Performance of Distribution Regression with Doubling Measure under the seek of Closest Point

Ramazanli, Ilqar

doi:10.48550/arxiv.2203.00155

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…Therefore, this result was concluding almost optimality of the nuclear norm minimization where sampling method is passive. However, in modern data analysis it has been show that adaptive sensing and sampling methods are outperforming passive sampling methods Ramazanli (2022); Haupt et al (2011); Warmuth & Kuzmin (2008); . In a follow up work the paper Krishnamurthy & Singh (2013) has proposed an adaptive matrix completion algorithm that can actually recover underlying matrix using at most O(µ 0 r 1.5 log r ǫ ) many observation.…”

Section: Introductionmentioning

confidence: 99%

Lifelong Matrix Completion with Sparsity-Number

Ramazanli¹

2022

Preprint

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Matrix completion problem has been previously studied under various adaptive and passive settings. Previously, researchers have proposed passive, two-phase and single-phase algorithms using coherence parameter, and multi phase algorithm using sparsity-number. It has been shown that the method using sparsity-number reaching to theoretical lower bounds in many conditions. However, the aforementioned method is running in many phases through the matrix completion process, therefore it makes much more informative decision at each stage. Hence, it is natural that the method outperforms previous algorithms. In this paper, we are using the idea of sparsity-number and propose and single-phase column space recovery algorithm which can be extended to two-phase exact matrix completion algorithm. Moreover, we show that these methods are as efficient as multi-phase matrix recovery algorithm. We provide experimental evidence to illustrate the performance of our algorithm.

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Section: Introductionmentioning

confidence: 99%

Lifelong Matrix Completion with Sparsity-Number

Ramazanli¹

2022

Preprint

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“…It has been shown in many problems, adaptive methods are outperforming passive traditional machine learning methods. Ramazanli (2022b) has show the power of adaptivity in distribution regression problem. Paramythis & Loidl-Reisinger (2003) has studied adaptive learning for environment learning, and famous adaptive learning algorithm also proposed in Riedmiller & Braun (1992) Specifically for matrix completion Krishnamurthy & Singh (2013, 2014; Ramazanli; Balcan & Zhang (2016) showed that for adaptivity helps us to reach theoretical bounds.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Noisy Matrix Completion

Ramazanli¹

2022

Preprint

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Low-rank matrix completion has been studied extensively under various type of categories. The problem could be categorized as noisy completion or exact completion, also active or passive completion algorithms. In this paper we focus on adaptive matrix completion with bounded type of noise. We assume that the matrix M we target to recover is composed as low-rank matrix with addition of bounded small noise. The problem has been previously studied by Balcan & Zhang (2016), in a fixed sampling model. Here, we study this problem in adaptive setting that, we continuously estimate an upper bound for the angle with the underlying low-rank subspace and noise-added subspace. Moreover, the method suggested here, could be shown requires much smaller observation than aforementioned method.

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Performance of Distribution Regression with Doubling Measure under the seek of Closest Point

Cited by 2 publications

References 11 publications

Lifelong Matrix Completion with Sparsity-Number

Lifelong Matrix Completion with Sparsity-Number

Adaptive Noisy Matrix Completion

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