reimplement auc in fluid (#13167)

* reimplement auc in pyton

* reimplement auc in fluid

* add auc unittest


* replace new auc in layers


* add batch Auc in Fluid

* name formated

paddle/fluid/API.spec

@@ -312,7 +312,7 @@ paddle.fluid.layers.iou_similarity ArgSpec(args=[], varargs='args', keywords='kw
 paddle.fluid.layers.box_coder ArgSpec(args=[], varargs='args', keywords='kwargs', defaults=None)
 paddle.fluid.layers.polygon_box_transform ArgSpec(args=[], varargs='args', keywords='kwargs', defaults=None)
 paddle.fluid.layers.accuracy ArgSpec(args=['input', 'label', 'k', 'correct', 'total'], varargs=None, keywords=None, defaults=(1, None, None))
-paddle.fluid.layers.auc ArgSpec(args=['input', 'label', 'curve', 'num_thresholds', 'topk'], varargs=None, keywords=None, defaults=('ROC', 200, 1))
+paddle.fluid.layers.auc ArgSpec(args=['input', 'label', 'curve', 'num_thresholds', 'topk'], varargs=None, keywords=None, defaults=('ROC', 4095, 1))
 paddle.fluid.layers.exponential_decay ArgSpec(args=['learning_rate', 'decay_steps', 'decay_rate', 'staircase'], varargs=None, keywords=None, defaults=(False,))
 paddle.fluid.layers.natural_exp_decay ArgSpec(args=['learning_rate', 'decay_steps', 'decay_rate', 'staircase'], varargs=None, keywords=None, defaults=(False,))
 paddle.fluid.layers.inverse_time_decay ArgSpec(args=['learning_rate', 'decay_steps', 'decay_rate', 'staircase'], varargs=None, keywords=None, defaults=(False,))

paddle/fluid/operators/auc_op.cc

@@ -13,7 +13,6 @@ See the License for the specific language governing permissions and
 limitations under the License. */
 
 #include "paddle/fluid/operators/auc_op.h"
-#include <string>
 
 namespace paddle {
 namespace operators {
@@ -36,15 +35,12 @@ class AucOp : public framework::OperatorWithKernel {
     PADDLE_ENFORCE_EQ(predict_height, label_height,
                       "Out and Label should have same height.");
 
-    int num_thres = ctx->Attrs().Get<int>("num_thresholds");
+    int num_pred_buckets = ctx->Attrs().Get<int>("num_thresholds") + 1;
 
     ctx->SetOutputDim("AUC", {1});
-    ctx->SetOutputDim("TPOut", {num_thres});
-    ctx->SetOutputDim("TNOut", {num_thres});
-    ctx->SetOutputDim("FPOut", {num_thres});
-    ctx->SetOutputDim("FNOut", {num_thres});
-
-    ctx->ShareLoD("Predict", /*->*/ "AUC");
+    ctx->SetOutputDim("BatchAUC", {1});
+    ctx->SetOutputDim("StatPosOut", {num_pred_buckets});
+    ctx->SetOutputDim("StatNegOut", {num_pred_buckets});
   }
 
  protected:
@@ -66,25 +62,24 @@ class AucOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("Label",
              "A 2D int tensor indicating the label of the training data. "
              "shape: [batch_size, 1]");
-    AddInput("TP", "True-Positive value.");
-    AddInput("FP", "False-Positive value.");
-    AddInput("TN", "True-Negative value.");
-    AddInput("FN", "False-Negative value.");
     // TODO(typhoonzero): support weight input
+    AddInput("StatPos", "Statistic value when label = 1");
+    AddInput("StatNeg", "Statistic value when label = 0");
+
     AddOutput("AUC",
               "A scalar representing the "
               "current area-under-the-curve.");
-    AddOutput("TPOut", "True-Positive value.");
-    AddOutput("FPOut", "False-Positive value.");
-    AddOutput("TNOut", "True-Negative value.");
-    AddOutput("FNOut", "False-Negative value.");
+    AddOutput("BatchAUC", "The AUC for current batch");
+    AddOutput("StatPosOut", "Statistic value when label = 1");
+    AddOutput("StatNegOut", "Statistic value when label = 0");
 
     AddAttr<std::string>("curve", "Curve type, can be 'ROC' or 'PR'.")
         .SetDefault("ROC");
+
     AddAttr<int>("num_thresholds",
                  "The number of thresholds to use when discretizing the"
                  " roc curve.")
-        .SetDefault(200);
+        .SetDefault((2 << 12) - 1);
 
     AddComment(R"DOC(
 Area Under The Curve (AUC) Operator.

paddle/fluid/operators/auc_op.h

@@ -13,9 +13,9 @@ See the License for the specific language governing permissions and
 limitations under the License. */
 
 #pragma once
+
 #include <string>
 #include <vector>
-#include "paddle/fluid/framework/eigen.h"
 #include "paddle/fluid/framework/op_registry.h"
 
 namespace paddle {
@@ -23,106 +23,85 @@ namespace operators {
 
 using Tensor = framework::Tensor;
 
-template <typename T, int MajorType = Eigen::RowMajor,
-          typename IndexType = Eigen::DenseIndex>
-using EigenVector = framework::EigenVector<T, MajorType, IndexType>;
-
 template <typename DeviceContext, typename T>
 class AucKernel : public framework::OpKernel<T> {
  public:
-  void Compute(const framework::ExecutionContext& ctx) const override {
-    auto* predict = ctx.Input<Tensor>("Predict");
-    auto* label = ctx.Input<Tensor>("Label");
-    auto* auc = ctx.Output<Tensor>("AUC");
+  void Compute(const framework::ExecutionContext &ctx) const override {
+    auto *predict = ctx.Input<Tensor>("Predict");
+    auto *label = ctx.Input<Tensor>("Label");
+
+    std::string curve = ctx.Attr<std::string>("curve");
+    int num_thresholds = ctx.Attr<int>("num_thresholds");
+    int num_pred_buckets = num_thresholds + 1;
+
     // Only use output var for now, make sure it's persistable and
     // not cleaned up for each batch.
-    auto* true_positive = ctx.Output<Tensor>("TPOut");
-    auto* false_positive = ctx.Output<Tensor>("FPOut");
-    auto* true_negative = ctx.Output<Tensor>("TNOut");
-    auto* false_negative = ctx.Output<Tensor>("FNOut");
+    auto *auc = ctx.Output<Tensor>("AUC");
+    auto *stat_pos = ctx.Output<Tensor>("StatPosOut");
+    auto *stat_neg = ctx.Output<Tensor>("StatNegOut");
 
-    auto* auc_data = auc->mutable_data<double>(ctx.GetPlace());
+    auto *stat_pos_data = stat_pos->mutable_data<int64_t>(ctx.GetPlace());
+    auto *stat_neg_data = stat_neg->mutable_data<int64_t>(ctx.GetPlace());
+    calcAuc(ctx, label, predict, stat_pos_data, stat_neg_data, num_thresholds,
+            auc);
 
-    std::string curve = ctx.Attr<std::string>("curve");
-    int num_thresholds = ctx.Attr<int>("num_thresholds");
-    std::vector<double> thresholds_list;
-    thresholds_list.reserve(num_thresholds);
-    for (int i = 1; i < num_thresholds - 1; i++) {
-      thresholds_list[i] = static_cast<double>(i) / (num_thresholds - 1);
+    auto *batch_auc = ctx.Output<Tensor>("BatchAUC");
+    std::vector<int64_t> stat_pos_batch(num_pred_buckets, 0);
+    std::vector<int64_t> stat_neg_batch(num_pred_buckets, 0);
+    calcAuc(ctx, label, predict, stat_pos_batch.data(), stat_neg_batch.data(),
+            num_thresholds, batch_auc);
+  }
+
+ private:
+  inline static double trapezoidArea(double X1, double X2, double Y1,
+                                     double Y2) {
+    return (X1 > X2 ? (X1 - X2) : (X2 - X1)) * (Y1 + Y2) / 2.0;
   }
-    const double kEpsilon = 1e-7;
-    thresholds_list[0] = 0.0f - kEpsilon;
-    thresholds_list[num_thresholds - 1] = 1.0f + kEpsilon;
 
+  inline static void calcAuc(const framework::ExecutionContext &ctx,
+                             const framework::Tensor *label,
+                             const framework::Tensor *predict,
+                             int64_t *stat_pos, int64_t *stat_neg,
+                             int num_thresholds,
+                             framework::Tensor *auc_tensor) {
     size_t batch_size = predict->dims()[0];
     size_t inference_width = predict->dims()[1];
+    const T *inference_data = predict->data<T>();
+    const auto *label_data = label->data<int64_t>();
 
-    const T* inference_data = predict->data<T>();
-    const auto* label_data = label->data<int64_t>();
-
-    auto* tp_data = true_positive->mutable_data<int64_t>(ctx.GetPlace());
-    auto* fn_data = false_negative->mutable_data<int64_t>(ctx.GetPlace());
-    auto* tn_data = true_negative->mutable_data<int64_t>(ctx.GetPlace());
-    auto* fp_data = false_positive->mutable_data<int64_t>(ctx.GetPlace());
+    auto *auc = auc_tensor->mutable_data<double>(ctx.GetPlace());
 
-    for (int idx_thresh = 0; idx_thresh < num_thresholds; idx_thresh++) {
-      // calculate TP, FN, TN, FP for current thresh
-      int64_t tp = 0, fn = 0, tn = 0, fp = 0;
     for (size_t i = 0; i < batch_size; i++) {
-        // NOTE: label_data used as bool, labels > 0 will be treated as true.
+      uint32_t binIdx = static_cast<uint32_t>(
+          inference_data[i * inference_width + 1] * num_thresholds);
       if (label_data[i]) {
-          if (inference_data[i * inference_width + 1] >=
-              (thresholds_list[idx_thresh])) {
-            tp++;
-          } else {
-            fn++;
-          }
-        } else {
-          if (inference_data[i * inference_width + 1] >=
-              (thresholds_list[idx_thresh])) {
-            fp++;
+        stat_pos[binIdx] += 1.0;
       } else {
-            tn++;
-          }
-        }
-      }
-      // store rates
-      tp_data[idx_thresh] += tp;
-      fn_data[idx_thresh] += fn;
-      tn_data[idx_thresh] += tn;
-      fp_data[idx_thresh] += fp;
-    }
-    // epsilon to avoid divide by zero.
-    double epsilon = 1e-6;
-    // Riemann sum to caculate auc.
-    Tensor tp_rate, fp_rate, rec_rate;
-    tp_rate.Resize({num_thresholds});
-    fp_rate.Resize({num_thresholds});
-    rec_rate.Resize({num_thresholds});
-    auto* tp_rate_data = tp_rate.mutable_data<double>(ctx.GetPlace());
-    auto* fp_rate_data = fp_rate.mutable_data<double>(ctx.GetPlace());
-    auto* rec_rate_data = rec_rate.mutable_data<double>(ctx.GetPlace());
-    for (int i = 0; i < num_thresholds; i++) {
-      tp_rate_data[i] = (static_cast<double>(tp_data[i]) + epsilon) /
-                        (tp_data[i] + fn_data[i] + epsilon);
-      fp_rate_data[i] =
-          static_cast<double>(fp_data[i]) / (fp_data[i] + tn_data[i] + epsilon);
-      rec_rate_data[i] = (static_cast<double>(tp_data[i]) + epsilon) /
-                         (tp_data[i] + fp_data[i] + epsilon);
+        stat_neg[binIdx] += 1.0;
       }
-    *auc_data = 0.0f;
-    if (curve == "ROC") {
-      for (int i = 0; i < num_thresholds - 1; i++) {
-        auto dx = fp_rate_data[i] - fp_rate_data[i + 1];
-        auto y = (tp_rate_data[i] + tp_rate_data[i + 1]) / 2.0f;
-        *auc_data = *auc_data + dx * y;
     }
-    } else if (curve == "PR") {
-      for (int i = 1; i < num_thresholds; i++) {
-        auto dx = tp_rate_data[i] - tp_rate_data[i - 1];
-        auto y = (rec_rate_data[i] + rec_rate_data[i - 1]) / 2.0f;
-        *auc_data = *auc_data + dx * y;
+
+    *auc = 0.0f;
+
+    double totPos = 0.0;
+    double totNeg = 0.0;
+    double totPosPrev = 0.0;
+    double totNegPrev = 0.0;
+
+    int idx = num_thresholds;
+
+    while (idx >= 0) {
+      totPosPrev = totPos;
+      totNegPrev = totNeg;
+      totPos += stat_pos[idx];
+      totNeg += stat_neg[idx];
+      *auc += trapezoidArea(totNeg, totNegPrev, totPos, totPosPrev);
+
+      --idx;
     }
+
+    if (totPos > 0.0 && totNeg > 0.0) {
+      *auc = *auc / totPos / totNeg;
     }
   }
 };

python/paddle/fluid/layers/metric_op.py

@@ -78,7 +78,7 @@ def accuracy(input, label, k=1, correct=None, total=None):
     return acc_out
 
 
-def auc(input, label, curve='ROC', num_thresholds=200, topk=1):
+def auc(input, label, curve='ROC', num_thresholds=2**12 - 1, topk=1):
     """
     **Area Under the Curve (AUC) Layer**
 
@@ -118,16 +118,14 @@ def auc(input, label, curve='ROC', num_thresholds=200, topk=1):
     """
     helper = LayerHelper("auc", **locals())
     auc_out = helper.create_tmp_variable(dtype="float64")
+    batch_auc_out = helper.create_tmp_variable(dtype="float64")
     # make tp, tn, fp, fn persistable, so that can accumulate all batches.
-    tp = helper.create_global_variable(
-        persistable=True, dtype='int64', shape=[num_thresholds])
-    tn = helper.create_global_variable(
-        persistable=True, dtype='int64', shape=[num_thresholds])
-    fp = helper.create_global_variable(
-        persistable=True, dtype='int64', shape=[num_thresholds])
-    fn = helper.create_global_variable(
-        persistable=True, dtype='int64', shape=[num_thresholds])
-    for var in [tp, tn, fp, fn]:
+    stat_pos = helper.create_global_variable(
+        persistable=True, dtype='int64', shape=[num_thresholds + 1])
+    stat_neg = helper.create_global_variable(
+        persistable=True, dtype='int64', shape=[num_thresholds + 1])
+
+    for var in [stat_pos, stat_neg]:
         helper.set_variable_initializer(
             var, Constant(
                 value=0.0, force_cpu=True))
@@ -137,18 +135,15 @@ def auc(input, label, curve='ROC', num_thresholds=200, topk=1):
         inputs={
             "Predict": [input],
             "Label": [label],
-            "TP": [tp],
-            "TN": [tn],
-            "FP": [fp],
-            "FN": [fn]
+            "StatPos": [stat_pos],
+            "StatNeg": [stat_neg]
         },
         attrs={"curve": curve,
                "num_thresholds": num_thresholds},
         outputs={
             "AUC": [auc_out],
-            "TPOut": [tp],
-            "TNOut": [tn],
-            "FPOut": [fp],
-            "FNOut": [fn]
+            "BatchAUC": [batch_auc_out],
+            "StatPosOut": [stat_pos],
+            "StatNegOut": [stat_neg]
         })
-    return auc_out, [tp, tn, fp, fn]
+    return auc_out, batch_auc_out, [stat_pos, stat_neg]

python/paddle/fluid/metrics.py

@@ -558,8 +558,6 @@ class Auc(MetricBase):
         name: metric name
         curve: Specifies the name of the curve to be computed, 'ROC' [default] or
           'PR' for the Precision-Recall-curve.
-        num_thresholds: The number of thresholds to use when discretizing the roc
-            curve.
 
     "NOTE: only implement the ROC curve type via Python now."
 
@@ -574,15 +572,14 @@ class Auc(MetricBase):
                 numpy_auc = metric.eval()
     """
 
-    def __init__(self, name, curve='ROC', num_thresholds=200):
+    def __init__(self, name, curve='ROC', num_thresholds=4095):
         super(Auc, self).__init__(name=name)
         self._curve = curve
         self._num_thresholds = num_thresholds
-        self._epsilon = 1e-6
-        self.tp_list = np.zeros((num_thresholds, ))
-        self.fn_list = np.zeros((num_thresholds, ))
-        self.tn_list = np.zeros((num_thresholds, ))
-        self.fp_list = np.zeros((num_thresholds, ))
+
+        _num_pred_buckets = num_thresholds + 1
+        self._stat_pos = [0] * _num_pred_buckets
+        self._stat_neg = [0] * _num_pred_buckets
 
     def update(self, preds, labels):
         if not _is_numpy_(labels):
@@ -590,41 +587,32 @@ class Auc(MetricBase):
         if not _is_numpy_(preds):
             raise ValueError("The 'predictions' must be a numpy ndarray.")
 
-        kepsilon = 1e-7  # to account for floating point imprecisions
-        thresholds = [(i + 1) * 1.0 / (self._num_thresholds - 1)
-                      for i in range(self._num_thresholds - 2)]
-        thresholds = [0.0 - kepsilon] + thresholds + [1.0 + kepsilon]
-
-        # calculate TP, FN, TN, FP count
-        for idx_thresh, thresh in enumerate(thresholds):
-            tp, fn, tn, fp = 0, 0, 0, 0
         for i, lbl in enumerate(labels):
+            value = preds[i, 1]
+            bin_idx = int(value * self._num_thresholds)
+            assert bin_idx <= self._num_thresholds
             if lbl:
-                    if preds[i, 1] >= thresh:
-                        tp += 1
-                    else:
-                        fn += 1
+                self._stat_pos[bin_idx] += 1.0
             else:
-                    if preds[i, 1] >= thresh:
-                        fp += 1
-                    else:
-                        tn += 1
-            self.tp_list[idx_thresh] += tp
-            self.fn_list[idx_thresh] += fn
-            self.tn_list[idx_thresh] += tn
-            self.fp_list[idx_thresh] += fp
+                self._stat_neg[bin_idx] += 1.0
+
+    @staticmethod
+    def trapezoid_area(x1, x2, y1, y2):
+        return abs(x1 - x2) * (y1 + y2) / 2.0
 
     def eval(self):
-        epsilon = self._epsilon
-        num_thresholds = self._num_thresholds
-        tpr = (self.tp_list.astype("float32") + epsilon) / (
-            self.tp_list + self.fn_list + epsilon)
-        fpr = self.fp_list.astype("float32") / (
-            self.fp_list + self.tn_list + epsilon)
-        rec = (self.tp_list.astype("float32") + epsilon) / (
-            self.tp_list + self.fp_list + epsilon)
-
-        x = fpr[:num_thresholds - 1] - fpr[1:]
-        y = (tpr[:num_thresholds - 1] + tpr[1:]) / 2.0
-        auc_value = np.sum(x * y)
-        return auc_value
+        tot_pos = 0.0
+        tot_neg = 0.0
+        auc = 0.0
+
+        idx = self._num_thresholds
+        while idx >= 0:
+            tot_pos_prev = tot_pos
+            tot_neg_prev = tot_neg
+            tot_pos += self._stat_pos[idx]
+            tot_neg += self._stat_neg[idx]
+            auc += self.trapezoid_area(tot_neg, tot_neg_prev, tot_pos,
+                                       tot_pos_prev)
+            idx -= 1
+
+        return auc / tot_pos / tot_neg if tot_pos > 0.0 and tot_neg > 0.0 else 0.0

python/paddle/fluid/tests/unittests/test_auc_op.py

@@ -26,18 +26,15 @@ class TestAucOp(OpTest):
         pred = np.random.random((128, 2)).astype("float32")
         labels = np.random.randint(0, 2, (128, 1))
         num_thresholds = 200
-        tp = np.zeros((num_thresholds, )).astype("int64")
-        tn = np.zeros((num_thresholds, )).astype("int64")
-        fp = np.zeros((num_thresholds, )).astype("int64")
-        fn = np.zeros((num_thresholds, )).astype("int64")
+
+        stat_pos = np.zeros((num_thresholds + 1, )).astype("int64")
+        stat_neg = np.zeros((num_thresholds + 1, )).astype("int64")
 
         self.inputs = {
             'Predict': pred,
             'Label': labels,
-            'TP': tp,
-            'TN': tn,
-            'FP': fp,
-            'FN': fn
+            "StatPos": stat_pos,
+            "StatNeg": stat_neg
         }
         self.attrs = {'curve': 'ROC', 'num_thresholds': num_thresholds}
 
@@ -47,11 +44,10 @@ class TestAucOp(OpTest):
         python_auc.update(pred, labels)
 
         self.outputs = {
-            'AUC': python_auc.eval(),
-            'TPOut': python_auc.tp_list,
-            'FNOut': python_auc.fn_list,
-            'TNOut': python_auc.tn_list,
-            'FPOut': python_auc.fp_list
+            'AUC': np.array(python_auc.eval()),
+            'BatchAUC': np.array(python_auc.eval()),
+            'StatPosOut': np.array(python_auc._stat_pos),
+            'StatNegOut': np.array(python_auc._stat_neg)
         }
 
     def test_check_output(self):