error_utils.py 18.2 KB
 1 ``````#!/usr/bin/env python `````` Amir MOHAMMADI committed May 08, 2018 2 3 ``````# Ivana Chingovska # Fri Dec 7 12:33:37 CET 2012 `````` 4 5 6 7 ``````"""Utility functions for computation of EPSC curve and related measurement""" import bob.measure import numpy `````` Amir MOHAMMADI committed Jun 20, 2018 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 ``````from bob.measure import ( far_threshold, eer_threshold, min_hter_threshold) def calc_threshold(method, neg, pos): """Calculates the threshold based on the given method. The scores should be sorted! Parameters ---------- method : str One of ``bpcer20``, ``eer``, ``min-hter``. neg : array_like The negative scores. They should be sorted! pos : array_like The positive scores. They should be sorted! Returns ------- float The calculated threshold. Raises ------ ValueError If method is unknown. """ method = method.lower() if method == 'bpcer20': threshold = far_threshold(neg, pos, 0.05, True) elif method == 'eer': threshold = eer_threshold(neg, pos, True) elif method == 'min-hter': threshold = min_hter_threshold(neg, pos, True) else: raise ValueError("Unknown threshold criteria: {}".format(method)) return threshold `````` 46 47 48 49 50 `````` def calc_pass_rate(threshold, attacks): """Calculates the rate of successful spoofing attacks `````` Theophile GENTILHOMME committed May 04, 2018 51 52 53 54 55 56 57 58 59 60 61 62 63 `````` Parameters ---------- threshold : the threshold used for classification scores : numpy with the scores of the spoofing attacks Returns ------- float rate of successful spoofing attacks """ return (attacks >= threshold).mean() `````` 64 65 66 67 68 69 70 `````` def weighted_neg_error_rate_criteria(data, weight, thres, beta=0.5, criteria='eer'): `````` Theophile GENTILHOMME committed Apr 13, 2018 71 72 73 `````` """Given the single value for the weight parameter balancing between impostors and spoofing attacks and a threshold, calculates the error rates and their relationship depending on the criteria (difference in case of `````` Theophile GENTILHOMME committed May 03, 2018 74 `````` 'eer', hter in case of 'min-hter' criteria) `````` 75 76 `````` Keyword parameters: `````` Theophile GENTILHOMME committed Apr 13, 2018 77 78 79 80 81 `````` - data - the development data used to determine the threshold. List on 4 numpy.arrays containing: negatives (licit), positives (licit), negatives (spoof), positivies (spoof) - weight - the weight parameter balancing between impostors and spoofing attacks `````` 82 `````` - thres - the given threshold `````` Theophile GENTILHOMME committed Apr 13, 2018 83 84 85 `````` - beta - the weight parameter balancing between real accesses and all the negative samples (impostors and spoofing attacks). Note that this parameter will be overriden and not considered if the selected criteria `````` Theophile GENTILHOMME committed May 03, 2018 86 87 `````` is 'min-hter'. - criteria - 'eer', 'wer' or 'min-hter' criteria for decision threshold `````` 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 `````` """ licit_neg = data[0] licit_pos = data[1] spoof_neg = data[2] spoof_pos = data[3] # unpacking the data farfrr_licit = bob.measure.farfrr(licit_neg, licit_pos, thres) farfrr_spoof = bob.measure.farfrr(spoof_neg, spoof_pos, thres) frr = farfrr_licit[1] # farfrr_spoof[1] should have the same value far_i = farfrr_licit[0] far_s = farfrr_spoof[0] far_w = (1 - weight) * far_i + weight * far_s if criteria == 'eer': if beta == 0.5: return abs(far_w - frr) else: `````` Amir MOHAMMADI committed May 08, 2018 107 `````` # return abs(far_w - frr) `````` 108 109 `````` return abs((1 - beta) * frr - beta * far_w) `````` Theophile GENTILHOMME committed May 03, 2018 110 `````` elif criteria == 'min-hter': `````` 111 112 113 114 115 116 117 118 119 120 121 122 `````` return (far_w + frr) / 2 else: return (1 - beta) * frr + beta * far_w def recursive_thr_search(data, span_min, span_max, weight, beta=0.5, criteria='eer'): `````` Theophile GENTILHOMME committed Apr 13, 2018 123 124 125 126 127 `````` """Recursive search for the optimal threshold given a criteria. It evaluates the full range of thresholds at 100 points, and computes the one which optimizes the threshold. In the next search iteration, it examines the region around the point that optimizes the threshold. The procedure stops when the search range is smaller then 1e-10. `````` 128 129 `````` Keyword arguments: `````` Theophile GENTILHOMME committed Apr 13, 2018 130 131 132 `````` - data - the development data used to determine the threshold. List on 4 numpy.arrays containing: negatives (licit), positives (licit), negatives (spoof), positivies (spoof) `````` 133 134 `````` - span_min - the minimum of the search range - span_max - the maximum of the search range `````` Theophile GENTILHOMME committed Apr 13, 2018 135 136 137 138 139 `````` - weight - the weight parameter balancing between impostors and spoofing attacks - beta - the weight parameter balancing between real accesses and all the negative samples (impostors and spoofing attacks). Note that methods called within this function will override this parameter and not considered if the `````` Theophile GENTILHOMME committed May 03, 2018 140 `````` selected criteria is 'min-hter'. `````` Theophile GENTILHOMME committed Apr 13, 2018 141 `````` - criteria - the decision threshold criteria ('eer' for EER, 'wer' for `````` Theophile GENTILHOMME committed May 03, 2018 142 `````` Minimum WER or 'min-hter' for Minimum HTER criteria). `````` 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 `````` """ quit_thr = 1e-10 steps = 100 if abs((span_max - span_min) / span_max) < quit_thr: return span_max # or span_min, it doesn't matter else: step_size = (span_max - span_min) / steps thresholds = numpy.array( [(i * step_size) + span_min for i in range(steps + 1)]) weighted_error_rates = numpy.array([ weighted_neg_error_rate_criteria(data, weight, thr, beta, criteria) for thr in thresholds ]) selected_thres = thresholds[numpy.where( weighted_error_rates == min(weighted_error_rates) )] # all the thresholds which have minimum weighted error rate thr = selected_thres[int( selected_thres.size / 2 )] # choose the centrally positioned threshold return recursive_thr_search(data, thr - step_size, thr + step_size, weight, beta, criteria) def weighted_negatives_threshold(licit_neg, licit_pos, spoof_neg, spoof_pos, weight, beta=0.5, criteria='eer'): `````` Theophile GENTILHOMME committed Apr 13, 2018 174 `````` """Calculates the threshold for achieving the given criteria between the `````` Amir MOHAMMADI committed May 08, 2018 175 `````` FAR_w and the FRR, given the single value for the weight parameter `````` Theophile GENTILHOMME committed Apr 13, 2018 176 177 178 `````` balancing between impostors and spoofing attacks and a single value for the parameter beta balancing between the real accesses and the negatives (impostors and spoofing attacks) `````` 179 180 181 182 183 184 `````` Keyword parameters: - licit_neg - numpy.array of scores for the negatives (licit scenario) - licit_pos - numpy.array of scores for the positives (licit scenario) - spoof_neg - numpy.array of scores for the negatives (spoof scenario) - spoof_pos - numpy.array of scores for the positives (spoof scenario) `````` Theophile GENTILHOMME committed Apr 13, 2018 185 186 187 188 189 `````` - weight - the weight parameter balancing between impostors and spoofing attacks - beta - the weight parameter balancing between real accesses and all the negative samples (impostors and spoofing attacks). Note that methods called within this function will override this parameter and not considered if the `````` Theophile GENTILHOMME committed May 03, 2018 190 `````` selected criteria is 'min-hter'. `````` Theophile GENTILHOMME committed Apr 13, 2018 191 `````` - criteria - the decision threshold criteria ('eer' for EER, 'wer' for `````` Theophile GENTILHOMME committed May 03, 2018 192 `````` Minimum WER or 'min-hter' for Minimum HTER criteria). `````` 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 `````` """ span_min = min( numpy.append(licit_neg, spoof_neg) ) # the min of the span where we will search for the threshold span_max = max( numpy.append(licit_pos, spoof_pos) ) # the max of the span where we will search for the threshold data = (licit_neg, licit_pos, spoof_neg, spoof_pos) # pack the data into a single list return recursive_thr_search(data, span_min, span_max, weight, beta, criteria) def epsc_weights(licit_neg, licit_pos, spoof_neg, spoof_pos, points=100): """Returns the weights for EPSC Keyword arguments: - points - number of points to calculate EPSC """ step_size = 1 / float(points) weights = numpy.array([(i * step_size) for i in range(points + 1)]) return weights def epsc_thresholds(licit_neg, licit_pos, spoof_neg, spoof_pos, points=100, criteria='eer', omega=None, beta=None): `````` Theophile GENTILHOMME committed Apr 13, 2018 226 227 228 229 `````` """Calculates the optimal thresholds for EPSC, for a range of the weight parameter balancing between impostors and spoofing attacks, and for a range of the beta parameter balancing between real accesses and all the negatives (impostors and spoofing attacks) `````` 230 231 232 233 234 235 236 237 `````` Keyword arguments: - licit_neg - numpy.array of scores for the negatives (licit scenario) - licit_pos - numpy.array of scores for the positives (licit scenario) - spoof_neg - numpy.array of scores for the negatives (spoof scenario) - spoof_pos - numpy.array of scores for the positives (spoof scenario) - points - number of points to calculate EPSC `````` Theophile GENTILHOMME committed May 03, 2018 238 `````` - criteria - the decision threshold criteria ('eer', 'wer' or 'min-hter') `````` Theophile GENTILHOMME committed Apr 13, 2018 239 240 241 242 `````` - omega - the value of the parameter omega, balancing between impostors and spoofing attacks. If None, it is going to span the full range [0,1]. Otherwise, can be set to a fixed value or a list of values. - beta - the value of the parameter beta, balancing between real accesses `````` Amir MOHAMMADI committed May 08, 2018 243 `````` and all the negatives (zero-effort impostors and spoofing attacks). If `````` Theophile GENTILHOMME committed Apr 13, 2018 244 245 `````` None, it is going to span the full range [0,1]. Otherwise, can be set to a fixed value or a list of values. `````` 246 247 248 249 `````` """ step_size = 1 / float(points) `````` Amir MOHAMMADI committed May 08, 2018 250 `````` if omega is None: `````` 251 252 253 254 255 256 257 `````` omega = numpy.array([(i * step_size) for i in range(points + 1)]) elif not isinstance(omega, list) and not isinstance( omega, tuple) and not isinstance(omega, numpy.ndarray): omega = numpy.array([omega]) else: omega = numpy.array(omega) `````` Amir MOHAMMADI committed May 08, 2018 258 `````` if beta is None: `````` 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 `````` beta = numpy.array([(i * step_size) for i in range(points + 1)]) elif not isinstance(beta, list) and not isinstance( beta, tuple) and not isinstance(beta, numpy.ndarray): beta = numpy.array([beta]) else: beta = numpy.array(beta) thresholds = numpy.ndarray([beta.size, omega.size], 'float64') for bindex, b in enumerate(beta): thresholds[bindex, :] = numpy.array([ weighted_negatives_threshold( licit_neg, licit_pos, spoof_neg, spoof_pos, w, b, criteria=criteria) for w in omega ], 'float64') return omega, beta, thresholds def weighted_err(error_1, error_2, weight): """Calculates the weighted error rate between the two input parameters Keyword arguments: `````` Theophile GENTILHOMME committed Apr 13, 2018 286 287 `````` - error_1 - the first input error rate (FAR for zero effort impostors usually) `````` 288 289 290 291 292 293 294 295 296 297 298 299 300 `````` - error_2 - the second input error rate (SFAR) - weight - the given weight """ return (1 - weight) * error_1 + weight * error_2 def error_rates_at_weight(licit_neg, licit_pos, spoof_neg, spoof_pos, omega, threshold, beta=0.5): `````` Theophile GENTILHOMME committed Apr 13, 2018 301 302 303 `````` """Calculates several error rates: FRR, FAR (zero-effort impostors), SFAR, FAR_w, HTER_w for a given value of w. It returns the calculated threshold as a last argument `````` 304 305 306 307 308 309 310 311 `````` Keyword arguments: - licit_neg - numpy.array of scores for the negatives (licit scenario) - licit_pos - numpy.array of scores for the positives (licit scenario) - spoof_neg - numpy.array of scores for the negatives (spoof scenario) - spoof_pos - numpy.array of scores for the positives (spoof scenario) - threshold - the given threshold `````` Theophile GENTILHOMME committed Apr 13, 2018 312 313 314 315 316 `````` - omega - the omega parameter balancing between impostors and spoofing attacks - beta - the weight parameter balancing between real accesses and all the negative samples (impostors and spoofing attacks). `````` 317 318 319 320 321 322 323 324 325 `````` """ farfrr_licit = bob.measure.farfrr( licit_neg, licit_pos, threshold) # calculate test frr @ threshold (licit scenario) farfrr_spoof = bob.measure.farfrr( spoof_neg, spoof_pos, threshold) # calculate test frr @ threshold (spoof scenario) `````` Amir MOHAMMADI committed May 08, 2018 326 327 `````` # we can take this value from farfrr_spoof as well, it doesn't matter frr = farfrr_licit[1] `````` 328 329 330 331 332 333 334 335 336 337 338 339 `````` far = farfrr_licit[0] sfar = farfrr_spoof[0] far_w = weighted_err(far, sfar, omega) hter_w = (far_w + frr) / 2 wer_wb = weighted_err(frr, far_w, beta) return (frr, far, sfar, far_w, wer_wb, hter_w, threshold) def epsc_error_rates(licit_neg, licit_pos, spoof_neg, spoof_pos, thresholds, omega, beta): `````` Amir MOHAMMADI committed May 08, 2018 340 341 `````` """Calculates several error rates: FAR_w and WER_wb for the given weights (omega and beta) and thresholds (the thresholds need to be computed first `````` Theophile GENTILHOMME committed Apr 13, 2018 342 `````` using the method: epsc_thresholds() before passing to this method) `````` 343 `````` `````` Theophile GENTILHOMME committed May 04, 2018 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 `````` Parameters ---------- licit_neg : array_like array of scores for the negatives (licit scenario) licit_pos : array_like array of scores for the positives (licit scenario) spoof_neg : array_like array of scores for the negatives (spoof scenario) spoof_pos : array_like array of scores for the positives (spoof scenario) thresholds : array_like ndarray with threshold values omega : array_like array of the omega parameter balancing between impostors and spoofing attacks beta : array_like array of the beta parameter balancing between real accesses and all negatives (impostors and spoofing attacks) Returns ------- far_w_errors: array_like FAR_w wer_wb_errors: array_like WER_wb """ `````` 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 `````` far_w_errors = numpy.ndarray((beta.size, omega.size), 'float64') wer_wb_errors = numpy.ndarray((beta.size, omega.size), 'float64') for bindex, b in enumerate(beta): errors = [ error_rates_at_weight(licit_neg, licit_pos, spoof_neg, spoof_pos, w, thresholds[bindex, windex], b) for windex, w in enumerate(omega) ] far_w_errors[bindex, :] = [errors[i][3] for i in range(len(errors))] wer_wb_errors[bindex, :] = [errors[i][4] for i in range(len(errors))] return far_w_errors, wer_wb_errors def all_error_rates(licit_neg, licit_pos, spoof_neg, spoof_pos, thresholds, omega, beta): `````` Amir MOHAMMADI committed May 08, 2018 388 389 `````` """Calculates several error rates: FAR_w and WER_wb for the given weights (omega and beta) and thresholds (the thresholds need to be computed first `````` Theophile GENTILHOMME committed Apr 13, 2018 390 `````` using the method: epsc_thresholds() before passing to this method) `````` 391 `````` `````` Theophile GENTILHOMME committed May 04, 2018 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 `````` Parameters ---------- licit_neg : array_like array of scores for the negatives (licit scenario) licit_pos : array_like array of scores for the positives (licit scenario) spoof_neg : array_like array of scores for the negatives (spoof scenario) spoof_pos : array_like array of scores for the positives (spoof scenario) thresholds : array_like ndarray with threshold values omega : array_like array of the omega parameter balancing between impostors and spoofing attacks beta : array_like array of the beta parameter balancing between real accesses and all negatives (impostors and spoofing attacks) Returns ------- far_w_errors: array_like FAR_w wer_wb_errors: array_like WER_wb """ `````` 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 `````` frr_errors = numpy.ndarray((beta.size, omega.size), 'float64') far_errors = numpy.ndarray((beta.size, omega.size), 'float64') sfar_errors = numpy.ndarray((beta.size, omega.size), 'float64') far_w_errors = numpy.ndarray((beta.size, omega.size), 'float64') wer_wb_errors = numpy.ndarray((beta.size, omega.size), 'float64') hter_wb_errors = numpy.ndarray((beta.size, omega.size), 'float64') for bindex, b in enumerate(beta): errors = [ error_rates_at_weight(licit_neg, licit_pos, spoof_neg, spoof_pos, w, thresholds[bindex, windex], b) for windex, w in enumerate(omega) ] frr_errors[bindex, :] = [errors[i][0] for i in range(len(errors))] far_errors[bindex, :] = [errors[i][1] for i in range(len(errors))] sfar_errors[bindex, :] = [errors[i][2] for i in range(len(errors))] far_w_errors[bindex, :] = [errors[i][3] for i in range(len(errors))] wer_wb_errors[bindex, :] = [errors[i][4] for i in range(len(errors))] hter_wb_errors[bindex, :] = [errors[i][5] for i in range(len(errors))] `````` Theophile GENTILHOMME committed Apr 13, 2018 439 440 `````` return (frr_errors, far_errors, sfar_errors, far_w_errors, wer_wb_errors, hter_wb_errors) `````` 441 442 443 444 445 446 447 448 449 450 451 452 453 454 `````` def calc_aue(licit_neg, licit_pos, spoof_neg, spoof_pos, thresholds, omega, beta, l_bound=0, h_bound=1, var_param='omega'): """Calculates AUE of EPSC for the given thresholds and weights `````` Theophile GENTILHOMME committed Apr 13, 2018 455 `````` Keyword arguments: `````` 456 457 458 459 460 461 462 463 `````` - licit_neg - numpy.array of scores for the negatives (licit scenario) - licit_pos - numpy.array of scores for the positives (licit scenario) - spoof_neg - numpy.array of scores for the negatives (spoof scenario) - spoof_pos - numpy.array of scores for the positives (spoof scenario) - l_bound - lower bound of integration - h_bound - higher bound of integration - points - number of points to calculate EPSC `````` Theophile GENTILHOMME committed May 03, 2018 464 `````` - criteria - the decision threshold criteria ('eer', 'wer' or 'min-hter') `````` Amir MOHAMMADI committed May 08, 2018 465 `````` - var_param - name of the parameter which is varied on the abscissa `````` Theophile GENTILHOMME committed Apr 13, 2018 466 `````` ('omega' or 'beta') `````` 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 `````` """ from scipy import integrate if var_param == 'omega': errors = all_error_rates(licit_neg, licit_pos, spoof_neg, spoof_pos, thresholds, omega, beta) weights = omega # setting the weights to the varying parameter else: errors = all_error_rates(licit_neg, licit_pos, spoof_neg, spoof_pos, thresholds, omega, beta) weights = beta # setting the weights to the varying parameter wer_errors = errors[4].reshape(1, errors[4].size) l_ind = numpy.where(weights >= l_bound)[0][0] h_ind = numpy.where(weights <= h_bound)[0][-1] aue = integrate.cumtrapz(wer_errors, weights) aue = numpy.append( [0], aue) # for indexing purposes, aue is cumulative integration aue = aue[h_ind] - aue[l_ind] return aue``````