Hands-On Quantum Machine Learning with Python/

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Calculating the log‐likelihood when ignoring the missing data

Calculating the log‐likelihood when ignoring the missing data

Learn the concept of log‐likelihood and refine the model.

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Calculate the log‐likelihood when ignoring the missing data

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def eval_qbn(model, prepare_data, data):
    results = model(prepare_data(data), hist=False)
    return round(log_likelihood(data, 
        results['11'], # prob_a_b
        results['01'], # prob_a_nb
        results['10'], # prob_na_b
        results['00']  # prob_na_nb
    ), 3)
print(eval_qbn(qbn, lambda dataset: list(filter(lambda item: item[1] is not None ,dataset)), data))

The function eval_qbn in line 1 takes the qbn-function as the model, but we can plug in any other model, too, as long as it takes a dataset of the given format and returns the results we obtain from Qiskit. The second parameter, prepare_data, is a function that takes care of the missing data point. We put in our data and expect the dataset we put into our model in line 2.

The function returns the log-likelihood score of the given model in line 3. Therefore, we provide the probability measures we get from the quantum circuit in lines 4 to 7. Note that the states we get from the quantum circuit read from the right (qubit at position 0 represents AA) to the left (qubit at position 1 represents BB).

In this example, we provide a function that filters out the missing item (filter(lambda item: item[1] is not None)) in line 10.

The results show a log-likelihood score of −9.499-9.499. As mentioned, the overall value does not say much. We can check how good it is when we compare it with other models.

Next, let’s try to fill in a value for the missing data. In three of the five cases where AA is 0, BB is 0, too. BB is ...