AggregateBalanceMeasure

These measures look at the distribution of records across all value combinations of sensitive feature columns. For example, if sex and race are specified as sensitive features, the API tries to quantify imbalance across all combinations of the specified features (e.g., [Male, Black], [Female, White], [Male, Asian Pacific Islander])

Measure	Description	Interpretation
Atkinson index	The Atkinson index presents the percentage of total income that a given society would have to forego in order to have more equal shares of income among its citizens. This measure depends on the degree of societal aversion to inequality (a theoretical parameter decided by the researcher), where a higher value entails greater social utility or willingness by individuals to accept smaller incomes in exchange for a more equal distribution. An important feature of the Atkinson index is that it can be decomposed into within-group and between-group inequality.	Range [0,1] 0 = perfect equality 1 = maximum inequality In this case, it is the proportion of records for a sensitive column’s combination.
Theil T index	GE(1) = Theil T, which is more sensitive to differences at the top of the distribution. The Theil index is a statistic used to measure economic inequality. The Theil index measures an entropic “distance” the population is away from the “ideal” egalitarian state of everyone having the same income.	If everyone has the same income, then T_T equals 0. If one person has all the income, then T_T gives the result ln(N). 0 means equal income and larger values mean higher level of disproportion.
Theil L index	GE(0) = Theil L, which is more sensitive to differences at the lower end of the distribution. Thiel L is the logarithm of (mean income)/(income i), over all the incomes included in the summation. It is also referred to as the mean log deviation measure. Because a transfer from a larger income to a smaller one will change the smaller income’s ratio more than it changes the larger income’s ratio, the transfer-principle is satisfied by this index.	Same interpretation as Theil T index.

class raimitigations.databalanceanalysis.aggregate_measures.AggregateBalanceMeasure(sensitive_cols: List[str])

Bases: BalanceMeasure

AGGREGATE_METRICS: Dict[Measures, Callable[[array], float]] = {Measures.ATKINSON_INDEX: <function get_atkinson_index>, Measures.THEIL_L_INDEX: <function get_theil_l_index>, Measures.THEIL_T_INDEX: <function get_theil_t_index>}

measures(df: DataFrame) → DataFrame

The output is a dataframe that maps the names of the different aggregate measures to their values:

The following measures are computed:

• Atkinson Index - https://en.wikipedia.org/wiki/Atkinson_index

• Theil Index (L and T) - https://en.wikipedia.org/wiki/Theil_index

Parameters

df (pd.DataFrame) – the df to calculate aggregate measures on

Returns

returns a dataframe that has one column that is the name of the aggregate measure, the second column contains the values for each of the metrics of interest.

Return type

pd.DataFrame