The Cost of Representation by Subset Repairs

TL;DR

This work studies the "cost of representation" in subset repairs for functional dependencies and targets the question of how many additional tuples have to be deleted if the authors want to satisfy not only the integrity constraints but also representation constraints for given sub-populations.

Abstract

Datasets may include errors, and specifically violations of integrity constraints, for various reasons. Standard techniques for ``minimal-cost'' database repairing resolve these violations by aiming for minimum change in the data, and in the process, may sway representations of different sub-populations. For instance, the repair may end up deleting more females than males, or more tuples from a certain age group or race, due to varying levels of inconsistency in different sub-populations. Such repaired data can mislead consumers when used for analytics, and can lead to biased decisions for downstream machine learning tasks. We study the ``cost of representation'' in subset repairs for functional dependencies. In simple terms, we target the question of how many additional tuples have to be deleted if we want to satisfy not only the integrity constraints but also representation constraints for given sub-populations. We study the complexity of this problem and compare it with the complexity of optimal subset repairs without representations. While the problem is NP-hard in general, we give polynomial-time algorithms for special cases, and efficient heuristics for general cases. We perform a suite of experiments that show the effectiveness of our algorithms in computing or approximating the cost of representation.

Figures (11)

• Figure 1: Disability status and cost of representation for ACS data. In (b), the % above the bars indicates remaining tuples, and the numbers on the bars show the deletion ratio relative to optimal S-repair (that does not satisfy representation).
• Figure 2: Our solutions vs. baselines
• Figure 3: Deletion overhead varying overall noise and input size (ACS, 80%-20% value distr., 20%-80% relative noise distr.)
• Figure 4: Percentage of remaining tuples varying the RC (ACS, 80%-20% value distr. and 20%-80% relative noise distr.)
• Figure 5: Runtimes for ACS and COMPAS data ($10\%$ noise level, 80%-20% value distribution) with chain and non-chain FD sets

Theorems & Definitions (31)

• Example 1
• Definition 1: Representation Constraint
• Example 2
• Definition 2: RS-repair
• Example 3
• Theorem 1
• Definition 3
• Proposition 3
• Theorem 2
• Proposition 3