alpha=.2,
zorder=2)
# Compute factor for histogram height
ylims = axes[i_clf].get_ylim()
factor = 1.5 * ylims[1] / len(hist_data)
# Plot annotation
axes[i_clf].set_xlabel("probability score")
# Plot histogram
if plot_hist:
axes[i_clf].hist(hist_data,
weights=factor * np.ones_like(hist_data),
bottom=ylims[0],
zorder=0,
color="gray",
alpha=0.4)
# Plot annotation and legend
axes[i_clf].set_title(clf_name_dict[clf_names[i_clf]])
if i_clf == 0:
axes[i_clf].set_ylabel("latent function")
if i_clf + 1 == len(clf_names):
axes[i_clf].legend(prop={'size': 9},
labelspacing=0.2) # loc="lower right"
# Save plot to file
texfig.savefig(filename)
plt.close("all")
fig, axes = texfig.subplots(width=7, ratio=.2, nrows=1, ncols=3, w_pad=1)
for i, (m, lab) in enumerate(var_list):
axes[i].plot(metrics_train["iter"][2::],
metrics_train[m][2::],
label="train")
axes[i].plot(metrics_test["iter"][2::],
metrics_test[m][2::],
label="test")
axes[i].set_xlabel("epoch")
axes[i].set_ylabel(lab)
for j, metric_calib in enumerate([
1 - metrics_calib["acc_calib"], metrics_calib["NLL_calib"],
metrics_calib["ECE_calib"]
]):
axes[j].axhline(y=metric_calib,
xmin=0,
xmax=1,
color="red",
linestyle="--")
axes[j].plot(metrics_test["iter"][-1],
metric_calib,
label="test + calibr.",
color="red",
marker='o',
markersize=6)
axes[2].legend(prop={'size': 9}, labelspacing=0.2)
texfig.savefig(os.path.join(dir_path, "ece_logloss"))
plt.close('all')
def plot(self,
file,
metrics_list,
width=None,
height=None,
scatter=False,
confidence=True):
"""
Plots the given list of metrics for the active learning experiment.
Parameters
----------
file : str
Filename of resulting plot.
metrics_list : list
List of names of metrics to plot.
Returns
-------
"""
# Initialization
n_subplots = len(metrics_list)
# Generate curves for the given metrics
if width is None:
width = 3.25 * n_subplots
if height is None:
height = 1.7
fig, axes = texfig.subplots(nrows=n_subplots,
width=width,
ratio=height * 1.0 / width,
w_pad=1,
sharex=True)
cmap = get_cmap(
"tab10"
) # https://matplotlib.org/gallery/color/colormap_reference.html
# Allow for one metric only
if n_subplots == 1:
axes = [axes]
for ax_ind, metric_name in enumerate(metrics_list):
# Plot calibration ranges
for cp in self.calib_points:
axes[ax_ind].axvspan(cp,
cp + self.calib_size,
alpha=0.3,
color='gray',
linewidth=0.0)
# Plot metric curves
for i_calmethod, calib_method in enumerate(
np.unique(self.result_df["calibration_method"])):
# Extract relevant data
df_tmp = self.result_df.loc[
self.result_df["calibration_method"] == calib_method]
xdata = np.array(df_tmp["n_samples_queried"], dtype="float64")
ydata = np.array(df_tmp[metric_name], dtype="float64")
# Compute average samples queried and restrict plot
grouped = df_tmp.groupby(["calibration_method", "cv_run"])
summ_stats = grouped.agg(np.max)
mean_n_samples_queried = np.mean(
summ_stats["n_samples_queried"])
std_n_samples_queried = np.std(summ_stats["n_samples_queried"])
print("{} samples queried: {} +- {}".format(
calib_method, mean_n_samples_queried,
std_n_samples_queried))
# Fit GP to result
k = gpflow.kernels.Matern52(
input_dim=1, lengthscales=1000,
variance=.1) + gpflow.kernels.White(input_dim=1,
variance=.01)
m = gpflow.models.GPR(xdata.reshape(-1, 1),
ydata.reshape(-1, 1),
kern=k)
opt = gpflow.train.ScipyOptimizer()
opt.minimize(m)
# Predict GP mean up to mean of n_samples_qeried
xx = np.linspace(np.min(xdata), mean_n_samples_queried,
1000).reshape(-1, 1)
mean, var = m.predict_f(xx)
axes[ax_ind].plot(xx,
mean,
color=cmap.colors[i_calmethod],
zorder=10,
label="MF entropy " + calib_method)
if scatter:
axes[ax_ind].scatter(xdata,
ydata,
color=cmap.colors[i_calmethod],
s=4,
alpha=0.3,
edgecolors='none')
if confidence:
axes[ax_ind].fill_between(
xx[:, 0],
mean[:, 0] - 1.96 * np.sqrt(var[:, 0]),
mean[:, 0] + 1.96 * np.sqrt(var[:, 0]),
alpha=0.3,
linewidth=0.0)
# Set labels and legend
if ax_ind + 1 == len(axes):
axes[ax_ind].set_xlabel("queried samples")
axes[ax_ind].set_ylabel(metric_name)
axes[ax_ind].legend(prop={'size': 9}, labelspacing=0.2)
# Save plot to file
texfig.savefig(os.path.join(file), bbox_inches='tight', pad_inches=0)
plt.close("all")
def plot_calibration_comparison(cal_metrics_df, cal_methods, alpha, beta,
beta_name, statistic, miscal_func,
miscal_func_name, cal_size, dir_out):
# --Plot confidence distribution-- #
xx = np.linspace(0.5, 1, 1000)
fig, ax = texfig.subplots()
for bp in np.column_stack([alpha, beta]):
ax.plot(xx,
scipy.stats.beta.pdf(2 * xx - 1, a=bp[0], b=bp[1]),
label="alpha={:.1f}, beta={:.1f}".format(bp[0], bp[1]),
color="blue")
ax.set_ylim([0, 5])
ax.set_xlabel("confidence")
ax.set_ylabel("density")
ax.set_title("confidence histogram")
texfig.savefig(filename=dir_out + '/plots/' + 'conf_dist_' + beta_name)
# --Plot miscalibration function -- #
fig, ax = texfig.subplots(ratio=1)
ax.plot(xx, xx, linestyle="dashed", color="gray")
ax.plot(xx, miscal_func(xx), label=miscal_func_name, color="red")
ax.legend()
ax.axis('equal')
ax.set_xlabel('confidence')
ax.set_ylabel('accuracy')
ax.set_title("reliability diagram")
texfig.savefig(filename=dir_out + '/plots/' + 'miscal_' +
miscal_func_name)
# --Plot given statistic -- #
if len(np.unique(alpha)) <= len(np.unique(beta)):
slice_param = np.unique(alpha)
slice_param_name = 'alpha'
x_param = beta
x_param_name = 'beta'
else:
slice_param = np.unique(beta)
slice_param_name = 'beta'
x_param = alpha
x_param_name = 'alpha'
fig, ax = texfig.subplots(width=6, ratio=0.4, sharey='row')
for i, sl_param in enumerate(slice_param):
for calm in cal_methods:
df_tmp = cal_metrics_df.loc[
(cal_metrics_df['model'] == calm) &
(cal_metrics_df['miscalibration_func'] == miscal_func_name)
& (cal_metrics_df['size'] == cal_size) &
(cal_metrics_df[slice_param_name] == sl_param) &
([el in x_param for el in cal_metrics_df[x_param_name]])]
ax.plot(df_tmp[x_param_name],
np.abs(df_tmp[statistic + '.mean']),
label=calm)
ax.fill_between(df_tmp[x_param_name],
np.abs(df_tmp[statistic + '.mean']) +
2 * df_tmp[statistic + '.std'],
np.abs(df_tmp[statistic + '.mean']) -
2 * df_tmp[statistic + '.std'],
alpha=0.15)
ax.set_title('{}={:.2f}'.format(slice_param_name, sl_param))
ax.set_xlabel(x_param_name)
# ax[i].set_yscale("log", nonposy='clip')
ax.set_ylabel(statistic)
ax.set_ylim(bottom=0, auto=True)
ax.legend(bbox_to_anchor=(1.04, 0.5),
loc="center left",
borderaxespad=0)
# Save to file
if not os.path.exists(dir_out + '/plots/' + statistic):
os.makedirs(dir_out + '/plots/' + statistic)
texfig.savefig(dir_out + '/plots/' + statistic + '/' + beta_name +
'_' + miscal_func_name + '_' + statistic + '_' +
str(cal_size))
plt.close('all')
def plot_feature_space_level_set(seed,
dir_out='pycalib/out/synthetic_data/'):
import sklearn.datasets
from sklearn.neural_network import MLPClassifier
import matplotlib.colors
# Setup
train_size = 1000
cal_size = 100
noise = .25
contour_levels = 10
# generate 2d classification dataset
np.random.seed(seed)
X, y = sklearn.datasets.make_circles(n_samples=train_size, noise=noise)
# train classifier
clf = MLPClassifier(hidden_layer_sizes=[10, 10], alpha=1, max_iter=200)
clf.fit(X, y)
# scatter plot, dots colored by class value
df = pd.DataFrame(dict(x=X[:, 0], y=X[:, 1], label=y))
markers = {0: 'x', 1: '.'}
fig, ax = texfig.subplots(width=8,
ratio=.3,
nrows=1,
ncols=3,
sharex=True,
sharey=True)
# grouped = df.groupby('label')
# for key, group in grouped:
# group.plot(ax=ax[0], kind='scatter', x='x', y='y', label=key, marker=markers[key], color='gray', alpha=.75)
# Put the result into a color plot
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
h = .02 # step size in the mesh
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, x_max]x[y_min, y_max].
if hasattr(clf, "decision_function"):
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
p_pred = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])
else:
p_pred = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])
Z = p_pred[:, 1]
Z0 = Z.reshape(xx.shape)
cm = plt.cm.RdBu_r # colormap
cm_bright = matplotlib.colors.ListedColormap(['#FF0000', '#0000FF'])
cont0 = ax[0].contourf(xx,
yy,
Z0,
cmap=cm,
alpha=.8,
levels=contour_levels,
vmin=0,
vmax=1)
ax[0].set_title("Classification Uncertainty")
# calibrate
X_cal, y_cal = sklearn.datasets.make_circles(n_samples=cal_size,
noise=noise)
p_cal = clf.predict_proba(X_cal)
clf_cal = cm.GPCalibration(SVGP=True)
clf_cal.fit(p_cal, y_cal)
# calibrated contour plot
Z1 = clf_cal.predict_proba(p_pred)[:, 1].reshape(xx.shape)
cont1 = ax[1].contourf(xx,
yy,
Z1,
cmap=cm,
alpha=.8,
levels=contour_levels,
vmin=0,
vmax=1)
ax[1].set_title("Calibrated Uncertainty")
# difference plot
cm_diff = plt.cm.viridis_r # colormap
cont1 = ax[2].contourf(xx, yy, Z1 - Z0, cmap=cm_diff, alpha=.8)
ax[2].set_title("Uncertainty Difference")
# color bar
# fig.subplots_adjust(right=0.8)
# cbar_ax = fig.add_axes([.96, 0.15, 0.05, 0.7])
# cbar = fig.colorbar(cont1, cax=cbar_ax)
# # contour labels
# ax[0].clabel(cont0, inline=1, fontsize=8)
# ax[1].clabel(cont1, inline=1, fontsize=8)
texfig.savefig(dir_out + '/plots/' + 'level_sets')
mean_time_inf = list(summ_stats["time_inf"]["mean"])
mean_time_pred = list(summ_stats["time_pred"]["mean"])
# Plot
fig, axs = texfig.subplots(nrows=1,
ncols=2,
width=5,
ratio=.5,
sharey=True)
axs[0].set_yscale("log")
axs[1].set_yscale("log")
axs[0].scatter(cal_methods, mean_time_inf)
axs[1].scatter(cal_methods, mean_time_pred)
minaxis = np.min(np.concatenate([mean_time_inf, mean_time_pred]))
maxaxis = np.max(np.concatenate([mean_time_inf, mean_time_pred]))
axs[0].set_ylim([minaxis - .0001, maxaxis + 1])
axs[0].title.set_text('Inference')
axs[1].title.set_text('Prediction')
axs[0].set_ylabel("seconds")
# Rotate tick labels
for ax in axs:
for tick in ax.get_xticklabels():
tick.set_rotation(45)
# Save plot to file
texfig.savefig(
"/home/j/Documents/research/projects/nonparametric_calibration/code/" +
"pycalib/figures/runtime_comparison/runtime_results_MNIST")
# Meshplot
fig = texfig.figure(width=6)
ax = fig.gca(projection='3d')
ax.plot_wireframe(X=f1,
Y=f2,
Z=h,
label="$\log p(y_n \mid f_n)$",
color="tab:blue")
ax.plot_wireframe(X=f1,
Y=f2,
Z=taylor_h,
label="Taylor approx.",
color="tab:orange")
ax.set_xlabel("$f_n^1$")
ax.set_ylabel("$f_n^2$")
ax.tick_params(axis='both', which='major', labelsize=10)
ax.legend()
# ax.legend(prop={'size': 9}, labelspacing=0.2)
texfig.savefig("figures/gpcalib_illustration/taylor_approx_mesh")
# Contour difference plot
fig, axes = texfig.subplots()
c = axes.contourf(f1, f2, h - taylor_h)
fig.colorbar(c, ax=axes)
axes.set_xlabel("$f_n^1$")
axes.set_ylabel("$f_n^2$")
texfig.savefig("figures/gpcalib_illustration/taylor_approx_contour")
plt.close("all")
plot_df = results_df.loc[results_df['classifier'] == plot_classifier]
grouped = plot_df.groupby(["cal_method", "classifier", "data"])
summ_stats = grouped.agg([np.mean, np.std])
cal_methods = list(summ_stats.index.levels[0])
mean_time_inf = list(summ_stats["time_inf"]["mean"])
mean_time_pred = list(summ_stats["time_pred"]["mean"])
# Plot
fig, axs = texfig.subplots(nrows=1, ncols=2, width=5, ratio=.5, sharey=True)
axs[0].set_yscale("log")
axs[1].set_yscale("log")
axs[0].scatter(cal_methods, mean_time_inf)
axs[1].scatter(cal_methods, mean_time_pred)
minaxis = np.min(np.concatenate([mean_time_inf, mean_time_pred]))
maxaxis = np.max(np.concatenate([mean_time_inf, mean_time_pred]))
axs[0].set_ylim([minaxis - .0001, maxaxis + 1])
axs[0].title.set_text('Inference')
axs[1].title.set_text('Prediction')
axs[0].set_ylabel("seconds")
# Rotate tick labels
for ax in axs:
for tick in ax.get_xticklabels():
tick.set_rotation(45)
# Save plot to file
texfig.savefig(out_dir + "/runtime_results_MNIST")
fig = texfig.figure(width=6)
ax = fig.gca(projection='3d')
ax.plot_wireframe(X=f1,
Y=f2,
Z=h,
label="$\log p(y_n \mid f_n)$",
color="tab:blue")
ax.plot_wireframe(X=f1,
Y=f2,
Z=taylor_h,
label="Taylor approx.",
color="tab:orange")
ax.set_xlabel("$f_n^1$")
ax.set_ylabel("$f_n^2$")
ax.tick_params(axis='both', which='major', labelsize=10)
ax.legend()
# ax.legend(prop={'size': 9}, labelspacing=0.2)
texfig.savefig(dir_path + "taylor_approx_mesh")
# Contour difference plot
fig, axes = texfig.subplots()
c = axes.contourf(f1, f2, h - taylor_h)
fig.colorbar(c, ax=axes)
axes.set_xlabel("$f_n^1$")
axes.set_ylabel("$f_n^2$")
# Save plot
texfig.savefig(dir_path + "taylor_approx_contour")
plt.close("all")
def reliability_diagram(y, p_pred, filename, title="Reliability Diagram", n_bins=100, show_ece=False, show_legend=False,
model_name = None, xlim=None, plot_height=4, plot_width=4):
"""
Plot a reliability diagram
This function plots the reliability diagram [1]_ [2]_ and histograms from the given confidence estimates. Reliability diagrams
are a visual aid to determine whether a classifier is calibrated or not.
Parameters
----------
y : array, shape = [n_methods, n_samples]
Ground truth labels.
y_pred : array, shape = [n_methods, n_samples]
Predicted labels.
p_pred : array or list
Array of confidence estimates. If this is a list, multiple reliability diagrams will be plotted and arranged
side-by-side.
filename : str
Path or name of output plot files.
title : str or list
Title of plot. If `p_pred` is a list, titles of each individual reliability diagram.
n_bins : int, optional, default=20
The number of bins into which the `y_pred` are partitioned.
show_ece : bool
Whether the expected calibration error (ECE) should be displayed in the plot.
show_legend : bool
Whether the legend should be displayed in the plot.
model_name : str
Name of the model from which the probabilities were generated. Displayed when showing the legend.
xlim : array, shape = (2,), default=None
X-axis limits. If note provided inferred from y.
References
----------
.. [1] DeGroot, M. H. & Fienberg, S. E. The Comparison and Evaluation of Forecasters. Journal of the Royal
Statistical Society. Series D (The Statistician) 32, 12–22.
.. [2] Niculescu-Mizil, A. & Caruana, R. Predicting good probabilities with supervised learning in Proceedings of
the 22nd International Conference on Machine Learning (2005)
"""
# Initialization
if xlim is None:
n_classes = len(np.unique(y))
xlim = [1 / n_classes, 1]
# Check whether multiple reliability diagrams should be plotted
n_plots = 1
if isinstance(p_pred, list):
n_plots = len(p_pred)
# Define bins
bins = np.linspace(xlim[0], xlim[1], n_bins + 1)
# Plot reliability diagram
fig, axes = texfig.subplots(nrows=2, ncols=n_plots, width=plot_width, ratio=plot_height/plot_width,
sharex=True, sharey=True,
gridspec_kw={'height_ratios': [2, 1]})
for i in range(n_plots):
if n_plots > 1:
current_plot_axes = axes[:, i]
y_pred = np.argmax(p_pred[i], axis=1)
p_max = np.max(p_pred[i], axis=1)
p_pred_current = p_pred[i]
else:
current_plot_axes = axes
y_pred = np.argmax(p_pred, axis=1)
p_max = np.max(p_pred, axis=1)
p_pred_current = p_pred
# Calibration line
current_plot_axes[0].plot(xlim, xlim, linestyle='--', color='grey')
# Compute bin means and empirical accuracy
bin_means = np.linspace(xlim[0] + xlim[1] / (2 * n_bins), xlim[1] - xlim[1] / (2 * n_bins), n_bins)
empirical_acc = scipy.stats.binned_statistic(p_max,
np.equal(y_pred, y).astype(int),
bins=n_bins,
range=xlim)[0]
empirical_acc[np.isnan(empirical_acc)] = bin_means[np.isnan(empirical_acc)]
# Plot accuracy
current_plot_axes[0].step(bins, np.concatenate(([xlim[0]], empirical_acc)), '-', label=model_name)
x = np.linspace(xlim[0], xlim[1], 1000)
bin_ind = np.digitize(x, bins)[1:-1] - 1
current_plot_axes[0].fill_between(x[1:-1], x[1:-1], (bin_means + (empirical_acc - bin_means))[bin_ind], facecolor='k', alpha=0.2)
if i == 0:
current_plot_axes[0].set_ylabel('accuracy')
if show_legend:
current_plot_axes[0].legend(loc='upper left')
if title is not None and n_plots > 1:
current_plot_axes[0].set_title(title[i])
elif title is not None:
current_plot_axes[0].set_title(title)
# Plot histogram
hist, ex = np.histogram(p_max, bins=bins)
current_plot_axes[1].fill_between(bins, np.concatenate(([0], hist / np.sum(hist))), lw=0.0, step="pre")
current_plot_axes[1].set_xlabel('confidence $\\hat{\\textnormal{z}}$')
if i == 0:
current_plot_axes[1].set_ylabel('sample frac.')
current_plot_axes[1].set_xlim(xlim)
fig.align_labels()
# Add textbox with ECE
if show_ece:
ece = pycalib.scoring.expected_calibration_error(y=y, p_pred=p_pred_current, n_bins=n_bins)
anchored_text = AnchoredText("$\\textup{ECE}_1 = " + "{:.3f}$".format(ece), loc='lower right')
anchored_text.patch.set_boxstyle("round,pad=0.,rounding_size=0.2")
anchored_text.patch.set_edgecolor("0.8")
anchored_text.patch.set_alpha(0.9)
current_plot_axes[0].add_artist(anchored_text)
# Save to file
texfig.savefig(filename=filename, bbox_inches='tight', pad_inches=0)
plt.close()