Approximation and streaming algorithms for histogram construction problems
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Histograms and related synopsis structures are popular techniques for approximating data distributions. These have been successful in query optimization and a variety of applications, including approximate querying, similarity searching, and data mining, to name a few. Histograms were a few of the earliest synopsis structures proposed and continue to be used widely. The histogram construction problem is to construct the best histogram restricted to a space bound that reflects the data distribution most accurately under a given error measure.The histograms are used as quick and easy estimates. Thus, a slight loss of accuracy, compared to the optimal histogram under the given error measure, can be offset by fast histogram construction algorithms. A natural question arises in this context: Can we find a fast near optimal approximation algorithm for the histogram construction problem? In this article, we give the first linear time (1+ϵ)-factor approximation algorithms (for any ϵ > 0) for a large number of histogram construction problems including the use of piecewise small degree polynomials to approximate data, workloads, etc. Several of our algorithms extend to data streams.Using synthetic and real-life data sets, we demonstrate that in many scenarios the approximate histograms are almost identical to optimal histograms in quality and are significantly faster to construct.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| 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