Unified error estimate for weak biorthogonal Greedy algorithms

Jiang, Bing; Ye, Peixin; Zhang, Wenhui

doi:10.1142/s0219691322500102

Cited by 6 publications

(6 citation statements)

References 17 publications

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“…Additionally, Jiang et al [5] developed a standardized benchmarking system for data valuation. They summarized four downstream machine learning tasks for evaluating the values estimated by different data valuation methods.…”

Section: A Data Valuationmentioning

confidence: 99%

“…Following previous research [5], [11], we conduct experiments using twelve classification datasets that encompass tabular, text, and image types. Their information is summarized in Table II, which includes their sample size, input dimension, number of classes, source, and proportion of minor classes.…”

Section: A Datasets and Baselinesmentioning

confidence: 99%

“…• LOO [5]: LOO, belonging to the marginal contributionbased category, measures the utility change when one data point of interest is removed from the entire dataset. Fig.…”

Section: A Datasets and Baselinesmentioning

confidence: 99%

“…Therefore, the construction of an effective data valuation method is of great importance for data-centric applications and transactions. Existing data valuation methods can be divided into four folds [5]: marginal contribution-based [6], [7], gradient-based [8], [9], importance weight-based [10],…”

Section: Introductionmentioning

confidence: 99%

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International Comparison on the Application of Information Technology in High School Mathematics Textbooks

Zhou

2021

School Mathematics Textbooks in China

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Ultra-dense networks are widely regarded as a promising solution to explosively growing applications of Internet-of-Things (IoT) mobile devices (IMDs). However, complicated and severe interferences need to be tackled properly in such networks. To this end, both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) are utilized at first. Then, in order to attain a goal of green and secure computation offloading, under the proportional allocation of computational resources and the constraints of latency and security cost, joint device association, channel selection, security service assignment, power control and computation offloading are done for minimizing the overall energy consumed by all IMDs. It is noteworthy that multi-step computation offloading is concentrated to balance the network loads and utilize computing resources fully. Since the finally formulated problem is in a nonlinear mixed-integer form, it may be very difficult to find its closed-form solution. To solve it, an improved whale optimization algorithm (IWOA) is designed. As for this algorithm, the convergence, computational complexity and parallel implementation are analyzed in detail. Simulation results show that the designed algorithm may achieve lower energy consumption than other existing algorithms under the constraints of latency and security cost.

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Section: A Data Valuationmentioning

confidence: 99%

Section: A Datasets and Baselinesmentioning

confidence: 99%

“…• LOO [5]: LOO, belonging to the marginal contributionbased category, measures the utility change when one data point of interest is removed from the entire dataset. Fig.…”

Section: A Datasets and Baselinesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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International Comparison on the Application of Information Technology in High School Mathematics Textbooks

Zhou

2021

School Mathematics Textbooks in China

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“…Among others, simultaneous sparse approximation has been utilized in signal vector processing and multi-task learning (see [11][12][13][14]). It is well known that the greedy-type algorithms are powerful tools for generating such sparse approximations (see [15][16][17][18][19]). In particular, vector greedy algorithms are very efficient at approximating a given finite number of target elements simultaneously( see [20][21][22][23]).…”

Section: Introductionmentioning

confidence: 99%

Approximation Properties of the Vector Weak Rescaled Pure Greedy Algorithm

Guo

et al. 2023

Mathematics

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We first study the error performances of the Vector Weak Rescaled Pure Greedy Algorithm for simultaneous approximation with respect to a dictionary D in a Hilbert space. We show that the convergence rate of the Vector Weak Rescaled Pure Greedy Algorithm on A1(D) and the closure of the convex hull of the dictionary D is optimal. The Vector Weak Rescaled Pure Greedy Algorithm has some advantages. It has a weaker convergence condition and a better convergence rate than the Vector Weak Pure Greedy Algorithm and is simpler than the Vector Weak Orthogonal Greedy Algorithm. Then, we design a Vector Weak Rescaled Pure Greedy Algorithm in a uniformly smooth Banach space setting. We obtain the convergence properties and error bound of the Vector Weak Rescaled Pure Greedy Algorithm in this case. The results show that the convergence rate of the VWRPGA on A1(D) is sharp. Similarly, the Vector Weak Rescaled Pure Greedy Algorithm is simpler than the Vector Weak Chebyshev Greedy Algorithm and the Vector Weak Relaxed Greedy Algorithm.

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