Why the ltv prediction part use probabilitity prediction multiply expectation as the final ltv prediction？ about lifetime_value HOT 2 OPEN

I also found it strange.

As far as I understood, regression part of the model is trained on the subset of customers who have observed nonzero LTV:

positive = tf.cast(labels > 0, tf.float32)

safe_labels = positive * labels + (
      1 - positive) * tf.keras.backend.ones_like(labels)

regression_loss = -tf.keras.backend.mean(
      positive * tfd.LogNormal(loc=loc, scale=scale).log_prob(safe_labels),
      axis=-1)`

If loc and scale give the best accuracy prediction on this subset of customers, then

preds = (positive_probs *
      tf.keras.backend.exp(loc + 0.5 * tf.keras.backend.square(scale)))

gives shifted estimation in general case, since positive_probs are not 0 or 1, but somewhere between them.

I think probability estimated by the classification part of the model should somehow be taken in consideration by the regression part of the model.

from lifetime_value.