query set concept
| Definition | The rows a retrieval benchmark asks about. Hubness and the never-retrieved floor are properties of it. Chapter 3 section 3.5 and chapter 10 section 10.2. Also queries. |
|---|---|
| Example | The 1000 queries of a benchmark decide which of the corpus’s rows become hubs. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id query-set, kind concept. |
| Status | measures [demonstrated]. Corrections: none recorded. |
| Defining equation | Book equation 10.3. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | geometric-observation/claims/LEDGER.md:93, lean/DataMiningAsObservation/Hub.lean, lean/DataMiningAsObservation/Hubness.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 10.3.
\[N_k(x\mid Q)=\big|\{q\in Q:\ x\in\operatorname{top}_k(q)\}\big|,\qquad \text{anti-hub}:\ N_k(x)=0.\]
Book equation 10.4.
\[\text{never retrieved}\ \ge\ 1-\frac{|Q|\,k}{n}\qquad\text{whenever}\quad |Q|\,k<n.\]
Book equation 0.17.
\[\Pr[X\ge c]=1-\sum_{i<c}e^{-\mu}\frac{\mu^{i}}{i!},\qquad c^{\star}=\max\{c:\ n\Pr[X\ge c]\ge 1\},\qquad \mu=\frac{n_q\,k}{n}.\]
Conditions
- The rows a retrieval benchmark asks about. Two query sets that retrieve the same lists have the same hubs, no queries give no hubs, and the rows never retrieved number at least the row count less the queries times k, so hubness and the never-retrieved floor are properties of the query set.
- Queries drawn from the corpus inflated the first hub counts by a factor of several, and a generator matched on the query budget would be matched on an artifact.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
- measures. NEG-15 (Bell boundary)
[demonstrated]. Query-conditioned hubness supplies a mechanism for Bell-inequality violation without action at a distance. Refuted as a mechanism; the settings-as-queries reframing survives only as vocabulary.geometric-observation/claims/LEDGER.md:93.
First stated
Chapter 3 section 3.5 and chapter 10 section 10.2 of Data Mining
as Observation, with the query-coupling artifact in
openvector-bench/results/QUERY_COUPLING_ARTIFACT.md:1-20.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 3 section 3.5 | query mass best single feature at every K for all four responses, seven features add at most 20 percent, threshold 1.25 on three of four, zero of four, 1000 real queries, 1024 dimensions | openvector-bench/results/R13_STAGE0_RESULT.md:40-50;
openvector-bench/results/R13_STAGE1_RESULT.md:1-40 |
| chapter 11 section 11.6 | query mass best single feature at every K for all four responses, seven features add at most 20 percent at 12 leaves, threshold 1.25 on three of four, zero of four, 1000 real queries, 1024 dimensions | openvector-bench/results/R13_STAGE0_RESULT.md:40-50;
openvector-bench/results/R13_STAGE1_RESULT.md:1-40 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Hub.lean,
theorems card_hubs_le, hubs_congr,
hubs_anti, hubs_empty, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
lean/DataMiningAsObservation/Hubness.lean,
theorems sum_count, sum_count_eq,
count_congr, antiHub_iff, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation primer S, chapters 0, 1, 2, 3, 4, 8, 10, 11, 12, 13.
Related
hub; hubness; Poisson ceiling; recall at k; harness.
See also
Ledger rows that cite the entry’s records without naming it: NEG-11.
Sources-table rows that share a record with the entry without naming it: chapter 3 section 3.5, chapter 8 section 8.1, chapter 10 section 10.2.
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.