Hands-On Quantum Machine Learning with Python/

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Estimating a Variable

Estimating a Variable

Learn how to estimate a variable.

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Let’s get back to our quantum Bayesian network, which consists of four nodes. The Age and Sex of a passenger determine the Norm. The Norm and the Pclass determine Survival.

Our data consists of all the cases of passengers onboard the Titanic. The dataset contains observations of Age, Sex, and Survival. These are observable variables. The values of the Norm are missing data. The Norm is a hidden variable.

The image above depicts the missing CPT of our Bayesian network.

We aim to find the CPTs that maximize the probability of the observed data.

Rather than writing a single big function, we split our code into small pieces we can put together at the end. Let’s start with the marginal probabilities of being a child (isChild) and a passenger’s gender (Sex).

Applying the known

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import pandas as pd
train = pd.read_csv('train.csv')
# the maximum age of a passenger we consider as a child
max_child_age = 8
# probability of being a child
population_child = train[train.Age.le(max_child_age)]
p_child = len(population_child)/len(train)
# probability of being female
population_female = train[train.Sex.eq("female")]
p_female = len(population_female)/len(train)
# positions of the qubits
QPOS_ISCHILD = 0
QPOS_SEX = 1
def apply_ischild_sex(qc):
    # set the marginal probability of isChild
    qc.ry(prob_to_angle(p_child), QPOS_ISCHILD)
    # set the marginal probability of Sex
    qc.ry(prob_to_angle(p_female), QPOS_SEX)

In line 5, we’ll keep the maximum age of 8 years of a passenger we consider as a child. The probability of being a child is given by the number of children in line 8, divided by the total number of passengers in line 9.

We’ll do the same calculation for the passenger being ...