def train_calibration(self, logits, labels):
"""Train a calibrator given logits and labels.
Args:
logits: A sequence of dimension (n, k) where n is the number of
data points, and k is the number of classes, representing
the output probabilities/confidences of the uncalibrated
model.
labels: A sequence of length n, where n is the number of data points,
representing the ground truth label for each data point.
"""
assert(len(logits) >= self._num_calibration)
logits = np.array(logits)
self._k = logits.shape[1] # Number of classes.
assert self._k == np.max(labels) - np.min(labels) + 1
labels_one_hot = utils.get_labels_one_hot(np.array(labels), self._k)
assert labels_one_hot.shape == logits.shape
self._platts = []
self._calibrators = []
for c in range(self._k):
# For each class c, get the probabilities the model output for that class, and whether
# the data point was actually class c, or not.
probs_c = logits[:, c]
labels_c = labels_one_hot[:, c]
platt_c = utils.get_platt_scaler(probs_c, labels_c)
self._platts.append(platt_c)
platt_probs_c = platt_c(probs_c)
bins = utils.get_equal_bins(platt_probs_c, num_bins=self._num_bins)
calibrator_c = utils.get_discrete_calibrator(platt_probs_c, bins)
self._calibrators.append(calibrator_c)
def train_calibration(self, logits, labels):
assert(len(logits) >= self._num_calibration)
predictions = utils.get_top_predictions(logits)
probs = utils.get_top_probs(logits)
correct = (predictions == labels)
self._platt = utils.get_platt_scaler(
probs, correct)
platt_probs = self._platt(probs)
bins = utils.get_equal_bins(platt_probs, num_bins=self._num_bins)
self._discrete_calibrator = utils.get_discrete_calibrator(
platt_probs, bins)
def lower_bound_experiment(logits,
labels,
calibration_data_size,
bin_data_size,
bins_list,
save_name='cmp_est',
binning_func=utils.get_equal_bins,
lp=2):
# Shuffle the logits and labels.
indices = np.random.choice(list(range(len(logits))),
size=len(logits),
replace=False)
logits = [logits[i] for i in indices]
labels = [labels[i] for i in indices]
predictions = utils.get_top_predictions(logits)
probs = utils.get_top_probs(logits)
correct = (predictions == labels)
print('num_correct: ', sum(correct))
# Platt scale on first chunk of data
platt = utils.get_platt_scaler(probs[:calibration_data_size],
correct[:calibration_data_size])
platt_probs = platt(probs)
lower, middle, upper = [], [], []
for num_bins in bins_list:
bins = binning_func(platt_probs[:calibration_data_size +
bin_data_size],
num_bins=num_bins)
verification_probs = platt_probs[calibration_data_size +
bin_data_size:]
verification_correct = correct[calibration_data_size + bin_data_size:]
verification_data = list(zip(verification_probs, verification_correct))
def estimator(data):
binned_data = utils.bin(data, bins)
return utils.plugin_ce(binned_data, power=lp)
print('estimate: ', estimator(verification_data))
estimate_interval = utils.bootstrap_uncertainty(verification_data,
estimator,
num_samples=1000)
lower.append(estimate_interval[0])
middle.append(estimate_interval[1])
upper.append(estimate_interval[2])
print('interval: ', estimate_interval)
lower_errors = np.array(middle) - np.array(lower)
upper_errors = np.array(upper) - np.array(middle)
plt.clf()
font = {'family': 'normal', 'size': 18}
rc('font', **font)
plt.errorbar(bins_list,
middle,
yerr=[lower_errors, upper_errors],
barsabove=True,
fmt='none',
color='black',
capsize=4)
plt.scatter(bins_list, middle, color='black')
plt.xlabel(r"No. of bins")
if lp == 2:
plt.ylabel("Calibration error")
else:
plt.ylabel("L%d Calibration error" % lp)
plt.xscale('log', basex=2)
ax = plt.gca()
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.yaxis.set_ticks_position('left')
ax.xaxis.set_ticks_position('bottom')
plt.tight_layout()
plt.savefig(save_name)
def calibrate_marginals_experiment(logits, labels, k):
num_calib = 3000
num_bin = 3000
num_cert = 4000
assert (logits.shape[0] == num_calib + num_bin + num_cert)
num_bins = 100
bootstrap_samples = 100
# First split by label? To ensure equal class numbers? Do this later.
labels = utils.get_labels_one_hot(labels[:, 0], k)
mse = np.mean(np.square(labels - logits))
print('original mse is ', mse)
calib_logits = logits[:num_calib, :]
calib_labels = labels[:num_calib, :]
bin_logits = logits[num_calib:num_calib + num_bin, :]
bin_labels = labels[num_calib:num_calib + num_bin, :]
cert_logits = logits[num_calib + num_bin:, :]
cert_labels = labels[num_calib + num_bin:, :]
mses = []
unbiased_ces = []
biased_ces = []
std_unbiased_ces = []
std_biased_ces = []
for num_bins in range(10, 21, 10):
# Train a platt scaler and binner.
platts = []
platt_binners_equal_points = []
for l in range(k):
platt_l = utils.get_platt_scaler(calib_logits[:, l],
calib_labels[:, l])
platts.append(platt_l)
cal_logits_l = platt_l(calib_logits[:, l])
# bins_l = utils.get_equal_bins(cal_logits_l, num_bins=num_bins)
# Get
# bins_l = utils.get_equal_prob_bins(num_bins=num_bins)
bins_l = [0.0012, 0.05, 0.01, 0.95, 0.985, 1.0]
cal_bin_logits_l = platt_l(bin_logits[:, l])
platt_binner_l = utils.get_discrete_calibrator(
cal_bin_logits_l, bins_l)
platt_binners_equal_points.append(platt_binner_l)
# Write a function that takes data and outputs the mse, ce
def get_mse_ce(logits, labels, ce_est):
mses = []
ces = []
logits = np.array(logits)
labels = np.array(labels)
for l in range(k):
cal_logits_l = platt_binners_equal_points[l](platts[l](
logits[:, l]))
data = list(zip(cal_logits_l, labels[:, l]))
bins_l = utils.get_discrete_bins(cal_logits_l)
binned_data = utils.bin(data, bins_l)
# probs = platts[l](logits[:, l])
# for p in [1, 5, 10, 20, 50, 85, 88.5, 92, 94, 96, 98, 100]:
# print(np.percentile(probs, p))
# import time
# time.sleep(100)
# print('lengths')
# print([len(d) for d in binned_data])
ces.append(ce_est(binned_data))
mses.append(
np.mean([(prob - label)**2 for prob, label in data]))
return np.mean(mses), np.mean(ces)
def plugin_ce_squared(data):
logits, labels = zip(*data)
return get_mse_ce(logits, labels,
lambda x: utils.plugin_ce(x)**2)[1]
def mse(data):
logits, labels = zip(*data)
return get_mse_ce(logits, labels,
lambda x: utils.plugin_ce(x)**2)[0]
def unbiased_ce_squared(data):
logits, labels = zip(*data)
return get_mse_ce(logits, labels,
utils.improved_unbiased_square_ce)[1]
mse, improved_unbiased_ce = get_mse_ce(
cert_logits, cert_labels, utils.improved_unbiased_square_ce)
mse, biased_ce = get_mse_ce(cert_logits, cert_labels,
lambda x: utils.plugin_ce(x)**2)
mses.append(mse)
unbiased_ces.append(improved_unbiased_ce)
biased_ces.append(biased_ce)
print('biased ce: ', np.sqrt(biased_ce))
print('mse: ', mse)
print('improved ce: ', np.sqrt(improved_unbiased_ce))
data = list(zip(list(cert_logits), list(cert_labels)))
std_biased_ces.append(
utils.bootstrap_std(data,
plugin_ce_squared,
num_samples=bootstrap_samples))
std_unbiased_ces.append(
utils.bootstrap_std(data,
unbiased_ce_squared,
num_samples=bootstrap_samples))
std_multiplier = 1.3 # For one sided 90% confidence interval.
upper_unbiased_ces = list(
map(lambda p: np.sqrt(p[0] + std_multiplier * p[1]),
zip(unbiased_ces, std_unbiased_ces)))
upper_biased_ces = list(
map(lambda p: np.sqrt(p[0] + std_multiplier * p[1]),
zip(biased_ces, std_biased_ces)))
# Get points on the Pareto curve, and plot them.
def get_pareto_points(data):
pareto_points = []
def dominated(p1, p2):
return p1[0] >= p2[0] and p1[1] >= p2[1]
for datum in data:
num_dominated = sum(map(lambda x: dominated(datum, x), data))
if num_dominated == 1:
pareto_points.append(datum)
return pareto_points
print(
get_pareto_points(
list(zip(upper_unbiased_ces, mses, list(range(5, 101, 5))))))
print(
get_pareto_points(
list(zip(upper_biased_ces, mses, list(range(5, 101, 5))))))
plot_unbiased_ces, plot_unbiased_mses = zip(
*get_pareto_points(list(zip(upper_unbiased_ces, mses))))
plot_biased_ces, plot_biased_mses = zip(
*get_pareto_points(list(zip(upper_biased_ces, mses))))
plt.title("MSE vs Calibration Error")
plt.scatter(plot_unbiased_ces,
plot_unbiased_mses,
c='red',
marker='o',
label='Ours')
plt.scatter(plot_biased_ces,
plot_biased_mses,
c='blue',
marker='s',
label='Plugin')
plt.legend(loc='upper left')
plt.ylim(0.0, 0.013)
plt.xlabel("L2 Calibration Error")
plt.ylabel("Mean-Squared Error")
plt.show()
plt.yticks([0, 1])
plt.xticks([0, 0.5, 1])
ax = plt.gca()
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.yaxis.set_ticks_position('left')
ax.xaxis.set_ticks_position('bottom')
ax.set_ylim([-0.05, 1.05])
# Set up points.
X = np.arange(1.0 / 18, 1.0, 1.0 / 9)
Y = [0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0]
plt.scatter(X, Y, marker='x', s=40, c='black')
# Add Platt curve.
platt_scaler = utils.get_platt_scaler(X, Y)
finer_x = np.arange(0.0, 1.0, 0.01)
platt_finer_y = platt_scaler(finer_x)
if calibrator == _PLATT_SCALING:
plt.plot(finer_x, platt_finer_y, c='red')
elif calibrator == _VAR_RED_BINNING:
plt.plot(finer_x, platt_finer_y, c='gray')
# Add bin lines.
if calibrator == _VAR_RED_BINNING or calibrator == _HIST_BINNING:
plt.axvline(x=1/3.0, linestyle='--', linewidth=2, c='gray')
plt.axvline(x=2/3.0, linestyle='--', linewidth=2, c='gray')
# Add platt values.
platt_y = platt_scaler(X)
if calibrator == _VAR_RED_BINNING:
def compare_estimators(logits,
labels,
platt_data_size,
bin_data_size,
num_bins,
ver_base_size=2000,
ver_size_increment=1000,
num_resamples=100,
save_name='cmp_est'):
# Convert logits to prediction, probs.
predictions = utils.get_top_predictions(logits)
probs = utils.get_top_probs(logits)
correct = (predictions == labels)
# Platt scale on first chunk of data
platt = utils.get_platt_scaler(probs[:platt_data_size],
correct[:platt_data_size])
platt_probs = platt(probs)
estimator_names = ['biased', 'unbiased']
estimators = [
lambda x: utils.plugin_ce(x)**2, utils.improved_unbiased_square_ce
]
bins = utils.get_equal_bins(platt_probs[:platt_data_size + bin_data_size],
num_bins=num_bins)
binner = utils.get_discrete_calibrator(
platt_probs[platt_data_size:platt_data_size + bin_data_size], bins)
verification_probs = binner(platt_probs[platt_data_size + bin_data_size:])
verification_correct = correct[platt_data_size + bin_data_size:]
verification_data = list(zip(verification_probs, verification_correct))
verification_sizes = list(
range(ver_base_size,
len(verification_probs) + 1, ver_size_increment))
# We want to compare the two estimators when varying the number of samples.
# However, a single point of comparison does not tell us much about the estimators.
# So we use resampling - we resample from the test set many times, and run the estimators
# on the resamples. We stores these values. This gives us a sense of the range of values
# the estimator might output.
# So estimates[i][j][k] stores the estimate when using estimator i, with verification_sizes[j]
# samples, in the k-th resampling.
estimates = np.zeros(
(len(estimators), len(verification_sizes), num_resamples))
# We also store the certified estimates. These represent the upper bounds we get using
# each estimator. They are computing using the std-dev of the estimator estimated by
# Bootstrap.
cert_estimates = np.zeros(
(len(estimators), len(verification_sizes), num_resamples))
for ver_idx, verification_size in zip(range(len(verification_sizes)),
verification_sizes):
for k in range(num_resamples):
# Resample
indices = np.random.choice(list(range(len(verification_data))),
size=verification_size,
replace=True)
cur_verification_data = [verification_data[i] for i in indices]
cur_verification_probs = [verification_probs[i] for i in indices]
bins = utils.get_discrete_bins(cur_verification_probs)
# Compute estimates for each estimator.
for i in range(len(estimators)):
def estimator(data):
binned_data = utils.bin(data, bins)
return estimators[i](binned_data)
cur_estimate = estimator(cur_verification_data)
estimates[i][ver_idx][k] = cur_estimate
# cert_resampling_estimates[j].append(
# cur_estimate + utils.bootstrap_std(cur_verification_data, estimator, num_samples=20))
estimates = np.sort(estimates, axis=-1)
lower_bound = int(0.1 * num_resamples)
median = int(0.5 * num_resamples)
upper_bound = int(0.9 * num_resamples)
lower_estimates = estimates[:, :, lower_bound]
upper_estimates = estimates[:, :, upper_bound]
median_estimates = estimates[:, :, median]
# We can also compute the MSEs of the estimator.
bins = utils.get_discrete_bins(verification_probs)
true_calibration = utils.plugin_ce(utils.bin(verification_data, bins))**2
print(true_calibration)
print(np.sqrt(np.mean(estimates[1, -1, :])))
errors = np.abs(estimates - true_calibration)
accumulated_errors = np.mean(errors, axis=-1)
error_bars_90 = 1.645 * np.std(errors, axis=-1) / np.sqrt(num_resamples)
print(accumulated_errors)
plt.errorbar(verification_sizes,
accumulated_errors[0],
yerr=[error_bars_90[0], error_bars_90[0]],
barsabove=True,
color='red',
capsize=4,
label='plugin')
plt.errorbar(verification_sizes,
accumulated_errors[1],
yerr=[error_bars_90[1], error_bars_90[1]],
barsabove=True,
color='blue',
capsize=4,
label='debiased')
plt.ylabel("Mean-Squared-Error")
plt.xlabel("Number of Samples")
plt.legend(loc='upper right')
plt.show()
plt.ylabel("Number of estimates")
plt.xlabel("Absolute deviation from ground truth")
bins = np.linspace(np.min(errors[:, 0, :]), np.max(errors[:, 0, :]), 40)
plt.hist(errors[0][0], bins, alpha=0.5, label='plugin')
plt.hist(errors[1][0], bins, alpha=0.5, label='debiased')
plt.legend(loc='upper right')
plt.gca().yaxis.set_major_formatter(PercentFormatter(xmax=num_resamples))
plt.show()
def train_calibration(self, zs, ys):
self._platt = utils.get_platt_scaler(zs, ys)
def train_calibration(self, zs, ys):
self._platt = utils.get_platt_scaler(zs, ys)
platt_probs = self._platt(zs)
bins = utils.get_equal_bins(platt_probs, num_bins=self._num_bins)
self._discrete_calibrator = utils.get_discrete_calibrator(platt_probs, bins)