pearsons linear coefficient keras

Question

I have tried to implement pearsons linear coefficient as a metric in Keras however because of placeholders I cannot compile my model using this metric.

def CC(y_true, y_pred):

y_true = K.clip(y_true, K.epsilon(), 1)
y_pred = K.clip(y_pred, K.epsilon(), 1)
n_y_true=y_true/(K.sum(y_true)+K.epsilon())
n_y_pred=y_pred/(K.sum(y_pred)+K.epsilon())
y_true_average=K.mean(y_true)
y_pred_average=K.mean(y_pred)
print((K.map_fn(lambda x: x-y_pred_average,n_y_pred)).shape[0])
if not(K.map_fn(lambda x: x-y_pred_average,n_y_pred)).shape[0]==None:
    return (K.sum(K.dot((K.map_fn(lambda x: x-y_pred_average,n_y_pred)),(K.map_fn(lambda x: x-y_true_average,n_y_true))))/(K.count_params(n_y_true)-1))/(K.dot(K.std(n_y_pred),K.std(n_y_true)))
else:
    return 0

I tried using K.dot instead of * however the same error remains. During compile I get the error unsupported operand type(s) for *: 'NoneType' and 'NoneType. And I cannot figure out how to solve it. It happens because I want to elementwise multiply two tensors but the batchsize in the shape is not difined during compile and represented as a ? in the shape of (?,224,224,3). Is there a way to set this or work around it?

Answer 1

The problem lies in two facts:

1. The first dimension of a tensor is a batch dimension (that's why during model compilation is set to None).
2. You are using sum and mean in such manner that you are also including this additional dimension in your computations.

Your Pearson's correlation loss should look the following:

def pearson_loss(y_true, y_pred):
    y_true = K.clip(y_true, K.epsilon(), 1)
    y_pred = K.clip(y_pred, K.epsilon(), 1)
    # reshape stage
    y_true = K.reshape(y_true, shape=(-1, 224 * 224 * 3))
    y_pred = K.reshape(y_pred, shape=(-1, 224 * 224 * 3))
    # normalizing stage - setting a 0 mean.
    y_true -= y_true.mean(axis=-1)
    y_pred -= y_pred.mean(axis=-1)
    # normalizing stage - setting a 1 variance
    y_true = K.l2_normalize(y_true, axis=-1)
    y_pred = K.l2_normalize(y_pred, axis=-1)
    # final result
    pearson_correlation = K.sum(y_true * y_pred, axis=-1)
    return pearson_correlation