def main():
sample_sizes = [250, 500, 1000, 2000, 10000]
rhos = [0, 0.3, 0.6, 0.9]
r = 2
s = 2
K = 50
time_results = {
rho: [{ssize: []
for ssize in sample_sizes}, None]
for rho in rhos
}
all_results = []
for rho in rhos:
for sample_size in sample_sizes:
cov = np.array([[1., rho], [rho, 1.]])
dist = MultivariateNormal(mean=np.zeros(2), cov=cov)
t_ci, t_nad, t_ml = [], [], []
delta = lambda x: chi2.ppf(0.97, x**2 - 1)
print(f"Timing samples {sample_size} for r = {rho}")
for k in range(K):
xy_sample = dist.sample(sample_size)
plane = Plane(xy_sample)
# Adaptive algorithm
t0_ad = time.time()
ad = AdaptiveAlgorithm(xy_sample, delta, r, s).run()
t_ci.append(time.time() - t0_ad)
t0_nad = time.time()
nad = NonAdaptivePartition(xy_sample, bins=[50, 50]).run()
t_nad.append(time.time() - t0_nad)
t0_ml = time.time()
ml = -np.log(
1 - pearsonr(xy_sample[:, 0], xy_sample[:, 1])[0]**2) / 2
t_ml.append(time.time() - t0_ml)
all_results.append((ad, nad, ml))
time_results[rho][0][sample_size] = [
np.mean(t_ml), np.mean(t_ci),
np.mean(t_nad)
]
print(
f"Times: ML: {np.mean(t_ml)}, CI: {np.mean(t_ci)}, NAD: {np.mean(t_nad)}"
)
generate_timing_table(time_results)
print(len(all_results))
def main():
sample_sizes = [250, 500, 1000, 2000, 10000]
rhos = [0, 0.3, 0.6, 0.9]
K = 20
rs_2 = []
rs_4 = []
rs_5 = []
rs_10 = []
results = {
rho: [{ssize: []
for ssize in sample_sizes}, None]
for rho in rhos
}
for rho in rhos:
rs_2_std = []
rs_4_std = []
rs_5_std = []
rs_10_std = []
real_mi = -np.log(1 - rho**2) / 2
results[rho][1] = real_mi
for sample_size in sample_sizes:
cov = np.array([[1., rho], [rho, 1.]])
dist = MultivariateNormal(mean=np.zeros(2), cov=cov)
rs_2_l, rs_4_l, rs_5_l, rs_10_l = [], [], [], []
delta = lambda x: chi2.ppf(0.97, x**2 - 1)
for k in range(K):
xy_sample = dist.sample(sample_size)
# Adaptive algorithm
plane = Plane(xy_sample)
rs_2_l.append(
kl_estimate(
plane,
AdaptiveAlgorithm(xy_sample, delta, 2, 2).run()))
plane = Plane(xy_sample)
rs_4_l.append(
kl_estimate(
plane,
AdaptiveAlgorithm(xy_sample, delta, 4, 4).run()))
plane = Plane(xy_sample)
rs_5_l.append(
kl_estimate(
plane,
AdaptiveAlgorithm(xy_sample, delta, 5, 5).run()))
plane = Plane(xy_sample)
rs_10_l.append(
kl_estimate(
plane,
AdaptiveAlgorithm(xy_sample, delta, 10, 10).run()))
results[rho][0][sample_size] = [
np.mean(rs_2_l),
np.mean(rs_4_l),
np.mean(rs_5_l),
np.mean(rs_10_l)
]
print(
"---------------------------------------------------------------------------------------------"
)
print("rho: %.2f, Sample Size: %d, Real MI: %.4f" %
(rho, sample_size, real_mi))
print("r=s=2: %.4f, r=s=4: %.4f, r=s=5: %.4f, r=s=10: %.4f" %
(np.mean(rs_2_l), np.mean(rs_4_l), np.mean(rs_5_l),
np.mean(rs_5_l)))
rs_2_std.append(np.std(rs_2_l))
rs_4_std.append(np.std(rs_4_l))
rs_5_std.append(np.std(rs_5_l))
rs_10_std.append(np.std(rs_5_l))
rs_2.append(rs_2_std)
rs_4.append(rs_4_std)
rs_5.append(rs_5_std)
rs_10.append(rs_10_std)
generate_rs_table(results)
all_std = [rs_2, rs_4, rs_5, rs_10]
for i, _ in enumerate(["r=s=2", "r=s=4", "r=s=5", "r=s=10"]):
plt.figure()
plt.semilogx(sample_sizes,
all_std[i][0],
'-o',
label=r'$\rho$ =' + f'{0.0}')
plt.semilogx(sample_sizes,
all_std[i][1],
'-o',
label=r'$\rho$ =' + f'{0.3}')
plt.semilogx(sample_sizes,
all_std[i][2],
'-o',
label=r'$\rho$ =' + f'{0.6}')
plt.semilogx(sample_sizes,
all_std[i][3],
'-o',
label=r'$\rho$ =' + f'{0.9}')
plt.xlabel('$\log_{10}$ of sample size')
if i == 0:
plt.ylabel("std($\hat{I}_{CI}^{r=s=2}$)")
plt.title(
"Standard deviation of MI estimator $I_{CI}$ with $r=s=2$")
elif i == 1:
plt.ylabel("std($\hat{I}_{CI}^{r=s=4}$)")
plt.title(
"Standard deviation of MI estimator $I_{CI}$ with $r=s=4$")
elif i == 2:
plt.ylabel("std($\hat{I}_{CI}^{r=s=5}$)")
plt.title(
"Standard deviation of MI estimator $I_{CI}$ with $r=s=5$")
else:
plt.ylabel("std($\hat{I}_{CI}^{r=s=10}$)")
plt.title(
"Standard deviation of MI estimator $I_{CI}$ with $r=s=10$")
plt.legend()
plt.show()
def main():
sample_sizes = [250, 500, 1000, 2000, 10000]
rhos = [0, 0.3, 0.6, 0.9]
r = 2
s = 2
K = 50
ci_mi_all_std = []
na_mi_all_std = []
ml_mi_all_std = []
results = {
rho: [{ssize: []
for ssize in sample_sizes}, None]
for rho in rhos
}
for rho in rhos:
ci_mi_std = []
na_mi_std = []
ml_mi_std = []
real_mi = -np.log(1 - rho**2) / 2
results[rho][1] = real_mi
for sample_size in sample_sizes:
cov = np.array([[1., rho], [rho, 1.]])
dist = MultivariateNormal(mean=np.zeros(2), cov=cov)
ci_mi_l, ml_mi_l, na_mi_l = [], [], []
delta = lambda x: chi2.ppf(0.97, x**2 - 1)
for k in range(K):
xy_sample = dist.sample(sample_size)
plane = Plane(xy_sample)
# Adaptive algorithm
ci_mi_l.append(
kl_estimate(
plane,
AdaptiveAlgorithm(xy_sample, delta, r, s).run()))
na_mi_l.append(
kl_estimate(
plane,
NonAdaptivePartition(xy_sample, bins=[50, 50]).run()))
ml_mi_l.append(
-np.log(1 -
pearsonr(xy_sample[:, 0], xy_sample[:, 1])[0]**2) /
2)
results[rho][0][sample_size] = [
np.mean(ml_mi_l),
np.mean(ci_mi_l),
np.mean(na_mi_l)
]
print(
"---------------------------------------------------------------------------------------------"
)
print("rho: %.2f, Sample Size: %d, Real MI: %.4f" %
(rho, sample_size, real_mi))
print(
"Adaptive Partition MI: %.4f, NA Partition MI: %.4f, ML MI: %.4f"
% (np.mean(ci_mi_l), np.mean(na_mi_l), np.mean(ml_mi_l)))
ci_mi_std.append(np.std(ci_mi_l))
na_mi_std.append(np.std(na_mi_l))
ml_mi_std.append(np.std(ml_mi_l))
ci_mi_all_std.append(ci_mi_std)
na_mi_all_std.append(na_mi_std)
ml_mi_all_std.append(ml_mi_std)
generate_table(results)
all_std = [ci_mi_all_std, na_mi_all_std, ml_mi_all_std]
for i, _ in enumerate(["CI", "NA", "ML"]):
plt.figure()
plt.semilogx(sample_sizes,
all_std[i][0],
'-o',
label=r'$\rho$ =' + f'{0.0}')
plt.semilogx(sample_sizes,
all_std[i][1],
'-o',
label=r'$\rho$ =' + f'{0.3}')
plt.semilogx(sample_sizes,
all_std[i][2],
'-o',
label=r'$\rho$ =' + f'{0.6}')
plt.semilogx(sample_sizes,
all_std[i][3],
'-o',
label=r'$\rho$ =' + f'{0.9}')
plt.xlabel('$\log_{10}$ of sample size')
if i == 0:
plt.ylabel("std($\hat{I}_{CI}$)")
plt.title("Standard deviation of MI estimator $I_{CI}$")
elif i == 1:
plt.ylabel("std($\hat{I}_{NA}$)")
plt.title("Standard deviation of MI estimator $I_{NA}$")
else:
plt.ylabel("std($\hat{I}_{ML}$)")
plt.title("Standard deviation of MI estimator $I_{ML}$")
plt.legend()
plt.show()