[Eeglablist] Ask a question again for Laplace distribution ~ Sech^2(X) distribution???

[Nolte, Guido (NIH/NINDS)]

Dear Stephen, 

do you have any reason why the Laplace distributed data should perform
worse? 

Infomax can be derived from a maximum likelihood principle in the sense
that: 

if the data have this specific distribution then that specific kernel is
optimal. 

 

Aren't you inverting this argument to: given that specific kernel then the 

respective distribution of the data performs best.  I don't think 

one can do that. To give a stupid counter-example: If an estimator 

is optimal for gaussian  noise, data with large gaussian noise will still
give worse results 

than data with small non-gaussian noise. 

For the ICA problem: If the Laplace-distribution deviates more from a
gaussian 

than the Sech^2(X) distribution,  then - I guess - the former will give
better separation (almost) no matter 

what method is used. 

 

 

- Guido

 

 

 

 

 

Guido Nolte

NINDS/NIH

10 Center Drive MSC 1428

Bldg 10, Room 5N226

Bethesda, MD 20892-1428

USA

 

e-mail:  <mailto:nolteg at ninds.nih.gov> nolteg at ninds.nih.gov

Tel.: +1-301-435-1578

 

-----Original Message-----
From: Stephen Hong [mailto:stephen_hong at yahoo.com] 
Sent: Friday, May 09, 2003 2:09 PM
To: smakeig at ucsd.edu; eeglablist at sccn.ucsd.edu
Subject: [Eeglablist] Ask a question again for Laplace distribution ~
Sech^2(X) distribution???

 

Hello,

I have a question again: I want to compare the performance between Laplace
distributed data and Hyperbolic functions.

 

When I use the runica ( ) for comparing the performance between the
statistically independent sources with  Laplace distribution and the
statistically independent sources with the pdf: f(x)= 0.25*sech^2(0.5x), in
which the default logistic algorithm is used, I don't understand why the
blind separation performance of Laplace distributed data is always better
than the latter. 

 

Checking their CDFs, the latter's CDF (i.e., 0.5*tanh(X)+0.5)  is identical
to the logistic kernel distribution ( in runica ( ), So the latter should be
better than the former (Laplace distributed data). Why the simulation
results are always inconsistent.

 IS there someone who can explain this contradictious results? 

Thank you very much!

 

PS: (Our simulation methods: We  tried 4 statistically independent Laplace
distributed data and the above hyperbolic function as 4 sources,
respectively. Then create 4 mixing signals using a mixing matrix A (4x4).
After calling the "runica" function, we calculate the correlation
coefficients between  ICs and the original source signals. 

We also tried 3 kinds of source signals (Gaussian, Laplace, Sech^())
together, the simulation results alwas show that Laplace case is better than
others. We ensurethe mean removed and source data with rough same varinace
for each distribution before the sepeartion process.)

 

 

Stephen

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