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Master's Dissertation
DOI
10.11606/D.45.2017.tde-28092017-182905
Document
Author
Full name
Jessica Katherine de Sousa Fernandes
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Birgin, Ernesto Julian Goldberg (President)
Krejic, Natasa
Perez, José Mario Martinez
Title in Portuguese
Estudo de algoritmos de otimização estocástica aplicados em aprendizado de máquina
Keywords in Portuguese
Aprendizado de máquina
Dynamic sample size selection
Métodos de redução de variância
Otimização estocástica
Sample size approximation
Abstract in Portuguese
Em diferentes aplicações de Aprendizado de Máquina podemos estar interessados na minimização do valor esperado de certa função de perda. Para a resolução desse problema, Otimização estocástica e Sample Size Selection têm um papel importante. No presente trabalho se apresentam as análises teóricas de alguns algoritmos destas duas áreas, incluindo algumas variações que consideram redução da variância. Nos exemplos práticos pode-se observar a vantagem do método Stochastic Gradient Descent em relação ao tempo de processamento e memória, mas, considerando precisão da solução obtida juntamente com o custo de minimização, as metodologias de redução da variância obtêm as melhores soluções. Os algoritmos Dynamic Sample Size Gradient e Line Search with variable sample size selection apesar de obter soluções melhores que as de Stochastic Gradient Descent, a desvantagem se encontra no alto custo computacional deles.
Title in English
Study of algorithms of stochastic optimization applied in machine learning problems
Keywords in English
Dynamic sample size selection
Machine Learning
Sample size approximation
Stochastic optimization
Variance reduction methods
Abstract in English
In different Machine Learnings applications we can be interest in the minimization of the expected value of some loss function. For the resolution of this problem, Stochastic optimization and Sample size selection has an important role. In the present work, it is shown the theoretical analysis of some algorithms of these two areas, including some variations that considers variance reduction. In the practical examples we can observe the advantage of Stochastic Gradient Descent in relation to the processing time and memory, but considering accuracy of the solution obtained and the cost of minimization, the methodologies of variance reduction has the best solutions. In the algorithms Dynamic Sample Size Gradient and Line Search with variable sample size selection, despite of obtaining better solutions than Stochastic Gradient Descent, the disadvantage lies in their high computational cost.
 
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Publishing Date
2017-10-06
 
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