Exponentially Weighted Aggregates for regression

Visual comparison between EWA and other procedures: DEMO_EWA_comparison.m


This script displays the proposed denoising method used in the corresponding paper , for various 1D signals. The signals are first transformed using DCT and then denoised using several methods of shrinkage, with or without aggregation (EWA, SS-ST, BJS, ORACLE). We consider one level of noise with standard deviation \( \sigma=0.33\). See also README.TXT in the associate zip file for more details.

Authors: \(\textbf{A. Dalalyan} \) and \( \textbf{J. Salmon} \)

Visualization of the original (non-noisy) signals considered

Parameters initialization

all_signal={'Piece-Regular','Ramp','Piece-Polynomial','HeaviSine',...
    'Doppler','Blocks'};
font_size=19;
sigma=1;
signal_size=2^9;
figure_size=[100,100, 1000, 1000];

Display signals of interest

fig_signaux1=figure('Position', figure_size);
for i=1:6
    subplot(3,2,i)
    htitle={char(all_signal(i))};
    [X,Y,absci]=generate_signal(signal_size,char(...
        all_signal(i)),sigma);
    data_axis=[0 1 min(X)-0.2 max(X)+0.2];
    plot_article(fig_signaux1,absci,X,htitle,font_size,data_axis);
end

Visualization of the denoised signals

smooth=0;
plot=1;
verb=0;
saving=0;

for i=1:6
    sigma=0.33;
    launching_performance_fft(sigma,all_signal(i),...
        signal_size,smooth,verb,plot,saving);
end


Papers:

"Optimal aggregation of affine estimators"
A. S. Dalalyan and J. Salmon, COLT 2011, PDF.

"Sharp Oracle Inequalities for Aggregation of Affine Estimators",
A. S. Dalalyan and J. Salmon, arXiv.

Corresponding Matlab toolbox ZIP.



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