Bibliographic record
Abstract
This thesis makes contributions to two problems in learning theory: prediction with expert advice and learning mixtures of Gaussians. The problem of prediction with expert advice can be cast as a sequential game between an algorithm and an adversary as follows. At each time step, an algorithm chooses one of n options (or experts) and the adversary sets a cost for each expert. The algorithm's goal is to minimize its regret, i.e. its cost relative to the best expert in hindsight. The celebrated multiplicative weights algorithm is known to be optimal if the the game is terminated at a fixed, known time and the number of experts is large. Optimal algorithms are also known when the number of experts is 2, 3, or 4. If the game does not terminate at a known time or is run indefinitely, the optimal algorithm is not known for any number of experts. We contribute to this problem by giving the optimal algorithm when there are 2 experts. Our algorithm is designed by considering a continuous analogue of the problem, which is solved using ideas from stochastic calculus. In the second part of the thesis, we look at distribution learning, which is a fundamental task in statistics that has been studied for over a century. We consider such a problem where the distribution is a mixture of k Gaussians in d dimensions. The objective is density estimation: given i.i.d. samples from the unknown distribution, produce a distribution whose total variation from the unknown distribution is within some desired accuracy. We contribute to this problem by designing an algorithm with near-optimal sample complexity.
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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 | 0.007 | 0.041 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.005 | 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".