A lower-bound on the number of rankings required in recommender systems using collaborativ filtering
Bibliographic record
Abstract
We consider the situation where users rank items from a given set, and each user ranks only a (small) subset of all items. We assume that users can be classified into C classes, and users in a given class c have the same ranking for all items. For this situation we are interested in the following question. As a function of the number of users N in a given class c and the numbers of items IN to be ranked, how many rankings mN per user are needed in order to be able to correctly identify all user in class c This question is of interest because correctly identifying all users in a class allows to accurately predict the ranking of an item by a given user that the user has not ranked, but that was ranked by another user in the same class. This is exactly the goal recommender systems using collaborative filtering. Therefore, being able to answer the above questions allows us to characterize how much data (i.e. how many rankings per user) is required by a recommender system using collaborative filtering to accurately predict user-item ranking pairs. We study the above question using a random graph model. Even though the resulting random graph is not a Erdos-Renyi graph, this allows us to use for our analysis similar techniques that have been developed for the analysis of Erdos-Renyi graphs.
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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 | 0.160 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.007 | 0.003 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.003 | 0.004 |
| Scholarly communication | 0.004 | 0.021 |
| Open science | 0.008 | 0.006 |
| Research integrity | 0.006 | 0.007 |
| Insufficient payload (model declined to judge) | 0.012 | 0.004 |
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".