Tensorflow distributions do not integrate/sum to 1

Question

I was experimenting with tensorflow-probability (tfp). I wanted to check, if the density of a Normal-distribution in tfp does integrate (sum) to one. I thought the following calculation inside the print should give me rougly 1, but instead I got 714.2143.

import tensorflow_probability as tfp
tfd = tfp.distributions

x = np.linspace(-7., 7., int(1e4), dtype=np.float64)
print(tf.reduce_sum( np.array( [tfd.Normal(loc=0, scale=1).prob(y) for y in x] )))

Output: tf.Tensor(714.2143, shape=(), dtype=float32)

What am I missing here?

Answer 1

If you want to calculate to area under the curve, which is integrating the pdf here, you need to divide by number of samples and multiply the length of support:

import tensorflow as tf
import tensorflow_probability as tfp

import numpy as np
tfd = tfp.distributions

num_samples = 1000
min_val = -7
max_val = 7
x = np.linspace(min_val, max_val,
                num_samples,
                dtype=np.float64)

dist = tfd.Normal(loc=0, scale=1)
normalized_vals = np.array([dist.prob(y) for y in x])/ num_samples * (max_val-(min_val))
print(tf.reduce_sum(normalized_vals)) # 0.99899995