How to batch a transformed (scaled and quantized) Beta distribution in tensorflow probability - tensorflow

Question

I'm trying to fit a beta distribution to the results of a survey with discrete scores (1, 2, 3, 4, 5).
For that to work I need a working log_prob of a Beta in TensorFlow probability. However, there is a problem with how batching is handled in Beta.
Here is a minimal example that gives me an error:
InvalidArgumentError: Shapes of a and x are inconsistent: [3] vs. [1000,1] [Op:Betainc]
The same code seems to work ok with Normal distribution...
What am I doing wrong here?
import numpy as np
import tensorflow_probability as tfp
tfd = tfp.distributions
#Generate fake data
np.random.seed(2)
data = np.random.beta(2.,2.,1000)*5.0
data = np.ceil(data)
data = data[:,None]
# Create a batch of three Beta distributions.
alpha = np.array([1., 2., 3.]).astype(np.float32)
beta = np.array([1., 2., 3.]).astype(np.float32)
bt = tfd.Beta(alpha, beta)
#bt = tfd.Normal(loc=alpha, scale=beta)
#Scale beta to 0-5
scbt = tfd.TransformedDistribution(
distribution=bt,
bijector=tfp.bijectors.AffineScalar(
shift=0.,
scale=5.))
# quantize beta to (1,2,3,4,5)
qdist = tfd.QuantizedDistribution(distribution=scbt,low=1,high=5)
#calc log_prob for 3 distributions
print(np.sum(qdist.log_prob(data),axis=0))
print(qdist.log_prob(data).shape)
TensorFlow 2.0.0
tensorflow_probability 0.8.0
EDIT:
As suggested by Chris Suter. Here is broadcasting by hand solution:
import numpy as np
import tensorflow as tf
import tensorflow_probability as tfp
tfd = tfp.distributions
from matplotlib import pyplot as plt
#Generate fake data
numdata = 100
numbeta = 3
np.random.seed(2)
data = np.random.beta(2.,2.,numdata)
data *= 5.0
data = np.ceil(data)
data = data[:,None].astype(np.float32)
#alpha and beta [[1., 2., 3.]]
alpha = np.expand_dims(np.arange(1,4),0).astype(np.float32)
beta = np.expand_dims(np.arange(1,4),0).astype(np.float32)
#tile to compensate for betainc
alpha = tf.tile(alpha,[numdata,1])
beta = tf.tile(beta,[numdata,1])
data = tf.tile(data,[1,numbeta])
bt = tfd.Beta(concentration1=alpha, concentration0=beta)
scbt = tfd.TransformedDistribution(
distribution=bt,
bijector=tfp.bijectors.AffineScalar(
shift=0.,
scale=5.))
# quantize beta to (1,2,3,4,5)
qdist = tfd.QuantizedDistribution(distribution=scbt,low=1,high=5)
#calc log_prob for numbeta number of distributions
print(np.sum(qdist.log_prob(data),axis=0))
EDIT2: The above solution does not work when I try to apply it in MCMC sampling.
The new code looks like this:
import os
os.environ["CUDA_VISIBLE_DEVICES"] = "-1"
from time import time
import tensorflow as tf
import tensorflow_probability as tfp
tfd = tfp.distributions
import numpy as np
#Generate fake data
numdata = 100
np.random.seed(2)
data = np.random.beta(2.,2.,numdata)
data *= 5.0
data = np.ceil(data)
data = data[:,None].astype(np.float32)
#tf.function
def sample_chain():
#Parameters of MCMC
num_burnin_steps = 300
num_results = 200
num_chains = 50
step_size = 0.01
#data tensor
outcomes = tf.convert_to_tensor(data, dtype=tf.float32)
def modeldist(alpha,beta):
bt = tfd.Beta(concentration1=alpha, concentration0=beta)
scbt = tfd.TransformedDistribution(
distribution=bt,
bijector=tfp.bijectors.AffineScalar(
shift=0.,
scale=5.))
# quantize beta to (1,2,3,4,5)
qdist = tfd.QuantizedDistribution(distribution=scbt,low=1,high=5)
return qdist
def joint_log_prob(con1,con0):
#manual broadcast
tcon1 = tf.tile(con1[None,:],[numdata,1])
tcon0 = tf.tile(con0[None,:],[numdata,1])
toutcomes = tf.tile(outcomes,[1,num_chains])
#model distribution with manual broadcast
dist = modeldist(tcon1,tcon0)
#joint log prob
return tf.reduce_sum(dist.log_prob(toutcomes),axis=0)
kernel = tfp.mcmc.HamiltonianMonteCarlo(
target_log_prob_fn=joint_log_prob,
num_leapfrog_steps=5,
step_size=step_size)
kernel = tfp.mcmc.SimpleStepSizeAdaptation(
inner_kernel=kernel, num_adaptation_steps=int(num_burnin_steps * 0.8))
init_state = [tf.identity(tf.random.uniform([num_chains])*10.0,name='init_alpha'),
tf.identity(tf.random.uniform([num_chains])*10.0,name='init_beta')]
samples, [step_size, is_accepted] = tfp.mcmc.sample_chain(
num_results=num_results,
num_burnin_steps=num_burnin_steps,
current_state=init_state,
kernel=kernel,
trace_fn=lambda _, pkr: [pkr.inner_results.accepted_results.step_size,
pkr.inner_results.is_accepted])
return samples
samples = sample_chain()
This ends up with an error message:
ValueError: Encountered None gradient. fn_arg_list: [tf.Tensor 'init_alpha:0' shape=(50,) dtype=float32, tf.Tensor 'init_beta:0' shape=(50,) dtype=float32] grads: [None, None]

Answer 1

Sadly tf.math.betainc doesn't support broadcasting at present, which causes the cdf computation, which QuantizedDistribution calls, to fail. If you must use Beta, the only workaround I can think of is to broadcast "manually" by tiling the data and Beta params.
Alternatively, you might be able to get away with using the Kumaraswamy distribution, which is similar to Beta but has some nicer analytical properties.