On the rates of convergence of parallelized averaged stochastic gradient algorithms

The growing interest for high-dimensional and functional data analysis led in the last decade to important research developing a consequent amount of techniques. Parallelized algorithms, which consist of distributing and treat the data into different machines, for example, are a good answer to deal...

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Vydané v:Statistics (Berlin, DDR) Ročník 54; číslo 3; s. 618 - 635
Hlavní autori: Godichon-Baggioni, Antoine, Saadane, Sofiane
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Abingdon Taylor & Francis 03.05.2020
Taylor & Francis Ltd
Taylor & Francis: STM, Behavioural Science and Public Health Titles
Predmet:
Algorithms
asynchronous parallel optimization
averaging
Central limit theorem
Convergence
Data analysis
Dimensional analysis
distributed estimation
Machinery
Normality
Parallel processing
Statistics
Stochastic gradient descent
Distributed estimation
Averaging
Central Limit Theorem
Stochastic Gradient Descent
Asynchronous parallel optimization
ISSN:0233-1888, 1029-4910
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Shrnutí:The growing interest for high-dimensional and functional data analysis led in the last decade to important research developing a consequent amount of techniques. Parallelized algorithms, which consist of distributing and treat the data into different machines, for example, are a good answer to deal with large samples taking values in high-dimensional spaces. We introduce here a parallelized averaged stochastic gradient algorithm, which enables to treat efficiently and recursively the data, and so, without taking care if the distribution of the data into the machines is uniform. The rate of convergence in quadratic mean, as well as the asymptotic normality of the parallelized estimates are given, for strongly and locally strongly convex objectives.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0233-1888
1029-4910
DOI:10.1080/02331888.2020.1764557