Capturing summarizability with integrity constraints in OLAP
Bibliographic record
Abstract
In multidimensional data models intended for online analytic processing (OLAP), data are viewed as points in a multidimensional space. Each dimension has structure, described by a directed graph of categories, a set of members for each category, and a child/parent relation between members. An important application of this structure is to use it to infer summarizability, that is, whether an aggregate view defined for some category can be correctly derived from a set of precomputed views defined for other categories. A dimension is called structurally heterogeneous if two members in a given category are allowed to have ancestors in different categories. In this article, we propose a class of integrity constraints, dimension constraints , that allow us to reason about summarizability in heterogeneous dimensions. We introduce the notion of frozen dimensions which are minimal homogeneous dimension instances representing the different structures that are implicitly combined in a heterogeneous dimension. Frozen dimensions provide the basis for efficiently testing the implication of dimension constraints and are a useful aid to understanding heterogeneous dimensions. We give a sound and complete algorithm for solving the implication of dimension constraints that uses heuristics based on the structure of the dimension and the constraints to speed up its execution. We study the intrinsic complexity of the implication problem and the running time of our algorithm.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.056 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.005 | 0.015 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".