tf.math.betainc is missing gradients

[jesnie]

I'm trying to fit a NegativeBinomial, but its cdf seems to be missing some gradients:

count = tf.compat.v1.get_variable("count", shape=())
logit = tf.compat.v1.get_variable("logit", shape=())
value = tf.compat.v1.get_variable("value", shape=())

cdf = tfpd.NegativeBinomial(total_count=count, logits=logit).cdf(value)

print(tf.gradients(cdf, [count]))  # Prints `None`.
print(tf.gradients(cdf, [logit]))  # Works.
print(tf.gradients(cdf, [value]))  # Prints `None`.

[csuter]

I think this is working as intended, in that the gradient w.r.t. discrete parameters/values is not defined. Is there a use case you're working with wherein one or both of these discrete quantities is relaxed to be continuous? Maybe we can help find an alternative implementation?

[jesnie]

In my case the value really is discrete, but I have a continuous count. What I really want is something that looks like a Poisson distribution, but with a tunable variance.

[jesnie]

Also, I would like to point out that NegativeBinomial.prob does have gradients, so cdf not having them is a bit surprising:

count = tf.compat.v1.get_variable("count", shape=())
logit = tf.compat.v1.get_variable("logit", shape=())
value = tf.compat.v1.get_variable("value", shape=())

prob = tfpd.NegativeBinomial(total_count=count, logits=logit).prob(value)

print(tf.gradients(prob, [count]))  # Works.
print(tf.gradients(prob, [logit]))  # Works.
print(tf.gradients(prob, [value]))  # Works.

[csuter]

Ah, looks like the issue is just that betainc doesn't have grads defined w.r.t. its first two arguments:

https://github.com/tensorflow/tensorflow/blob/master/tensorflow/python/ops/math_grad.py#L922

I'm sure TF would welcome this upstream contribution, if you were so inclined!

[nicocheh]

Any news or solution to this? @csuter @jesnie

[leandrolcampos]

Hi @jesnie and @nicocheh!

I hope this message finds you well.

Since the last release, tfp.math.betainc has gradients w.r.t. all parameters.

All the best,