tensorflow
Implemention of Mean Method in distributions.Categorical
Proposition for correcting issue #685 Error with Implementation of Mean Method in distributions.Categorical
NotImplementedError: mean is not implemented: Categorical
import tensorflow_probability as tfp
prob_dist = tfp.distributions.Categorical(probs=[1.0])
print(prob_dist.mean())
Defined a _mean method for implementing mean
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This implementation is not correct. The mean of a categorical is defined as sum(i * prob(x=i) for i in range(num_categories). You should be able to modify the implementation of the _entropy to implement this.
This will also need tests to verify the implementation is correct (entropy tests, again, should provide a good set of test cases).
Hello @SiegeLordEx, Thanks for your response. I have updated the formula for Mean
tf.reduce_sum(tf.math.multiply_no_nan(i , self._probs(x=i)) for i in range(self._num_categories), axis=-1
Check this out
The previous implementation was incorrect. I've written an example implementation of how the Categorical mean should be, the code below works for me and produces the desired result. The mean should also account for unnormalised probabilities between the classes, since there are cases where the probabilities might not sum up to 1.
def _mean(self):
probs = self.probs_parameter()
num_categories = self._num_categories(probs)
# Initialise the mean with zeros
categorical_mean = tf.zeros(tf.shape(probs[...,0]))
# Compute the normalisation factors such that all probabilities sum up to 1
normalisation = tf.reduce_sum(probs, axis=-1)
# Sum up all the normalised probabilities
# sum(i * prob(X=i) for i in range(num_categories) )
for i in range(num_categories):
categorical_mean = categorical_mean + tf.cast(i,probs.dtype) * probs[...,i] / normalisation
return categorical_mean
Shall I make a new commit/pull request with this?
I don't think there is currently an implementation.
The following might be simpler: tf.reduce_sum(tf.range(self._num_categories(probs)) * probs, axis=-1) / tf.reduce_sum(probs, axis=-1)
You could send a PR, sure.
On Fri, May 5, 2023 at 9:58 AM Fotis Drakopoulos @.***> wrote:
The previous implementation was incorrect. I've written an example implementation of how the Categorical mean should be like, the code below works for me and produces the desired result. The mean should also account for unnormalised probabilities between the classes, since there are cases where the probabilities don't sum up to 1.
def _mean(self): probs = self.probs_parameter() num_categories = self._num_categories(probs) # Initialise the mean with zeros categorical_mean = tf.zeros(tf.shape(probs[...,0])) # Compute the normalisation factors such that all probabilities sum up to 1 normalisation = tf.reduce_sum(probs, axis=-1) # Sum up all the normalised probabilities # sum(i * prob(X=i) for i in range(num_categories) ) for i in range(num_categories): categorical_mean = categorical_mean + tf.cast(i,probs.dtype) * probs[...,i] / normalisation
return categorical_meanShall I make a new commit for this?
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I don't think there is currently an implementation. The following might be simpler: tf.reduce_sum(tf.range(self._num_categories(probs)) * probs, axis=-1) / tf.reduce_sum(probs, axis=-1) You could send a PR, sure.
Hi,
Indeed this looks much simpler, thanks! We want to ensure that the multiplication is applied across the last axis of probs, i.e. each slice of probs across the last dimension (probs[...,i]) gets multiplied by each number i in tf.range(self._num_categories(probs)). The multiplication should be doing this by default, but I will test the code and submit a new PR.