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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| Veröffentlicht in: | Statistics (Berlin, DDR) Jg. 54; H. 3; S. 618 - 635 |
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Taylor & Francis
03.05.2020
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| Abstract | 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. |
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| AbstractList | 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. The growing interest for high dimensional and functional data analysis led in the last decade to an important research developing a consequent amount of techniques. Parallelized algorithms, which consist in 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. |
| Author | Saadane, Sofiane Godichon-Baggioni, Antoine |
| Author_xml | – sequence: 1 givenname: Antoine surname: Godichon-Baggioni fullname: Godichon-Baggioni, Antoine email: antoine.godichon@insa-rouen.fr, antoine.godichon_baggioni@upmc.fr organization: Laboratoire de Mathématiques de l'INSA de Rouen, INSA de Rouen – sequence: 2 givenname: Sofiane surname: Saadane fullname: Saadane, Sofiane organization: Institut de Mathématiques de Toulouse, INSA de Toulouse |
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| Keywords | Distributed estimation Averaging Central Limit Theorem Stochastic Gradient Descent Asynchronous parallel optimization |
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| SubjectTerms | Algorithms asynchronous parallel optimization averaging Central limit theorem Convergence Data analysis Dimensional analysis distributed estimation Machinery Normality Parallel processing Statistics Stochastic gradient descent |
| Title | On the rates of convergence of parallelized averaged stochastic gradient algorithms |
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