lsynth 0.1.3

Evaluation of how good a synthetic dataset is compared to the original with presuppossing structural constraints

MAP-alignment fidelity and dataset distance for synthetic tabular data

This package implements the one-sided MAP-alignment fidelity statistic introduced by Chattopadhyay et al. and described in the manuscript “How Good Is Your Synthetic Data?”.

The core idea

For a synthetic record to be realistic, each coordinate should agree with the conditional MAP prediction inferred from real data.

Formally, for a data record x and coordinate i:

υ(x, i) = φ_i(x_i | x_{-i}) / max_y φ_i(y | x_{-i})

Averaged over samples and coordinates:

Υ(D) in [0,1]

• High Υ: synthetic preserves real conditional structure

• Low Υ: structural distortion (even if marginals / covariance match)

Installation

pip install lsynth

Quick Example

import pandas as pd
from lsynth import compute_upsilon

df_real = pd.read_csv("gss_2018.csv").sample(200)

ups_lsm, syn_lsm = compute_upsilon(
    num=100,
    model_path="gss_2018.joblib",
    generate=True,
    gen_algorithm="LSM",
    orig_df=df_real,
    n_workers=8,
)

print("LSM mean Upsilon:", ups_lsm.mean())

Interpretation

• ~1.0: synthetic matches conditional structure closely

• ~0.7: Gaussian-like distortions

• < 0.7: strong structural mismatch

Why MAP-alignment?

Because covariance matching is insufficient.

Section VII of the manuscript gives explicit examples where:

• Real and synthetic share identical means, variances, covariance matrices

• Yet they differ strongly in conditional structure

• MAP-alignment catches the discrepancy immediately

This method:

• Detects nonlinear and higher-order structure

• Avoids feature-embedding artifacts

• Comes with finite-sample uncertainty control

Supported Generators

• "LSM": use QuasiNet as a generative model via qsample

• "BASELINE": independent-column null model

• "CTGAN": uses SDV CTGAN synthesizer

• Custom generators also supported

Relationship to Theory

This package implements practical instantiations of:

• Eq. (2): MAP-alignment for a coordinate

• Eq. (3): aggregate Upsilon

• Algorithm 2: one-sided fidelity score

• Section VI: uncertainty (Hoeffding bounds)

All without assumptions about the synthetic generator internals.

Citation

Chattopadhyay I, et al.
"How Good Is Your Synthetic Data?"