Lernen Global Sensitivity | Differential Privacy Mechanisms

Global sensitivity is a key concept in differential privacy that measures how much a single individual's data can influence the output of a function or query. Specifically, the global sensitivity of a function is defined as the maximum change in the function's output when a single record in the input dataset is changed, added, or removed. This value is crucial because it determines the minimum amount of noise that must be added to the output to ensure differential privacy.

If the global sensitivity is high, a single individual's data can have a large impact on the result, requiring more noise to protect privacy. Conversely, if the global sensitivity is low, less noise is needed, which allows for more accurate results. Therefore, understanding and calculating global sensitivity is essential for designing effective differentially private mechanisms. For example, when answering a count query — such as "How many users are over 18?" — the global sensitivity is 1, since adding or removing one person can change the count by at most 1.


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def global_sensitivity_count(dataset):
    """
    Computes the global sensitivity of a count query on the dataset.
    For count queries, the global sensitivity is always 1, but this function
    demonstrates the reasoning by comparing datasets differing by one record.
    """
    # Create two neighboring datasets: one with, one without the last record
    dataset1 = dataset
    dataset2 = dataset[:-1]
    count1 = len(dataset1)
    count2 = len(dataset2)
    sensitivity = abs(count1 - count2)
    return sensitivity

# Example usage:
dataset = ["Alice", "Bob", "Charlie"]
print("Global sensitivity of count query:", global_sensitivity_count(dataset))

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Abschnitt 2. Kapitel 1

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Suggested prompts:

Can you explain how global sensitivity would change for other types of queries?

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              1234567891011121314151617
            
def global_sensitivity_count(dataset):
    """
    Computes the global sensitivity of a count query on the dataset.
    For count queries, the global sensitivity is always 1, but this function
    demonstrates the reasoning by comparing datasets differing by one record.
    """
    # Create two neighboring datasets: one with, one without the last record
    dataset1 = dataset
    dataset2 = dataset[:-1]
    count1 = len(dataset1)
    count2 = len(dataset2)
    sensitivity = abs(count1 - count2)
    return sensitivity

# Example usage:
dataset = ["Alice", "Bob", "Charlie"]
print("Global sensitivity of count query:", global_sensitivity_count(dataset))

War alles klar?

Danke für Ihr Feedback!

Abschnitt 2. Kapitel 1