Detecting approximate replicate components of a high-dimensional random vector with latent structure
Bibliographic record
Abstract
High-dimensional feature vectors are likely to contain sets of measurements that are approximate replicates of one another. In complex applications, or automated data collection, these feature sets are not known a priori, and need to be determined. This work proposes a class of latent factor models on the observed, high-dimensional, random vector X∈Rp, for defining, identifying and estimating the index set of its approximately replicate components. The model class is parametrized by a p×K loading matrix A that contains a hidden sub-matrix whose rows can be partitioned into groups of parallel vectors. Under this model class, a set of approximate replicate components of X corresponds to a set of parallel rows in A: these entries of X are, up to scale and additive error, the same linear combination of the K latent factors; the value of K is itself unknown. The problem of finding approximate replicates in X reduces to identifying, and estimating, the location of the hidden sub-matrix within A, and of the partition H of its row index set H. Both H and H can be fully characterized in terms of a new family of criteria based on the correlation matrix of X, and their identifiability, as well as that of the unknown latent dimension K, are obtained as consequences. The constructive nature of the identifiability arguments enables computationally efficient procedures, with consistency guarantees. Furthermore, when the loading matrix A has a particular sparse structure, provided by the errors-in-variable parametrization, the difficulty of the problem is elevated. The task becomes that of separating out groups of parallel rows that are proportional to canonical basis vectors from other, possibly dense, parallel rows in A. This is met under a scale assumption, via a principled way of selecting the target row indices, guided by the successive maximization of Schur complements of appropriate covariance matrices. The resulting procedure is an enhanced version of that developed for recovering general parallel rows in A. It is also computationally efficient, consistent. It has immediate applications to latent space overlapping clustering and the estimation of loading matrices that satisfy a canonical parametrization.
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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 | 0.008 | 0.045 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".