Variational Gaussian process loss- possible math error

In the documentation for variational Gaussian process applied to minibatches (https://github.com/tensorflow/probability/blob/v0.12.1/tensorflow_probability/python/distributions/variational_gaussian_process.py#L572), the KL term is rescaled by batch_size/num_training_points_. I assume the reconstruction error term (expected log-likelihood) is not scaled and represents a sum over all data points in the minibatch. My understanding is the unbiased estimator for the full-data variational loss should instead be given -(num_training_points_/batch_size)*reconstruction_error + KL_term (or, on a per-observation basis, this could be divided by the total observations constant: -(1/batch_size)*reconstruction_error + (1/num_training_points_)*KL_term). Otherwise, if the batch size is not constant across minibatches, the estimator will be biased. If this is true, perhaps the weight should be on the reconstruction error term instead of the KL term in the variational_loss. Please let me know if I am missing something.

Start with the variational Gaussian process documentation and implementation around line 572 of tensorflow_probability/python/distributions/variational_gaussian_process.py, then inspect the variational_loss API behavior. Verify how reconstruction and KL terms are scaled for minibatches of different sizes; done means the estimator's scaling is confirmed and the implementation or documentation is corrected accordingly.