Bibliographic record
Abstract
The past decade has witnessed the emergence of compressed sensing as a way of acquiring sparsely representable signals in a compressed form. These developments have greatly motivated research in sparse signal recovery, which lies at the heart of compressed sensing, and which has recently found its use in altogether new applications. In the first part of this thesis we study the theoretical aspects of joint-sparse recovery by means of sum-of-norms minimization, and the ReMBo-l₁ algorithm, which combines boosting techniques with l₁-minimization. For the sum-of-norms approach we derive necessary and sufficient conditions for recovery, by extending existing results to the joint-sparse setting. We focus in particular on minimization of the sum of l₁, and l₂ norms, and give concrete examples where recovery succeeds with one formulation but not with the other. We base our analysis of ReMBo-l₁ on its geometrical interpretation, which leads to a study of orthant intersections with randomly oriented subspaces. This work establishes a clear picture of the mechanics behind the method, and explains the different aspects of its performance. The second part and main contribution of this thesis is the development of a framework for solving a wide class of convex optimization problems for sparse recovery. We provide a detailed account of the application of the framework on several problems, but also consider its limitations. The framework has been implemented in the SPGL1 algorithm, which is already well established as an effective solver. Numerical results show that our algorithm is state-of-the-art, and compares favorably even with solvers for the easier---but less natural---Lagrangian formulations. The last part of this thesis discusses two supporting software packages: Sparco, which provides a suite of test problems for sparse recovery, and Spot, a Matlab toolbox for the creation and manipulation of linear operators. Spot greatly facilitates rapid prototyping in sparse recovery and compressed sensing, where linear operators form the elementary building blocks. Following the practice of reproducible research, all code used for the experiments and generation of figures is available online at http://www.cs.ubc.ca/labs/scl/thesis/09vandenBerg/.
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How this classification was reachedexpand
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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".