Veritable uncertainty quantification examples

example1.py

pr = analysis.predict({'petal_length': 1.5, 'petal_width': None})
interval = pr.credible_values('petal_width')
# => (0.06619570898596525, 0.45519138428493605)
interval[1] - interval[0]
# => 0.38899567529897083

pr = analysis.predict({'petal_length': 5.0, 'petal_width': None})
interval = pr.credible_values('petal_width')
# => (1.3341578189754613, 2.4761532421771784)
interval[1] - interval[0]
# => 1.141995423201717

# Answer: different petal lengths lead to different degrees of uncertainty about petal width.  
# Veritable is able to model this kind of "heteroskedastic" relationship because the model it 
# learns can include various kinds of nonlinearities.

example2.py

query1 = {
    'petal_length': 1.5,
    'sepal_length': None,
    'sepal_width': None }
pr1 = analysis.predict(query1)
pr1.credible_values('sepal_length')
# => (4.334787896697201, 5.639183256498405)
pr1.credible_values('sepal_width')
# => (2.7258301944595824, 4.1180270245192565)

query2 = {
    'petal_length': 1.5,
    'petal_width': 0.2,
    'sepal_length': None,
    'sepal_width': None }
pr2 = analysis.predict(query2)
pr2.credible_values('sepal_length')
# => (4.468544865668935, 5.67907462278871)
pr2.credible_values('sepal_width')
# => (2.7279822552513515, 4.113270938023062)

# At least for these particular petal dimensions, petal width does not seem to add much in 
# the way of uncertainty reduction.  That is, once you know that it's a short petal, also 
# knowing that it's skinny doesn't provide much more.  Of course, measuring both variables
# might be important in other cases --- and if so, Veritable will identify these relationships
# too.

example3.py

query = {
    'class': 'Iris-setosa',
    'petal_length': None,
    'petal_width': None,
    'sepal_length': None,
    'sepal_width': None }
pr = analysis.predict(query)

pr.credible_values('petal_length')
# => (1.0413860198602414, 1.8600456565417642)
pr.credible_values('petal_width')
# => (0.11534704664999318, 0.49745028429888877)
pr.credible_values('sepal_length')
# => (4.430450802336802, 5.885512229758362)
pr.credible_values('sepal_width')
# => (2.6854970916482346, 3.9249199743156242)

# These represent the credible range of dimensions for a synthetic population of setosa flowers.
# Veritable's predictions can be used in a number of ways to generate and learn from synthetic
# populations; we'll say more about this in future posts.