7.3 BDL and sources of uncertainty

In this case study, we will look at how we can model aleatoric and epistemic uncertainty in a regression problem when we are trying to predict a continuous outcome variable. We will use a real-life dataset of diamonds that contains the physical attributes of more than 50,000 diamonds as well as their prices. In particular, we will look at the relationship between the weight of a diamond (measured as its carat) and the price paid for the diamond.

Step 1: Setting up the environment

To set up the environment, we import several packages. We import tensorflow and tensorflow_probability for building and training vanilla and probabilistic neural networks, tensorflow_datasets for importing the diamonds data set, numpy for performing calculations and operations on numerical arrays (such as calculating the mean), pandas for handling DataFrames, and matplotlib for plotting:

 
import matplotlib.pyplot as plt  
import numpy as np ...