add weighted crossentropy

tflearn/objectives.py

@@ -103,6 +103,54 @@ def binary_crossentropy(y_pred, y_true):
             logits=y_pred, labels=y_true))
 
 
+def weighted_crossentropy(y_pred, y_true):
+    """ Weighted Crossentropy.
+
+    Computes weighted sigmoid cross entropy between y_pred (logits) and y_true
+    (labels).
+
+    Computes a weighted cross entropy.
+
+    This is like sigmoid_cross_entropy_with_logits() except that pos_weight,
+    allows one to trade off recall and precision by up- or down-weighting the
+    cost of a positive error relative to a negative error.
+
+    The usual cross-entropy cost is defined as:
+
+    `targets * -log(sigmoid(logits)) + (1 - targets) * -log(1 - sigmoid(logits))`
+
+    The argument pos_weight is used as a multiplier for the positive targets:
+
+    `targets * -log(sigmoid(logits)) * pos_weight + (1 - targets) * -log(1 - sigmoid(logits))`
+
+    For brevity, let x = logits, z = targets, q = pos_weight. The loss is:
+
+    ```
+      qz * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x))
+    = qz * -log(1 / (1 + exp(-x))) + (1 - z) * -log(exp(-x) / (1 + exp(-x)))
+    = qz * log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x)))
+    = qz * log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x))
+    = (1 - z) * x + (qz +  1 - z) * log(1 + exp(-x))
+    = (1 - z) * x + (1 + (q - 1) * z) * log(1 + exp(-x))
+    ```
+
+    Setting l = (1 + (q - 1) * z), to ensure stability and avoid overflow,
+    the implementation uses
+
+    `(1 - z) * x + l * (log(1 + exp(-abs(x))) + max(-x, 0))`
+
+    logits and targets must have the same type and shape.
+
+    Arguments:
+        y_pred: `Tensor` of `float` type. Predicted values.
+        y_true: `Tensor` of `float` type. Targets (labels).
+
+    """
+    with tf.name_scope("WeightedCrossentropy"):
+        return tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(
+            logits=y_pred, labels=y_true))
+
+
 def mean_square(y_pred, y_true):
     """ Mean Square Loss.