Combining multiple 2-dimensional histograms

Determine a principled method to combine multiple two-dimensional histograms over attribute pairs (such as XY, XZ, and YZ) to estimate the selectivity of predicates involving three attributes X, Y, and Z in density-based cardinality estimation.

Background

Within the review of density-based cardinality estimation, the authors note that while 2-dimensional histograms can capture correlations, their practical deployment faces challenges. One highlighted challenge is the lack of a clear method to combine multiple 2D histograms to estimate selectivity for predicates involving more than two attributes.

The inability to combine XY, XZ, and YZ histograms to estimate a predicate over X, Y, Z limits the usefulness of 2D histograms in multi-attribute selectivity estimation, motivating the need for a concrete approach.

References

It is unclear how to combine multiple 2-d histograms, e.g. in order to estimate a predicate on 3 attributes $(X,Y,Z)$ from 2-d histograms on $XY, XZ, YZ$.

— Pessimistic Cardinality Estimation (2412.00642 - Khamis et al., 1 Dec 2024) in Section 2 (Brief Review of CE), footnote on 2-Dimensional Histograms