{"arxiv_id":"1203.5483","incoming":{"papers":1,"sentences":1,"groups":[{"kind":"background","label":"Cites it as background","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2502.13432","title":"Brief introduction in greedy approximation","url":"/paper/2502.13432","section":"Introduction","sentence":"We refer the reader to the papers [ref] and [ref] for concise surveys of some results on greedy algorithms from the point of view of convex optimization and signal processing.","intent_p":0.98,"contests_p":null}]}],"unlabelled_sentences":0},"outgoing":{"papers":3,"sentences":14,"groups":[{"kind":"comparison","label":"Compares with","papers":2,"sentences":4,"quotes":[{"arxiv_id":"1010.2731","title":"A Unified Framework for High-Dimensional Analysis of M-Estimators with Decomposable Regularizers","url":"/paper/1010.2731","section":"Sparse Reconstruction Conditions","sentence":"The SRH and SRL conditions are similar to various forms of the Restricted Strong Convexity (RSC) and Restricted Strong Smoothness (RSS) conditions [ref] in the sense that they all bound the curvature of the objective function over a restricted set.","intent_p":0.96,"contests_p":null},{"arxiv_id":"1104.4824","title":"Fast global convergence of gradient methods for high-dimensional statistical recovery","url":"/paper/1104.4824","section":"Sparse Reconstruction Conditions","sentence":"The SRH and SRL conditions are similar to various forms of the Restricted Strong Convexity (RSC) and Restricted Strong Smoothness (RSS) conditions [ref] in the sense that they all bound the curvature of the objective function over a restricted set.","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":3,"sentences":4,"quotes":[{"arxiv_id":"1010.2731","title":"A Unified Framework for High-Dimensional Analysis of M-Estimators with Decomposable Regularizers","url":"/paper/1010.2731","section":"Introduction","sentence":"A more general frame of study is proposed and analyzed by [ref] where regularization with “decomposable” norms is considered in M-estimation problems.","intent_p":0.91,"contests_p":null},{"arxiv_id":"1012.0621","title":"The Convex Geometry of Linear Inverse Problems","url":"/paper/1012.0621","section":"Introduction","sentence":"[ref] also proposed a coordinate-descent type algorithm for minimization of a convex and smooth objective over the convex signal/parameter models introduced in [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"1104.4824","title":"Fast global convergence of gradient methods for high-dimensional statistical recovery","url":"/paper/1104.4824","section":"Sparse Linear Regression and Compressed Sensing","sentence":"Therefore, several first-order convex optimization methods are developed and analyzed as more efficient alternatives (see e.g., [ref] and [ref] ).","intent_p":0.87,"contests_p":null}]}],"unlabelled_sentences":6},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1203.5483"}}