Improving Convergence Rate of Sign Algorithm using Natural Gradient Method

2021 ◽  
Author(s):  
Taiyo Mineo ◽  
Hayaru Shouno
Keyword(s):  
Convergence Rate ◽  
Gradient Method ◽  
Natural Gradient ◽  
Sign Algorithm

An ICA Algorithm Based on Symmetric and Asymmetric Generalized Gaussian Model

2011 ◽  
Vol 204-210 ◽  
pp. 470-475
Author(s):  
Feng Zhao ◽  
Yun Jie Zhang ◽  
Min Cai
Keyword(s):  
Independent Component Analysis ◽  
Gradient Method ◽  
Gaussian Model ◽  
Component Analysis ◽  
Independent Component ◽  
Blind Signal Separation ◽  
Natural Gradient ◽  
Analysis Model ◽  
Practical Applications ◽  
Source Signal

Maximum likelihood estimation is a very popular method to estimate the independent component analysis model because of good performance. Independent component analysis algorithm (the natural gradient method) based on this method is widely used in the field of blind signal separation. It potentially assumes that the source signal was symmetrical distribution, in fact in practical applications, source signals may be asymmetric. This article by distinguishing that the source signal is symmetrical or asymmetrical, proposes an improved natural gradient method based on symmetric generalized Gaussian model (People usually call generalized Gaussian model) and asymmetric generalized Gaussian model. The random mixed-signal simulation results show that the improved algorithm is better than the natural gradient separation method.

Deformed exponentials and portfolio selection

2018 ◽  
Vol 29 (03) ◽  
pp. 1850029 ◽  
Author(s):  
Ana Flávia P. Rodrigues ◽  
Igor M. Guerreiro ◽  
Charles Casimiro Cavalcante
Keyword(s):  
Convergence Rate ◽  
Portfolio Selection ◽  
Heavy Tails ◽  
Time Instant ◽  
Gradient Algorithm ◽  
Natural Gradient ◽  
Economic Crises ◽  
Good Convergence ◽  
Markowitz Portfolio ◽  
Mean Variance

In this paper, we present a method for portfolio selection based on the consideration on deformed exponentials in order to generalize the methods based on the gaussianity of the returns in portfolio, such as the Markowitz model. The proposed method generalizes the idea of optimizing mean-variance and mean-divergence models and allows a more accurate behavior for situations where heavy-tails distributions are necessary to describe the returns in a given time instant, such as those observed in economic crises. Numerical results show the proposed method outperforms the Markowitz portfolio for the cumulated returns with a good convergence rate of the weights for the assets which are searched by means of a natural gradient algorithm.

Tri-Diagonal Preconditioner for Toeplitz Systems from Finance

2011 ◽  
Vol 1 (1) ◽  
pp. 82-88
Author(s):  
Hong-Kui Pang ◽  
Ying-Ying Zhang ◽  
Xiao-Qing Jin
Keyword(s):  
Differential Equation ◽  
Theoretical Analysis ◽  
Convergence Rate ◽  
Option Pricing ◽  
Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Superlinear Convergence Rate ◽  
Pricing Problems ◽  
Toeplitz Systems ◽  
Toeplitz System

AbstractWe consider a nonsymmetric Toeplitz system which arises in the discretization of a partial integro-differential equation in option pricing problems. The preconditioned conjugate gradient method with a tri-diagonal preconditioner is used to solve this system. Theoretical analysis shows that under certain conditions the tri-diagonal preconditioner leads to a superlinear convergence rate. Numerical results exemplify our theoretical analysis.

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