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Record W2787899424 · doi:10.1137/17m1136225

Learning Theory of Randomized Sparse Kaczmarz Method

2018· article· en· W2787899424 on OpenAlex
Yunwen Lei, Ding‐Xuan Zhou

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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueSIAM Journal on Imaging Sciences · 2018
Typearticle
Languageen
FieldEngineering
TopicSparse and Compressive Sensing Techniques
Canadian institutionsToronto Metropolitan University
FundersResearch Grants Council, University Grants CommitteeNational Natural Science Foundation of China
KeywordsMathematicsBregman divergenceCompressed sensingConvergence (economics)ConvexityThresholdingSequence (biology)GeneralizationCombinatoricsFunction (biology)Applied mathematicsAlgorithmDiscrete mathematicsMathematical analysisArtificial intelligenceComputer scienceImage (mathematics)

Abstract

fetched live from OpenAlex

In this paper we propose an online learning algorithm, a general randomized sparse Kaczmarz method, for generating sparse approximate solutions to linear systems and present learning theory analysis for its convergence. Under a mild assumption covering the case of noisy random measurements in the sampling process or nonlinear regression function, we show that the algorithm converges in expectation if and only if the step size sequence $\{\eta_t\}_{t\in\mathbb{N}}$ satisfies $\lim_{t\to\infty}\eta_t=0$ and $\sum_{t=1}^{\infty}\eta_t=\infty$. Convergence rates are also obtained and linear convergence is shown to be impossible under the assumption of positive variance of the sampling process. A sufficient condition for almost sure convergence is derived with an additional restriction $\sum_{t=1}^{\infty}\eta_t^2 <\infty$. Our novel analysis is performed by interpreting the randomized sparse Kaczmarz method as a special online mirror descent algorithm with a nondifferentiable mirror map and using the Bregman distance. The sufficient and necessary conditions are derived by establishing a restricted variant of strong convexity for the involved generalization error and using the special structures of the soft-thresholding operator.

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 imitation

Not 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.

metaresearch head score (Codex)0.004
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Other design · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.774
Threshold uncertainty score0.365

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0040.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.018
GPT teacher head0.296
Teacher spread0.278 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it