Normal Distribution (Gaussian Distribution) is widely used in deep learning model. In this tutorial, we will introduce how to compute it in tensorflow.
Normal Distribution can be defined as:
Here is the tutorial:
An Introduction to Gaussian Distribution or Normal Distribution
In tensorflow, we can use tf.distributions.Normal() to compute it.
Syntax
tf.distributions.Normal() is defined as:
__init__(
loc,
scale,
validate_args=False,
allow_nan_stats=True,
name='Normal'
)
Parameters are:
loc: the mean of distribution, which is \(\mu\).
scale: the standard deviation of distribution, which is \(\sigma\).
How to use tf.distributions.Normal()?
We will use some examples to show you how to do.
As to normal distribution\(f(x) = N(x)\)
Example 1:
If we have got the \(x\) value, how to compute its probability?
import tensorflow as tf import numpy as np x = tf.convert_to_tensor(np.array([0.0, 1.0]), dtype = tf.float32)
In this code, we have got \(x = 0.0\) or \(x = 1.0\), how to get the probability \(P(x \leqslant 0.0)\) and \(P(x \leqslant 1.0)\)?
First, we can build a standard normal distribution.
#mean = 0, standard deviation = 1.0 std_norm = tf.distributions.Normal(0.0, 1.0)
Then we can use std_norm.cdf() to compute.
att2 = std_norm.cdf(x) #compute probility of x<=0 and x<=1.0
Run this code, you will get the value:
[0.5 0.8413]
It means:
\(P(x \leqslant 0.0) = 0.5\)
\(P(x \leqslant 1.0) = 0.8413\)
Example 2:
If we have got \(x\) value, how to get the value of \(f(x)\)?
We can use std_norm.prob() to compute.
Here is the example code:
att = std_norm.prob(x)
Run this code, we will get the value:
[0.3989 0.242 ]
It means, in standard normal distribution
\(f(0.0) = 0.3989\)
\(f(1.0) = 0.242\)
Example 3:
If we have got the probability value \(P(x)\), how to get the \(x\) value?
For example, if \(P(x) = 0.8413\), how about \(x\)?
We can use std_norm.quantile() to compute.
x_v = std_norm.quantile(att2)
Run this code, we will get the value:
[0. 1.]
It means \(x = [0., 1]\).
Here is the full example code:
import tensorflow as tf
import numpy as np
x = tf.convert_to_tensor(np.array([0.0, 1.0]), dtype = tf.float32)
#mean = 0, standard deviation = 1.0
std_norm = tf.distributions.Normal(0.0, 1.0)
att = std_norm.prob(x)
att2 = std_norm.cdf(x) #compute probility of x<0 and x<1.0
x_v = std_norm.quantile(att2)
init = tf.global_variables_initializer()
init_local = tf.local_variables_initializer()
with tf.Session() as sess:
sess.run([init, init_local])
np.set_printoptions(precision=4, suppress=True)
print(sess.run(x))
print(sess.run(att))
print(sess.run(att2))
print(sess.run(x_v))