Improve accuracy of ROC, DET, and PR plots

PR - > precision_recall
Internally computes thresholds using both far and frr values for more
accurate plots.
Fixes #60

bob/measure/__init__.py

@@ -8,6 +8,7 @@ from .version import module as __version__
 
 from . import plot
 from . import calibration
+from . import load
 import numpy
 
 

bob/measure/cpp/error.cpp

@@ -238,31 +238,80 @@ double bob::measure::minWeightedErrorRateThreshold(
   return bob::measure::minimizingThreshold(neg, pos, predicate);
 }
 
+blitz::Array<double, 1>
+bob::measure::log_values(size_t points_, int min_power) {
+  int points = (int)points_;
+  blitz::Array<double, 1> retval(points);
+  double counts_per_step = points / (-min_power) ;
+  for (int i = 1-points; i <= 0; ++i) {
+    retval(i+points-1) = std::pow(10., (double)i/counts_per_step);
+  }
+  return retval;
+}
+
+
+blitz::Array<double, 1>
+bob::measure::meaningfulThresholds(
+    const blitz::Array<double, 1> &negatives,
+    const blitz::Array<double, 1> &positives,
+    size_t points_, int min_far, bool is_sorted) {
+
+  int points = (int)points_;
+  int half_points = points / 2;
+  blitz::Array<double, 1> thresholds(points);
+  blitz::Array<double, 1> neg, pos;
+
+  // sort negatives and positives
+  sort(negatives, neg, is_sorted);
+  sort(positives, pos, is_sorted);
+
+  // Create an far_list and frr_list
+  auto frr_list = bob::measure::log_values(half_points, min_far);
+  auto far_list = bob::measure::log_values(points - half_points, min_far);
+
+  // Compute thresholds for far_list and frr_list
+  for (int i = 0; i < points; ++i) {
+    if (i < half_points)
+      thresholds(i) = bob::measure::frrThreshold(neg, pos, frr_list(i), true);
+    else
+      thresholds(i) = bob::measure::farThreshold(neg, pos, far_list(i-half_points), true);
+  }
+
+  // Sort the thresholds
+  bob::core::array::sort(thresholds);
+
+  return thresholds;
+}
+
+
 blitz::Array<double, 2>
 bob::measure::roc(const blitz::Array<double, 1> &negatives,
-                  const blitz::Array<double, 1> &positives, size_t points) {
-  // Uses roc_for_far internally
-  // Create an far_list
-  blitz::Array<double, 1> far_list((int)points);
-  int min_far = -8;  // minimum FAR in terms of 10^(min_far)
-  double counts_per_step = points / (-min_far) ;
-  for (int i = 1-(int)points; i <= 0; ++i) {
-    far_list(i+(int)points-1) = std::pow(10., (double)i/counts_per_step);
+                  const blitz::Array<double, 1> &positives,
+                  size_t points_, int min_far) {
+  int points = (int)points_;
+  blitz::Array<double, 2> retval(2, points);
+
+  auto thresholds = bob::measure::meaningfulThresholds(
+    negatives, positives, points_, min_far);
+
+  // compute far and frr based on these thresholds
+  for (int i = 0; i < points; ++i) {
+    auto temp = bob::measure::farfrr(negatives, positives, thresholds(i));
+    retval(0, i) = temp.first;
+    retval(1, i) = temp.second;
   }
-  return bob::measure::roc_for_far(negatives, positives, far_list, false);
+  return retval;
 }
 
 blitz::Array<double, 2>
 bob::measure::precision_recall_curve(const blitz::Array<double, 1> &negatives,
                                      const blitz::Array<double, 1> &positives,
                                      size_t points) {
-  double min = std::min(blitz::min(negatives), blitz::min(positives));
-  double max = std::max(blitz::max(negatives), blitz::max(positives));
-  double step = (max - min) / ((double)points - 1.0);
   blitz::Array<double, 2> retval(2, points);
+  auto thresholds = bob::measure::meaningfulThresholds(
+    negatives, positives, points);
   for (int i = 0; i < (int)points; ++i) {
-    std::pair<double, double> ratios =
-        bob::measure::precision_recall(negatives, positives, min + i * step);
+    auto ratios = bob::measure::precision_recall(negatives, positives, thresholds(i));
     retval(0, i) = ratios.first;
     retval(1, i) = ratios.second;
   }
@@ -441,6 +490,7 @@ bob::measure::roc_for_far(const blitz::Array<double, 1> &negatives,
   return retval;
 }
 
+
 /**
  * The input to this function is a cumulative probability.  The output from
  * this function is the Normal deviate that corresponds to that probability.
@@ -511,9 +561,9 @@ double bob::measure::ppndf(double value) { return _ppndf(value); }
 
 blitz::Array<double, 2>
 bob::measure::det(const blitz::Array<double, 1> &negatives,
-                  const blitz::Array<double, 1> &positives, size_t points) {
+                  const blitz::Array<double, 1> &positives, size_t points, int min_far) {
   blitz::Array<double, 2> retval(2, points);
-  retval = blitz::_ppndf(bob::measure::roc(negatives, positives, points));
+  retval = blitz::_ppndf(bob::measure::roc(negatives, positives, points, min_far));
   return retval;
 }
 

bob/measure/cpp/error.h

@@ -226,11 +226,11 @@ double minimizingThreshold(const blitz::Array<double, 1> &negatives,
   // now we just double check choosing the threshold higher than all scores will not improve the min_predicate
   if (neg_it != negatives.end() || pos_it != positives.end()) {
     double last_threshold = current_threshold;
-    if (neg_it != negatives.end()) 
+    if (neg_it != negatives.end())
       last_threshold = std::nextafter(negatives(negatives.extent(0)-1), negatives(negatives.extent(0)-1)+1);
     else {
-      if (pos_it != positives.end()) 
-        last_threshold = std::nextafter(positives(positives.extent(0)-1), positives(positives.extent(0)-1)+1);      
+      if (pos_it != positives.end())
+        last_threshold = std::nextafter(positives(positives.extent(0)-1), positives(positives.extent(0)-1)+1);
     }
     current_predicate = predicate(0., 1.);
     if (current_predicate < min_predicate) {
@@ -314,18 +314,43 @@ double farThreshold(const blitz::Array<double, 1> &negatives,
 double frrThreshold(const blitz::Array<double, 1> &negatives,
                     const blitz::Array<double, 1> &positives, double frr_value,
                     bool is_sorted = false);
+/**
+ * Computes log-scaled values between :math:`10^{min_power}` and 1
+ */
+blitz::Array<double, 1> log_values(size_t points, int min_power);
+
+/**
+ * This function creates a list of far (and frr) values that we are interested
+ * to see on the curve. Computes thresholds for those points. Sorts the
+ * thresholds so we get sorted numbers to plot on the curve and returns the
+ * thresholds. Some points will be duplicate but in terms of resolution and
+ * accuracy this is better than just changing the threshold from min of scores
+ * to max of scores with equal spaces.
+ */
+blitz::Array<double, 1> meaningfulThresholds(
+    const blitz::Array<double, 1> &negatives,
+    const blitz::Array<double, 1> &positives,
+    size_t points_, int min_far = -8, bool is_sorted = false);
 
 /**
  * Calculates the ROC curve given a set of positive and negative scores and a
  * number of desired points. Returns a two-dimensional blitz::Array of
- * doubles that express the X (FNR) and Y (FPR) coordinates in this order.
- * The points in which the ROC curve are calculated are distributed
- * uniformly in the range [min(negatives, positives), max(negatives,
- * positives)].
+ * doubles that express the X (FPR) and Y (FNR) coordinates in this order.
+ * Internally it uses roc_for_far and roc_for_frr to compute X and Y. This will make
+ * sure all corner cases are addressed. It is recommended to use a very large number of
+ * points (say 2000) to get a smooth output.
+ *
+ * @param negatives The impostor scores
+ * @param positives The genuine scores
+ * @param points    The number of points in of X and Y. It should be multiples of 2.
+ * @param min_far   Minimum FAR in terms of 10^(min_far). This value is also used for
+ *                  min_frr.
+ *
+ * @return A two dimensional array with shape of <2, 2*(points//2)>
  */
 blitz::Array<double, 2> roc(const blitz::Array<double, 1> &negatives,
                             const blitz::Array<double, 1> &positives,
-                            size_t points);
+                            size_t points, int min_far = -8);
 
 /**
  * Calculates the precision-recall curve given a set of positive and negative
@@ -406,7 +431,7 @@ double ppndf(double value);
  */
 blitz::Array<double, 2> det(const blitz::Array<double, 1> &negatives,
                             const blitz::Array<double, 1> &positives,
-                            size_t points);
+                            size_t points, int min_far = -8);
 
 /**
  * Calculates the EPC curve given a set of positive and negative scores and a

bob/measure/main.cpp

@@ -151,13 +151,17 @@ static auto det_doc =
         "recommended by NIST. "
         "The derivative scales are computed with the "
         ":py:func:`bob.measure.ppndf` function.")
-        .add_prototype("negatives, positives, n_points", "curve")
+        .add_prototype("negatives, positives, n_points, [min_far]", "curve")
         .add_parameter(
             "negatives, positives", "array_like(1D, float)",
             "The list of negative and positive scores to compute the DET for")
         .add_parameter("n_points", "int", "The number of points on the DET "
                                           "curve, for which the DET should be "
                                           "evaluated")
+        .add_parameter("min_far", "int", "Minimum FAR in terms of 10^(min_far). "
+                                         "This value is also used for min_frr. "
+                                         "Default value is -8. Values should be "
+                                         "negative.")
         .add_return("curve", "array_like(2D, float)",
                     "The DET curve, with the FPR in the first and the FNR in "
                     "the second row");
@@ -168,10 +172,11 @@ static PyObject *det(PyObject *, PyObject *args, PyObject *kwds) {
   PyBlitzArrayObject *neg;
   PyBlitzArrayObject *pos;
   Py_ssize_t n_points;
+  int min_far = -8;
 
-  if (!PyArg_ParseTupleAndKeywords(args, kwds, "O&O&n", kwlist,
+  if (!PyArg_ParseTupleAndKeywords(args, kwds, "O&O&n|i", kwlist,
                                    &double1d_converter, &neg,
-                                   &double1d_converter, &pos, &n_points))
+                                   &double1d_converter, &pos, &n_points, &min_far))
     return 0;
 
   // protects acquired resources through this scope
@@ -180,7 +185,7 @@ static PyObject *det(PyObject *, PyObject *args, PyObject *kwds) {
 
   auto result =
       bob::measure::det(*PyBlitzArrayCxx_AsBlitz<double, 1>(neg),
-                        *PyBlitzArrayCxx_AsBlitz<double, 1>(pos), n_points);
+                        *PyBlitzArrayCxx_AsBlitz<double, 1>(pos), n_points, min_far);
 
   return PyBlitzArrayCxx_AsNumpy(result);
   BOB_CATCH_FUNCTION("det", 0)
@@ -218,7 +223,7 @@ static auto roc_doc =
         "Calculates points of an Receiver Operating Characteristic (ROC)",
         "Calculates the ROC curve given a set of negative and positive scores "
         "and a desired number of points. ")
-        .add_prototype("negatives, positives, n_points", "curve")
+        .add_prototype("negatives, positives, n_points, [min_far]", "curve")
         .add_parameter("negatives, positives", "array_like(1D, float)",
                        "The negative and positive scores, for which the ROC "
                        "curve should be calculated")
@@ -227,6 +232,10 @@ static auto roc_doc =
                                           "distributed uniformly in the range "
                                           "``[min(negatives, positives), "
                                           "max(negatives, positives)]``")
+        .add_parameter("min_far", "int", "Minimum FAR in terms of 10^(min_far). "
+                                         "This value is also used for min_frr. "
+                                         "Default value is -8. Values should be "
+                                         "negative.")
         .add_return("curve", "array_like(2D, float)",
                     "A two-dimensional array of doubles that express the X "
                     "(FPR) and Y (FNR) coordinates in this order");
@@ -237,10 +246,12 @@ static PyObject *roc(PyObject *, PyObject *args, PyObject *kwds) {
   PyBlitzArrayObject *neg;
   PyBlitzArrayObject *pos;
   Py_ssize_t n_points;
+  int min_far = -8;
 
-  if (!PyArg_ParseTupleAndKeywords(args, kwds, "O&O&n", kwlist,
+
+  if (!PyArg_ParseTupleAndKeywords(args, kwds, "O&O&n|i", kwlist,
                                    &double1d_converter, &neg,
-                                   &double1d_converter, &pos, &n_points))
+                                   &double1d_converter, &pos, &n_points, &min_far))
     return 0;
 
   // protects acquired resources through this scope
@@ -249,7 +260,7 @@ static PyObject *roc(PyObject *, PyObject *args, PyObject *kwds) {
 
   auto result =
       bob::measure::roc(*PyBlitzArrayCxx_AsBlitz<double, 1>(neg),
-                        *PyBlitzArrayCxx_AsBlitz<double, 1>(pos), n_points);
+                        *PyBlitzArrayCxx_AsBlitz<double, 1>(pos), n_points, min_far);
 
   return PyBlitzArrayCxx_AsNumpy(result);
   BOB_CATCH_FUNCTION("roc", 0)

bob/measure/plot.py

@@ -47,7 +47,7 @@ def _semilogx(x, y, **kwargs):
   return pyplot.semilogx(x, y, **kwargs)
 
 
-def roc(negatives, positives, npoints=100, CAR=False, **kwargs):
+def roc(negatives, positives, npoints=2000, CAR=False, min_far=-8, **kwargs):
   """Plots Receiver Operating Characteristic (ROC) curve.
 
   This method will call ``matplotlib`` to plot the ROC curve for a system which
@@ -98,7 +98,7 @@ def roc(negatives, positives, npoints=100, CAR=False, **kwargs):
 
   from matplotlib import pyplot
   from . import roc as calc
-  out = calc(negatives, positives, npoints)
+  out = calc(negatives, positives, npoints, min_far)
   if not CAR:
     return pyplot.plot(out[0, :], out[1, :], **kwargs)
   else:
@@ -164,7 +164,7 @@ def roc_for_far(negatives, positives, far_values=log_values(), CAR=True,
     return _semilogx(out[0, :], (1 - out[1, :]), **kwargs)
 
 
-def precision_recall_curve(negatives, positives, npoints=100, **kwargs):
+def precision_recall_curve(negatives, positives, npoints=2000, **kwargs):
   """Plots a Precision-Recall curve.
 
   This method will call ``matplotlib`` to plot the precision-recall curve for a
@@ -279,7 +279,7 @@ def epc(dev_negatives, dev_positives, test_negatives, test_positives,
   return pyplot.plot(out[0, :], 100.0 * out[1, :], **kwargs)
 
 
-def det(negatives, positives, npoints=100, **kwargs):
+def det(negatives, positives, npoints=2000, min_far=-8, **kwargs):
   """Plots Detection Error Trade-off (DET) curve as defined in the paper:
 
   Martin, A., Doddington, G., Kamm, T., Ordowski, M., & Przybocki, M. (1997).
@@ -395,7 +395,7 @@ def det(negatives, positives, npoints=100, **kwargs):
   from . import det as calc
   from . import ppndf
 
-  out = calc(negatives, positives, npoints)
+  out = calc(negatives, positives, npoints, min_far)
   retval = pyplot.plot(out[0, :], out[1, :], **kwargs)
 
   # now the trick: we must plot the tick marks by hand using the PPNDF method

bob/measure/script/common_options.py

@@ -246,7 +246,7 @@ def points_curve_option(**kwargs):
             ctx.meta['points'] = value
             return value
         return click.option(
-            '-n', '--points', type=INT, default=100, show_default=True,
+            '-n', '--points', type=INT, default=2000, show_default=True,
             help='The number of points use to draw curves in plots',
             callback=callback, **kwargs)(func)
     return custom_points_curve_option

bob/measure/script/figure.py

@@ -427,7 +427,7 @@ class PlotBase(MeasureBase):
     def __init__(self, ctx, scores, evaluation, func_load):
         super(PlotBase, self).__init__(ctx, scores, evaluation, func_load)
         self._output = ctx.meta.get('output')
-        self._points = ctx.meta.get('points', 100)
+        self._points = ctx.meta.get('points', 2000)
         self._split = ctx.meta.get('split')
         self._axlim = ctx.meta.get('axlim')
         self._disp_legend = ctx.meta.get('disp_legend', True)
@@ -550,6 +550,7 @@ class Roc(PlotBase):
         # custom defaults
         if self._axlim is None:
             self._axlim = [None, None, -0.05, 1.05]
+        self._min_dig = -4 if self._min_dig is None else self._min_dig
 
     def compute(self, idx, input_scores, input_names):
         ''' Plot ROC for dev and eval data using
@@ -564,10 +565,11 @@ class Roc(PlotBase):
         mpl.figure(1)
         if self._eval:
             LOGGER.info("ROC dev. curve using %s", dev_file)
-            plot.roc_for_far(
+            plot.roc(
                 dev_neg, dev_pos,
-                far_values=plot.log_values(self._min_dig or -4),
+                npoints=self._points,
                 CAR=self._semilogx,
+                min_far=self._min_dig,
                 color=self._colors[idx], linestyle=self._linestyles[idx],
                 label=self._label('dev', idx)
             )
@@ -576,10 +578,11 @@ class Roc(PlotBase):
 
             linestyle = '--' if not self._split else self._linestyles[idx]
             LOGGER.info("ROC eval. curve using %s", eval_file)
-            plot.roc_for_far(
+            plot.roc(
                 eval_neg, eval_pos, linestyle=linestyle,
-                far_values=plot.log_values(self._min_dig or -4),
+                npoints=self._points,
                 CAR=self._semilogx,
+                min_far=self._min_dig,
                 color=self._colors[idx],
                 label=self._label('eval.', idx)
             )
@@ -595,10 +598,11 @@ class Roc(PlotBase):
                     self._eval_points[line].append((eval_fmr, eval_fnmr))
         else:
             LOGGER.info("ROC dev. curve using %s", dev_file)
-            plot.roc_for_far(
+            plot.roc(
                 dev_neg, dev_pos,
-                far_values=plot.log_values(self._min_dig or -4),
+                npoints=self._points,
                 CAR=self._semilogx,
+                min_far=self._min_dig,
                 color=self._colors[idx], linestyle=self._linestyles[idx],
                 label=self._label('dev', idx)
             )
@@ -625,6 +629,8 @@ class Det(PlotBase):
         if self._min_dig is not None:
             self._axlim[0] = math.pow(10, self._min_dig) * 100
 
+        self._min_dig = -4 if self._min_dig is None else self._min_dig
+
     def compute(self, idx, input_scores, input_names):
         ''' Plot DET for dev and eval data using
         :py:func:`bob.measure.plot.det`'''
@@ -639,7 +645,8 @@ class Det(PlotBase):
         if self._eval and eval_neg is not None:
             LOGGER.info("DET dev. curve using %s", dev_file)
             plot.det(
-                dev_neg, dev_pos, self._points, color=self._colors[idx],
+                dev_neg, dev_pos, self._points, min_far=self._min_dig,
+                color=self._colors[idx],
                 linestyle=self._linestyles[idx],
                 label=self._label('dev.', idx)
             )
@@ -648,7 +655,8 @@ class Det(PlotBase):
             linestyle = '--' if not self._split else self._linestyles[idx]
             LOGGER.info("DET eval. curve using %s", eval_file)
             plot.det(
-                eval_neg, eval_pos, self._points, color=self._colors[idx],
+                eval_neg, eval_pos, self._points, min_far=self._min_dig,
+                color=self._colors[idx],
                 linestyle=linestyle,
                 label=self._label('eval.', idx)
             )
@@ -664,7 +672,8 @@ class Det(PlotBase):
         else:
             LOGGER.info("DET dev. curve using %s", dev_file)
             plot.det(
-                dev_neg, dev_pos, self._points, color=self._colors[idx],
+                dev_neg, dev_pos, self._points, min_far=self._min_dig,
+                color=self._colors[idx],
                 linestyle=self._linestyles[idx],
                 label=self._label('dev.', idx)
             )

bob/measure/test_error.py

@@ -492,8 +492,7 @@ def test_open_set_rates():
 
 
 def test_mindcf():
-  """ Test outlier scores in negative set
-  """
+  # Test outlier scores in negative set
   from bob.measure import min_weighted_error_rate_threshold, farfrr
   cost = 0.99
   negatives = [-3, -2, -1, -0.5, 4]

buildout.cfg

@@ -11,4 +11,4 @@ verbose = true
 
 [scripts]
 recipe = bob.buildout:scripts
-dependent-scripts = true
\ No newline at end of file
+dependent-scripts = true

version.txt

-4.1.1b0
\ No newline at end of file
+5.0.0b0