MutualInformation
MutualInformation(dataset, column_list, filter_condition_dict=None, duckdb_connection=None, decimal_places=6)
¶
Calculate Mutual Information (MI) between pairs of columns using DuckDB.
Computes the mutual information metric between specified column pairs to measure their statistical dependence. Supports both categorical and continuous variables with optional filtering conditions.
Details¶
The function calculates mutual information using the formula: MI(X,Y) = Σ P(x,y) * log(P(x,y)/(P(x)*P(y)))
Where: - P(x,y) is the joint probability - P(x) and P(y) are marginal probabilities - The sum is over all possible value pairs
Higher MI values indicate stronger relationships between variables: - MI = 0: Variables are independent - MI > 0: Variables share information - Higher values suggest stronger dependencies
Example¶
Consider salary and department columns: Salary: [50000, 60000, 50000, 75000, 55000] Dept: ['IT', 'HR', 'IT', 'Fin', 'IT']
Example calculation: 1. Calculate joint probabilities P(salary,dept) 2. Calculate marginal probabilities P(salary) and P(dept) 3. Compute MI using the formula above
Code example:
df = pl.DataFrame({ ... 'salary': [50000, 60000, 50000, 75000, 55000], ... 'department': ['IT', 'HR', 'IT', 'Finance', 'IT'], ... 'age': [25, 30, 25, 35, 28] ... }) result = MutualInformation(df, [{'salary': 'department'}]) print(result) [{'columns': 'salary,department', 'mutual_information': 0.682345, 'table_name': 'mutual_info_abc123', 'execution_timestamp_utc': '2024-01-25 10:30:45', 'filter_conditions': None}]
Parameters¶
dataset : Any Input dataset (DataFrame or table name). Can be: - Polars DataFrame - Pandas DataFrame - PyArrow Table - String representing existing table name in DuckDB connection The dataset must contain all columns specified in column_list.
List[Dict[str, str]]
List of column pairs to analyze. Each pair is a single-item dictionary where key and value are column names. Example: [{'salary': 'department'}, {'age': 'experience'}] Both categorical and numeric columns are supported. Columns must exist in dataset and contain non-null values.
Optional[Dict[str, Union[str, int, float]]]
Row filter conditions to apply before MI calculation. Example: {'department': 'IT', 'age': 25} Keys must be valid column names. Values must match column data types. Default: None (no filtering)
Optional[DuckDBPyConnection]
Existing DuckDB connection to use. If None, creates temporary connection. Connection must have access to dataset if table name provided. Default: None
int
Number of decimal places for MI values. Must be non-negative integer. Affects precision of returned MI values. Default: 6
Returns¶
List[Dict[str, Union[str, float, dict, None]]] Analysis results for each column pair: - columns : str Comma-separated column pair names (e.g., "salary,department") - mutual_information : float Calculated MI value rounded to specified decimal places - table_name : str Name of analyzed table - execution_timestamp_utc : str UTC timestamp of execution - filter_conditions : Optional[Dict] Applied filter conditions if any, else None
Raises¶
ValueError - Empty or invalid column_list format - Column not found in dataset - Invalid decimal_places (negative) - Invalid filter column names - Type mismatch in filter conditions
Source code in src/whistlingduck/analyzers/MutualInformation.py
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