Lower bounds on performance of metric tree indexing schemes for exact similarity search in high dimensions
Bibliographic record
Abstract
Within a mathematically rigorous model borrowed from statistical learning theory, we analyse the curse of dimensionality for similarity based information retrieval in the context of popular indexing schemes: metric trees. The datasets X are sampled randomly from a domain Ω, equipped with a distance, ρ, and an underlying probability distribution, μ. While performing an asymptotic analysis, we send the intrinsic dimension d of Ω to infinity, and assume that the size of a dataset, n, grows superpolynomially yet subexponentially in d. Exact similarity search refers to finding the nearest neighbour in the dataset X to a query point ω ∈ Ω, where the query points are subject to the same probability distribution μ as datapoints. Let F denote a class of all 1-Lipschitz functions on Ω that can be used as decision functions in constructing a hierarchical metric tree indexing scheme. Suppose the VC dimension of all sets {ω: ƒ(ω) ≥ a}, a ∈ R is dO(1). (In view of a 1995 result of Goldberg and Jerrum, this is a reasonable complexity assumption.) We deduce superpolynomial in d lower bounds on the expected average case performance of hierarchical metric-tree based indexing schemes for exact similarity search in (Ω, X).
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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 | 0.020 | 0.137 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.002 |
| Bibliometrics | 0.004 | 0.008 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.008 | 0.019 |
| Open science | 0.006 | 0.008 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
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".