Add metric for general MSAS statistics

[npatki]

Problem Description

In this paper, we introduced a new methodology for calculating multi-sequence metrics called MSAS. We should add the MSAS-related metrics to SDMetrics so that users with sequential data can use them for evaluation.

Expected behavior

Add a metric called StatisticMSAS that performs the MSAS algorithm for a given statistic.

Data compatibility: 1 ID column (representing the sequence key), and 1 continuous column (datetime or numerical)

Parameters:

• (required) real_data: A tuple of 2 pandas.Series objects. The first represents the sequence key of the real data and the second represents a continuous column of data.
• (required) synthetic_data: A tuple of 2 pandas.Series objects. The first represents the sequence key of the synthetic data and the second represents a continuous column of data.
• statistic: A string representing the statistic function to use when computing MSAS
  • (default) 'mean': The arithmetic mean
  • 'median': The median value
  • 'std': The standard deviation
  • 'min': The min value
  • 'max': The max value

Output: A score in range [0, 1] -- 0 being the worst and 1 being the best

from sdmetrics.column_pairs import StatisticMSAS

score = StatisticMSAS.compute(
  real_data=(real_table['patient_id'], real_table['heart_rate']),
  synthetic_data = (synthetic_table['patient_id'], synthetic_table['heart_rate']),
  statistic='std'
)

How does it work? The sequence key determines which continuous values belong to which sequence. This metric computes a statistic for all sequences in the real and synthetic data, and then compares those distributions.

1. Calculate the statistic value of each sequence in the real data (call this distribution D_r)
2. Calculate the statistic value of each sequence in the synthetic data (call this distribution D_s)
3. Now apply the KSComplement metric to compare the similarities of the distributions (D_r, D_s). Return this score.