
sns.barplot(np.arange(3), self_teaching_posterior, palette='Greys')
plt.xticks(np.arange(3), ['x1', 'x2', 'x3'])
plt.savefig('figures/example/mismatching_self_teaching_posterior.pdf')
# hard code new likelihood
likelihood_flat = np.array([[0, 0, 0, 0],
[1, 1, 1, 1],
[0, 0, 1, 1],
[1, 1, 0, 0],
[0, 2/3, 2/3, 2/3],
[1, 1/3, 1/3, 1/3]])
obs_lik = np.sum(likelihood_flat * 1/4, axis=1)
plt.figure()
sns.barplot(np.arange(6), obs_lik, palette='Greys')
plt.xticks(np.arange(6), ['x=1, y=0', 'x=1, y=1', 'x=2, y=0',
'x=2, y=1', 'x=3, y=0', 'x=3, y=1'])
plt.savefig('figures/example/mismatching_observation_likelihood.pdf')
prior_entropy = np.array([2, 2, 2])
posterior_entropy = -np.sum(learner_posterior_flat *
np.nan_to_num(np.log2(learner_posterior_flat)), axis=1)
plt.figure()
sns.barplot(np.arange(6), posterior_entropy, palette='Greys')
plt.xticks(np.arange(6), ['x=1, y=0', 'x=1, y=1', 'x=2, y=0',
'x=2, y=1', 'x=3, y=0', 'x=3, y=1'])
plt.savefig('figures/example/mismatching_posterior_entropy.pdf')
prior_entropy = np.array([2, 2, 2])
weighted_posterior_entropy = np.array([
obs_lik[0] * posterior_entropy[0] + obs_lik[1] * posterior_entropy[1],
obs_lik[2] * posterior_entropy[2] + obs_lik[3] * posterior_entropy[3],
obs_lik[4] * posterior_entropy[4] + obs_lik[5] * posterior_entropy[5],
])
expected_information_gain = prior_entropy - weighted_posterior_entropy
expected_information_gain = expected_information_gain / \
np.sum(expected_information_gain)
plt.figure()
sns.barplot(np.arange(3), expected_information_gain, palette='Greys')
plt.xticks(np.arange(3), ['x1', 'x2', 'x3'])
plt.savefig('figures/example/mismatching_expected_information_gain.pdf')
prior_entropy = np.array([2, 2, 2, 2, 2, 2])
information_gain = prior_entropy - posterior_entropy
plt.figure()
sns.barplot(np.arange(6), information_gain, palette='Greys')
plt.xticks(np.arange(6), ['x=1, y=0', 'x=1, y=1', 'x=2, y=0',
'x=2, y=1', 'x=3, y=0', 'x=3, y=1'])
plt.savefig('figures/example/mismatching_information_gain.pdf')