def PlotCredibleIntervals(self):
# plots credible intervals ("weather plot") for each order we're interested in
try:
# kernel for fit
self.kernel_fit = RBF(length_scale = self.ls) + \
WhiteKernel(noise_level = self.nugget, noise_level_bounds = 'fixed')
# truncation GP
self.gp_trunc = gm.TruncationGP(kernel = self.kernel_fit, ref = self.ref, \
ratio = self.ratio, center = self.center, disp = self.disp, \
df = self.df, scale = self.scale)
self.gp_trunc.fit(self.X[self.x_train_mask], y = self.data[self.x_train_mask], \
orders = self.orders_array)
# extracts truncation error for each x-value
self.norm_trunc_cov = self.gp_trunc.cov(self.X[self.x_valid_mask],
start=0,
end=0)
self.norm_residuals = (self.data_true[self.x_valid_mask, None] - \
self.data[self.x_valid_mask]) / \
(self.ratio**(self.orders_array+1) / np.sqrt(1 - self.ratio**2))
self.gr_dgn_trunc = gm.GraphicalDiagnostic(self.norm_residuals, \
mean = np.zeros(self.x[self.x_valid_mask].shape[0]), \
cov = self.norm_trunc_cov, colors = self.colors, gray = gray, \
black = softblack)
fig, ax = plt.subplots(figsize=(3.4, 3.2))
# plots the curves
for i, n in enumerate(self.orders_array):
norm_residuals_alt = self.data_true[self.x_valid_mask] - \
self.data[self.x_valid_mask][:,i]
norm_trunc_cov_alt = self.gp_trunc.cov(
self.X[self.x_valid_mask], start=n + 1)
gr_dgn_trunc_alt = gm.GraphicalDiagnostic(
norm_residuals_alt, mean = np.zeros(self.x[self.x_valid_mask].shape[0]), \
cov = norm_trunc_cov_alt, colors = [self.colors[i]], gray = gray, black = softblack)
gr_dgn_trunc_alt.credible_interval(
np.linspace(1e-5, 1, 100),
band_perc=[0.68, 0.95],
ax=ax,
title=None,
xlabel=r'Credible Interval ($100\alpha\%$)',
ylabel=r'Empirical Coverage ($\%$)')
ax.set_xticks([0, 0.2, 0.4, 0.6, 0.8, 1])
ax.set_xticklabels([0, 20, 40, 60, 80, 100])
ax.set_yticks([0, 0.2, 0.4, 0.6, 0.8, 1])
ax.set_yticklabels([0, 20, 40, 60, 80, 100])
fig.tight_layout()
except:
print(
"The credible intervals could not be calculated at one or more orders."
)
def PlotPC(self):
# plots the pivoted Cholesky decomposition in one of two ways
try:
# kernel for GP fit
self.kernel_fit = RBF(length_scale = self.ls) + \
WhiteKernel(noise_level = self.nugget, noise_level_bounds = 'fixed')
# fits GP and extracts error bars
self.gp_diagnostic = gm.ConjugateGaussianProcess(kernel = self.kernel_fit, center = self.center, \
disp = self.disp, df = self.df, scale = self.scale, n_restarts_optimizer = 2, \
random_state = 32)
self.gp_diagnostic.fit(self.X[self.x_train_mask],
self.coeffs[self.x_train_mask])
self.pred, self.std = self.gp_diagnostic.predict(self.X,
return_std=True)
self.underlying_std = np.sqrt(self.gp_diagnostic.cov_factor_)
# extracts underlying covariance matrix and calculates the diagnostics
self.mean_underlying = self.gp_diagnostic.mean(
self.X[self.x_valid_mask])
self.cov_underlying = self.gp_diagnostic.cov(
self.X[self.x_valid_mask])
self.gdgn = gm.GraphicalDiagnostic(self.coeffs[self.x_valid_mask], \
self.mean_underlying, self.cov_underlying, colors = self.colors,
gray = gray, black = softblack)
# plots the pivoted Cholesky decomposition
with plt.rc_context({
"text.usetex": True,
"text.latex.preview": True
}):
# with plt.rc_context({"text.usetex": True}):
fig, ax = plt.subplots(figsize=(3.2, 3.2))
self.gdgn.pivoted_cholesky_errors(ax=ax, title=None)
ax.set_xticks([2, 4, 6, 8, 10, 12])
ax.set_xticks([1, 3, 5, 7, 9, 11], minor=True)
ax.set_yticks([-2, -1, 0, 1, 2])
ax.text(0.04, 0.967, r'$\mathrm{D}_{\mathrm{PC}}$', bbox = text_bbox, \
transform = ax.transAxes, va = 'top', ha = 'left')
fig.tight_layout()
plt.show()
except:
print(
"The pivoted Cholesky decomposition could not be calculated at one or more orders."
)
def PlotMD(self, plot_type='box'):
# plots the Mahalanobis distance in one of two ways (box-and-whisker or histogram)
try:
# kernel for GP fit
self.kernel_fit = RBF(length_scale = self.ls) + \
WhiteKernel(noise_level = self.nugget, noise_level_bounds = 'fixed')
# fits GP and extracts error bars
self.gp_diagnostic = gm.ConjugateGaussianProcess(kernel = self.kernel_fit, \
center = self.center, disp = self.disp, df = self.df, scale = self.scale, \
n_restarts_optimizer = 2, random_state = 32)
self.gp_diagnostic.fit(self.X[self.x_train_mask],
self.coeffs[self.x_train_mask])
self.pred, self.std = self.gp_diagnostic.predict(self.X,
return_std=True)
self.underlying_std = np.sqrt(self.gp_diagnostic.cov_factor_)
# extracts underlying covariance matrix and calculates the diagnostics
self.mean_underlying = self.gp_diagnostic.mean(
self.X[self.x_valid_mask])
self.cov_underlying = self.gp_diagnostic.cov(
self.X[self.x_valid_mask])
self.gdgn = gm.GraphicalDiagnostic(self.coeffs[self.x_valid_mask], \
self.mean_underlying, self.cov_underlying, colors = self.colors,
gray = gray, black = softblack)
# plots the Mahalanobis distance
if plot_type == 'box':
fig, ax = plt.subplots(figsize=(1.5, 3.0))
ax = self.gdgn.md_squared(type = plot_type, trim = False, title = None, \
xlabel = r'$\mathrm{D}_{\mathrm{MD}}^2$')
elif plot_type == 'hist':
fig, ax = plt.subplots(figsize=(9, 3.2))
ax = self.gdgn.md_squared(type = plot_type, title = None, \
xlabel = r'$\mathrm{D}_{\mathrm{MD}}^2$')
ax.set_ylim(0, 25)
else:
return 0
offset_xlabel(ax)
# fig.tight_layout()
except:
print(
"The Mahalanobis distance could not be calculated at one or more orders."
)
def PlotTruncations(self):
# plots the data summed to each order we're interested in
try:
# kernel for fit
self.kernel_fit = RBF(length_scale = self.ls) + \
WhiteKernel(noise_level = self.nugget, noise_level_bounds = 'fixed')
# fits truncation GP to data given a mask
self.gp_trunc = gm.TruncationGP(kernel = self.kernel_fit, ref = self.ref, \
ratio = self.ratio, center = self.center, disp = self.disp, \
df = self.df, scale = self.scale)
self.gp_trunc.fit(self.X[self.x_train_mask], y = self.data[self.x_train_mask], \
orders = self.orders_array)
# extracts truncation error for each x-value
self.norm_trunc_cov = self.gp_trunc.cov(self.X[self.x_valid_mask],
start=0,
end=0)
self.norm_residuals = (self.data_true[self.x_valid_mask, None] - \
self.data[self.x_valid_mask]) / \
(self.ratio**(self.orders_array+1) / np.sqrt(1 - self.ratio**2))
self.gr_dgn_trunc = gm.GraphicalDiagnostic(self.norm_residuals, \
mean = np.zeros(self.x[self.x_valid_mask].shape[0]), \
cov = self.norm_trunc_cov, colors = self.colors, gray = gray, \
black = softblack)
fig, axes = plt.subplots(math.ceil(self.n_orders / 2), 2, sharex = True, sharey = True, \
figsize = (3.9, 3.2))
# plots curves with error
for i, n in enumerate(self.orders_array):
_, std_trunc = self.gp_trunc.predict(self.X, order = n, return_std = True, \
kind = 'trunc')
for j in range(i, self.n_orders):
ax = axes.ravel()[j]
ax.plot(self.x,
self.data[:, i],
zorder=i - 5,
c=self.colors[i])
ax.fill_between(self.x, self.data[:, i] + 2 * std_trunc, \
self.data[:, i] - 2 * std_trunc, zorder = i-5, \
facecolor = self.light_colors[i], edgecolor = self.colors[i], \
lw = edgewidth)
ax = axes.ravel()[i]
ax.plot(self.x, self.data_true, color=softblack, lw=1, ls='--')
ax.set_xticks([0.25, 0.5, 0.75])
ax.set_xticks(self.x[self.x_valid_mask], minor=True)
ax.set_xticklabels([0.25, 0.5, 0.75])
ax.set_yticks([0, 10, 20])
ax.set_yticks([-10, 0, 10, 20, 30])
ax.set_ylim(-15, 37)
axes[1, 0].set_xlabel(r'$x$')
axes[1, 1].set_xlabel(r'$x$')
fig.tight_layout(h_pad=0.3, w_pad=0.3)
except:
print(
"The truncation error curves could not be calculated at one or more orders."
)