data = loadmat("../data/02-solar.mat")
X = data['X']
y = data['y']
X_train, y_train, X_test, y_test, N, N_test = prepare_dataset(X, y)
print "num_train:", len(X_train)
print "num_test:", len(X_test)
kernel = RBF(input_dim=1, variance=1., lengthscale=1.)
m = GPRegression(X_train, y_train, kernel)
m.optimize()
res = 100
pred_mean, pred_std = m.predict(X_test)
plt.plot(X_test, pred_mean, 'b-')
plt.plot(X_test, pred_mean + 2 * pred_std, 'b--')
plt.plot(X_test, pred_mean - 2 * pred_std, 'b--')
plt.plot(X_train, y_train, 'b.', markersize=3)
plt.plot(X_test, y_test, 'r.', markersize=5)
plt.grid(True)
plt.xlabel(r"$X$")
plt.ylabel(r"$y$")
plt.savefig("gp_regression_data_fit.eps", bbox_inches='tight')
plt.show()
s = GaussianQuadraticTest(None)
gradients = compute_gp_regression_gradients(y_test, pred_mean, pred_std)
U_matrix, stat = s.get_statistic_multiple_custom_gradient(y_test[:, 0], gradients[:, 0])
num_test_samples = 10000
thinning = np.argmin(np.abs(autocorrelation - 0.5)) + 1
return thinning, autocorrelation
def normal_mild_corr(N):
X = metropolis_hastings(log_normal,
chain_size=N,
thinning=1,
x_prev=np.random.randn(),
step=0.55)
return X
X = normal_mild_corr(TEST_CHAIN_SIZE)
sgld_thinning, autocorr = get_thinning(X, 500)
print('thinning for sgld t-student simulation ', sgld_thinning,
autocorr[sgld_thinning])
X = normal_mild_corr(sgld_thinning * 100000)
X = X[::sgld_thinning]
r = acf(X, nlags=30)
print(r)
seaborn.set_style("whitegrid")
plt.plot(r)
plt.xlabel('lags')
plt.ylabel('auto correlation')
plt.ylim([0, 1])
plt.tight_layout()
plt.savefig('../write_up/img/sgld_lags.eps')
return DataFrame(data)
p_values = to_data_frame(p_values[::5], epsilon[::5])
# likelihood_evaluations = to_data_frame(likelihood_evaluations, epsilon)
plt.figure()
sns.boxplot(x=0, y=1, data=p_values, palette="BuGn_d")
plt.ylabel("p values")
plt.xlabel("epsilon")
plt.tight_layout()
plt.savefig('../../write_up/img/Heiko1.pdf')
plt.figure()
plt.plot(epsilon[::2], np.mean(likelihood_evaluations[::2], axis=1), 'g')
plt.ylabel("likelihood evaluations")
plt.xlabel("epsilon")
plt.tight_layout()
plt.savefig('../../write_up/img/Heiko2.pdf')
#
# f, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 4), sharex=True)
#
# sns.boxplot(x=0, y=1, data=p_values, palette="BuGn_d", ax=ax1)
# ax1.set_ylabel("p values")
# ax1.set_xlabel("")
#
# y2 = likelihood_evaluations
# sns.barplot(x=0, y=1, data=likelihood_evaluations, palette="RdBu_d", ax=ax2)
#
# ax2.set_ylabel("Likelihood evaluations")
# estimate size of thinning
def get_thinning(X,nlags = 50):
autocorrelation = acf(X, nlags=nlags, fft=True)
# find correlation closest to given v
thinning = np.argmin(np.abs(autocorrelation - 0.5)) + 1
return thinning, autocorrelation
def normal_mild_corr(N):
X = metropolis_hastings(log_normal, chain_size=N, thinning=1, x_prev=np.random.randn(),step=0.55)
return X
X = normal_mild_corr(TEST_CHAIN_SIZE)
sgld_thinning, autocorr = get_thinning(X,500)
print('thinning for sgld t-student simulation ', sgld_thinning,autocorr[sgld_thinning])
X = normal_mild_corr(sgld_thinning *100000)
X = X[::sgld_thinning]
r= acf(X,nlags=30)
print(r)
seaborn.set_style("whitegrid")
plt.plot(r)
plt.xlabel('lags')
plt.ylabel('auto correlation')
plt.ylim([0,1])
plt.tight_layout()
plt.savefig('../write_up/img/sgld_lags.eps')
X_train, y_train, X_test, y_test, N, N_test = prepare_dataset(X, y)
print "num_train:", len(X_train)
print "num_test:", len(X_test)
kernel = RBF(input_dim=1, variance=0.608, lengthscale=0.207)
m = GPRegression(X_train, y_train, kernel, noise_var=0.283)
m.optimize()
res = 100
pred_mean, pred_std = m.predict(X_test)
X_test_plot = X_test[:, 0] * 116.502738394 + 1815.93213296
fig, ax = plt.subplots()
plt.plot(X_test_plot, pred_mean, "r-")
# plt.plot(X_test, pred_mean + 2 * pred_std, 'b--')
# plt.plot(X_test, pred_mean - 2 * pred_std, 'b--')
# some hacks to make x axis ok again
lower = (pred_mean - 2 * pred_std)[:, 0]
upper = (pred_mean + 2 * pred_std)[:, 0]
plt.fill_between(X_test_plot, lower, upper, color="r", alpha=0.3)
plt.plot(X_train * 116.502738394 + 1815.93213296, y_train, "b.", markersize=3)
plt.plot(X_test_plot, y_test, "*", color="black", markersize=5)
plt.grid(True)
plt.xlabel(r"Year")
plt.ylabel(r"Solar activity (normalised)")
start, end = ax.get_xlim()
ax.xaxis.set_ticks(np.arange(start, end, 100))
data.append([epsilon[i], eval])
return DataFrame(data)
p_values = to_data_frame(p_values[::5], epsilon[::5])
# likelihood_evaluations = to_data_frame(likelihood_evaluations, epsilon)
plt.figure()
sns.boxplot(x=0, y=1, data=p_values, palette="BuGn_d")
plt.ylabel("p values")
plt.xlabel("epsilon")
plt.tight_layout()
plt.savefig('../../write_up/img/Heiko1.pdf')
plt.figure()
plt.plot(epsilon[::2],np.mean(likelihood_evaluations[::2],axis=1),'g')
plt.ylabel("likelihood evaluations")
plt.xlabel("epsilon")
plt.tight_layout()
plt.savefig('../../write_up/img/Heiko2.pdf')
#
# f, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 4), sharex=True)
#
# sns.boxplot(x=0, y=1, data=p_values, palette="BuGn_d", ax=ax1)
# ax1.set_ylabel("p values")
# ax1.set_xlabel("")
#
# y2 = likelihood_evaluations
# sns.barplot(x=0, y=1, data=likelihood_evaluations, palette="RdBu_d", ax=ax2)
#
# ax2.set_ylabel("Likelihood evaluations")
