data/analyzor.txt

[
    {
        "expression": "I(X;Y;Z)",
        "operators": [
            "Interaction Information"
        ],
        "dependency": "Conditional Independence",
        "theoretical_advantage": "Interaction Information is a measure of the unique information shared between three random variables X, Y, and Z. It can be used to detect conditional independence relationships, which can be useful for feature selection and model simplification.",
        "complexity": "medium"
    }
],
[
    {
        "expression": "I(X;Y)",
        "operators": [
            "Mutual Information"
        ],
        "dependency": "measures the mutual dependence between two random variables X and Y",
        "theoretical_advantage": "Mutual Information can be used for feature selection in machine learning, as it measures the dependence between features and the target variable.",
        "complexity": "low"
    }
],
[
    {
        "expression": "I(X;Y|Z)",
        "operators": [
            "MI"
        ],
        "dependency": "Conditional Independence",
        "theoretical_advantage": "It can help identify relevant features for classification or regression tasks.",
        "complexity": "low"
    }
],
[
    {
        "expression": "I(X;Y) - I(X;Z)",
        "operators": [
            "MI",
            "MI"
        ],
        "dependency": "X and Y are independent of Z",
        "theoretical_advantage": "It can be used to identify features that are relevant to the target variable but not related to each other.",
        "complexity": "low"
    }
],
[
    {
        "expression": "I(X;Y|Z) - I(X;Y)",
        "operators": [
            "Mutual Information",
            "Conditional Mutual Information"
        ],
        "dependency": "Conditional Independence",
        "theoretical_advantage": "It can help identify features that are relevant to the target variable given a set of other features.",
        "complexity": "medium"
    }
],