Dotted Representations of Mean-Variance Efficient Frontiers and their Computation
Bibliographic record
Abstract
This paper is about dotted representations of efficient frontiers. Dotted representations, as in portfolio selection, can often be the most practical way of communicating an efficient frontier. The most popular method is to minimize variance subject to fixed levels of expected return. However, even when the fixed levels are evenly dispersed, one can not count on the resulting dots being evenly dispersed. Another method uses fixed values of a risk tolerance parameter, but with this method the resulting dots are even less controllable. In this paper we develop a third approach applicable to what we call Markowitz problems (mean-variance problems with all linear constraints). The approach utilizes the results of algorithms that can compute all hyperbolic segments of a Markowitz efficient frontier. Then the approach can place dots on the hyperbolic segments of the efficient frontier in a variety ways including equally spaced. The advantage of the approach is the speed at which dotted representations can be produced and modified, particularly on large applications.
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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 | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
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".