Scale and Shift of Gaussian Distribution using Tensorflow Bijector

In [1]:

    

import numpy as np
import matplotlib.pyplot as plt
import tensorflow_probability as tfp
import tensorflow as tf
tf.enable_eager_execution()

tfd = tfp.distributions
tfb = tfp.bijectors


    

    




WARNING: The TensorFlow contrib module will not be included in TensorFlow 2.0.
For more information, please see:
  * https://github.com/tensorflow/community/blob/master/rfcs/20180907-contrib-sunset.md
  * https://github.com/tensorflow/addons
If you depend on functionality not listed there, please file an issue.

In [2]:

    

batch_size=512
target_dist = tfd.Normal(loc=5, scale=5)
target_samples = target_dist.sample(batch_size)


    

In [3]:

    

def draw_data(data):
    plt.hist(data)
    plt.title("Values")
    plt.xlabel("x")
    plt.show()
draw_data(target_samples)


    

In [4]:

    

mu = tf.Variable([1.0])
sigma = tf.Variable([1.0])

class ScaleAndShift(tfb.Bijector):
    def __init__(self, mu=0.0, sigma=0.0, validate_args=False, name="exp"):
        super(ScaleAndShift, self).__init__(
          validate_args=validate_args,
          forward_min_event_ndims=0,
          name=name)

    def forward(self, x):
        # Calling forward
        return x * sigma + mu

    def _inverse(self, y):
        return (y - mu) / sigma

    def _inverse_log_det_jacobian(self, y):
        return -self._forward_log_det_jacobian(self._inverse(y))

    def _forward_log_det_jacobian(self, x):
      # Notice that we needn't do any reducing, even when`event_ndims > 0`.
      # The base Bijector class will handle reducing for us; it knows how
      # to do so because we called `super` `__init__` with
      # `forward_min_event_ndims = 0`.
        return tf.log(sigma)

scale_shift = ScaleAndShift(mu, sigma)


    

In [5]:

    

base_dist = tfd.Normal(loc=0, scale=1)

dist = tfd.TransformedDistribution(
    distribution=base_dist,
    bijector=scale_shift
)

print (sigma)


    

    




<tf.Variable 'Variable:0' shape=(1,) dtype=float32, numpy=array([1.], dtype=float32)>

In [6]:

    

samples = dist.sample(1024)
draw_data(samples)


    

    




WARNING:tensorflow:From /home/jiayuye/anaconda3/lib/python3.6/site-packages/tensorflow/python/ops/resource_variable_ops.py:642: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.
Instructions for updating:
Colocations handled automatically by placer.






    

In [9]:

    

def loss():
    return -tf.reduce_mean(dist.log_prob(target_samples))

optimizer = tf.train.AdamOptimizer(learning_rate=0.2)
for i in range(1000):
    optimizer.minimize(loss, var_list=[mu, sigma])

print (mu)
print (sigma)


    

    




<tf.Variable 'Variable:0' shape=(1,) dtype=float32, numpy=array([4.9208164], dtype=float32)>
<tf.Variable 'Variable:0' shape=(1,) dtype=float32, numpy=array([5.0056963], dtype=float32)>

In [8]:

    

samples = dist.sample(1024)
draw_data(samples)


    

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