def ppm_experiment_1d(seed, sigma, L, b, Ncopy, use_signal_prior):
np.random.seed(seed)
n_iter = 1000
tol = 1e-7
# Generate MRA measurements
y, s, n, x = make_data_1d(L, Ncopy, sigma, b)
if use_signal_prior:
b_prior = b
else:
b_prior = None
t = time()
y_s, s = synchronize_1d(y, method='ppm')
x_init = np.expand_dims(np.mean(y_s, axis=1), axis=-1)
t_ppm = time() - t
err_ppm = relative_error_1d(x_init, x)
results = pd.DataFrame()
results = results.append(
{
'use_signal_prior': use_signal_prior,
'L': L,
'b': b,
'sigma': sigma,
'seed': seed,
'N': Ncopy,
'err': err_ppm,
'num_iter': 0,
't': t_ppm
},
ignore_index=True)
return results
def ppm_synch_em_experiment(seed, sigma, L, b, Ncopy, use_signal_prior):
np.random.seed(seed)
n_iter = 1000
tol = 1e-7
# Generate MRA measurements
y, s, n, x = make_data_1d(L, Ncopy, sigma, b)
if use_signal_prior:
b_prior = b
else:
b_prior = None
y_s, s_est = synchronize_1d(y, method='ppm')
x_init = np.expand_dims(np.mean(y_s, axis=1), axis=-1)
print('start em processing')
t = time()
x_est_em, rho_est_em, num_iter_em_uniform = em_1d(y_s,
sigma,
n_iter,
tol,
x_init,
b=b_prior,
rho_prior=None,
uniform=False)
t_em_uniform = time() - t
err_em_uniform = relative_error_1d(x_est_em, x)
h, bin_edges = np.histogram((s_est - s) % L, bins=np.arange(-0.5, L + 0.5))
measured_rho = h / np.sum(h)
results = pd.DataFrame()
results = results.append(
{
'use_signal_prior': use_signal_prior,
'L': L,
'b': b,
'sigma': sigma,
'seed': seed,
'N': Ncopy,
'err': err_em_uniform,
'num_iter': num_iter_em_uniform,
't': t_em_uniform
},
ignore_index=True)
return results
def synchronize_and_match_em_experiment(seed, sigma, L, b, Ncopy,
use_signal_prior, P):
np.random.seed(seed)
n_iter = 1000
tol = 1e-7
# Generate MRA measurements
y, s, n, x = make_data_1d(L, Ncopy, sigma, b)
if use_signal_prior:
b_prior = b
else:
b_prior = None
y_s, s, _, _ = synchronize_and_match_1d(y, P)
x_init = np.expand_dims(np.mean(y_s, axis=1), axis=-1)
print('start em processing')
t = time()
x_est_em, rho_est_em, num_iter_em_uniform = em_1d(y_s,
sigma,
n_iter,
tol,
x_init,
b=b_prior,
rho_prior=None,
uniform=False)
t_em_uniform = time() - t
err_em_uniform = relative_error_1d(x_est_em, x)
results = pd.DataFrame()
results = results.append(
{
'use_signal_prior': use_signal_prior,
'L': L,
'b': b,
'sigma': sigma,
'seed': seed,
'N': Ncopy,
'err': err_em_uniform,
'num_iter': num_iter_em_uniform,
't': t_em_uniform
},
ignore_index=True)
return results
def synch_em_1d_experiment(seed, sigma, L, b, Ncopy, use_signal_prior, P,
gamma):
np.random.seed(seed)
n_iter = 1000
tol = 1e-7
# Generate MRA measurements
y, s, n, x = make_data_1d(L, Ncopy, sigma, b)
if use_signal_prior:
b_prior = b
else:
b_prior = None
t = time()
y_s, s_est, _, _ = synchronize_and_match_1d(y, P)
#y_s, s_est = synchronize_1d(y,method='ppm')
t_synch = time() - t
x_init = np.expand_dims(np.mean(y_s, axis=1), axis=-1)
h, bin_edges = np.histogram((s_est - s) % L, bins=np.arange(-0.5, L + 0.5))
measured_rho = h / np.sum(h)
print('start synch em 1d processing')
t = time()
x_est_em, rho_est_em, num_iter_em_uniform = em_1d(y_s,
sigma,
n_iter,
tol,
x_init,
b=b_prior,
rho_prior=(measured_rho,
gamma),
uniform=False)
t_em_uniform = time() - t
err_em_uniform = relative_error_1d(x_est_em, x)
plt.plot(measured_rho)
plt.xlabel('shift')
plt.ylabel('Probability')
plt.savefig(
'est_dist/rho_est_L_%d_sigma_%.2f_N_%d_b_%d_seed_%d_SNR_%.2f.png' %
(L, sigma, Ncopy, b, seed, 1 / sigma**2))
plt.clf()
results = pd.DataFrame()
results = results.append(
{
'use_signal_prior': use_signal_prior,
'L': L,
'b': b,
'sigma': sigma,
'seed': seed,
'N': Ncopy,
'err': err_em_uniform,
'num_iter': num_iter_em_uniform,
't': t_synch + t_em_uniform
},
ignore_index=True)
return results
def pearson_test():
np.random.seed(1)
R = 10
sigma = 2
L = 21
N = 1000
P = 100
r_vec = []
pval_vec = []
r_vec2 = []
pval_vec2 = []
r_vec3 = []
pval_vec3 = []
dist = scipy.stats.beta(N / 2 - 1, N / 2 - 1, loc=-1, scale=2)
r = np.arange(0, 1, 0.001)
p = 2 * dist.cdf(-abs(r))
p_critical = 0.05
r_critical = r[p <= 0.05][0]
for q in range(R):
y, s, n, x = make_data_1d(L,N,sigma,0)
y_s_new, s_est_new = synchronize_1d(y, method='ppm')
y_s_new2, s_est_new2, y_s_old, s_est_old = synchronize_and_match_1d(y, P=P)
s_est_new = np.asarray(s_est_new, dtype=int)
s_est_new2 = np.asarray(s_est_new2, dtype=int)
n_shifted = np.zeros((L, N))
n_shifted2 = np.zeros((L, N))
x_shifted = np.zeros((L, N))
x_shifted2 = np.zeros((L, N))
x_only = np.zeros((L, N))
for i in range(N):
n_shifted[:, i] = np.roll(n[:, i], -s_est_new[i])
n_shifted2[:, i] = np.roll(n[:, i], -s_est_new2[i])
x_shifted[:, i] = np.roll(x, s[i] - s_est_new[i])
x_shifted2[:, i] = np.roll(x, s[i] - s_est_new2[i])
x_only[:, i] = np.roll(x, s[i])
for i in range(L):
for j in range(L):
r, pval = stats.pearsonr(x_only[i], n[j])
r_vec.append(r)
pval_vec.append(pval)
r, pval = stats.pearsonr(x_shifted[i], n_shifted[j])
r_vec2.append(r)
pval_vec2.append(pval)
r, pval = stats.pearsonr(x_shifted2[i], n_shifted2[j])
r_vec3.append(r)
pval_vec3.append(pval)
rmin = -.25
dr = 0.01
rmax = np.abs(rmin) + dr
weights = np.ones_like(r_vec) / len(r_vec)
weights2 = np.ones_like(r_vec2) / len(r_vec2)
alpha = 1
plt.hist(r_vec2, bins=np.arange(rmin, rmax, dr), alpha=alpha, weights=weights2)
plt.hist(r_vec3, bins=np.arange(rmin, rmax, dr), alpha=alpha, weights=weights2)
plt.hist(r_vec, bins=np.arange(rmin, rmax, dr), alpha=alpha, weights=weights)
plt.xlabel('Pearson correlation coefficient')
plt.ylabel('Probability')
plt.legend(['After Synchronization', 'After Synchronize and Match', 'Before Synchronization'], fontsize='small')
plt.axvline(r_critical, color='k', linestyle='dashed', linewidth=1)
plt.axvline(-r_critical, color='k', linestyle='dashed', linewidth=1)
if not os.path.exists('1d_figures/'):
os.mkdir('1d_figures/')
plt.savefig('1d_figures/pearson_test_1d_N_%d_R_%d_sigma_%.2f_L_%d_pval_%.4f_.png'%(N,R,sigma,L,p_critical))
plt.savefig('1d_figures/pearson_test_1d_N_%d_R_%d_sigma_%.2f_L_%d_pval_%.4f.eps'%(N,R,sigma,L,p_critical))