Streaming kernel regression with provably adaptive mean, variance, and regularization
Why this work is in the frame
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Bibliographic record
Abstract
We consider the problem of streaming kernel regression, when the observations\narrive sequentially and the goal is to recover the underlying mean function,\nassumed to belong to an RKHS. The variance of the noise is not assumed to be\nknown. In this context, we tackle the problem of tuning the regularization\nparameter adaptively at each time step, while maintaining tight confidence\nbounds estimates on the value of the mean function at each point. To this end,\nwe first generalize existing results for finite-dimensional linear regression\nwith fixed regularization and known variance to the kernel setup with a\nregularization parameter allowed to be a measurable function of past\nobservations. Then, using appropriate self-normalized inequalities we build\nupper and lower bound estimates for the variance, leading to Bersntein-like\nconcentration bounds. The later is used in order to define the adaptive\nregularization. The bounds resulting from our technique are valid uniformly\nover all observation points and all time steps, and are compared against the\nliterature with numerical experiments. Finally, the potential of these tools is\nillustrated by an application to kernelized bandits, where we revisit the\nKernel UCB and Kernel Thompson Sampling procedures, and show the benefits of\nthe novel adaptive kernel tuning strategy.\n
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it