# [Eeglablist] AMICA lrate gets stuck

Jason Palmer japalmer29 at gmail.com
Mon Aug 24 21:28:36 PDT 2015

Sorry this line should be:

>> [W,S,mods] = runamica12(newdat, ....);

From: Jason Palmer [mailto:japalmer at ucsd.edu]
Sent: Monday, August 24, 2015 9:17 PM
To: 'Kevin Tan'; 'mmiyakoshi at ucsd.edu'; 'EEGLAB List'
Subject: RE: [Eeglablist] AMICA lrate gets stuck

Hi Kevin,

Sorry, there is a bug in the code tries to take the sqrt of the negative eigenvalue (even though that dimension is being removed) making the LL=NaN and aborting. The eigenvalue is actually essentially zero, resulting from rank deficiency likely due to re-referencing, so more cleaning won’t necessarily change the arbitrarily small value to positive, unless you increase the dimensionality of the data. I’m currently fixing this bug along with some other sphering and PCA issues and will release debugged versions soon.

For now you can do the work around of sphering before Amica, e.g.

>> [U,D] = eig(cov(EEG.data(:,:)’));

>> U = fliplr(U); D = fliplr(flipud(D));  % make descending order

>> dd = diag(D);  numeig = sum(dd > 1e-9);

>> Sph = diag(sqrt(1./dd(1:numeig))) * U(:,1:numeig)‘;

>> newdat = Sph * EEG.data(:,:);   % reduce to numeigs dimensions

>> [W,S,mods] = runamica12(EEG.data(:,:), ....);

>> EEG.icasphere = S*Sph;

>> EEG.icaweights = W;

This should run amica on full rank data an avoid the negative near zero eigenvalue problem until it is fixed in the Amica code.

Best,

Jason

From: Kevin Tan [mailto:kevintan at cmu.edu]
Sent: Monday, August 24, 2015 6:39 PM
To: Jason Palmer; mmiyakoshi at ucsd.edu; EEGLAB List
Subject: Re: [Eeglablist] AMICA lrate gets stuck

Hi Jason,

I'm running into a negative min eigenvalue issue for ~25% of my subjects. This results in the binary not exporting anything to the amica output dir, stopping the main loop prematurely.

Before running AMICA, the data is fairly aggressively cleaned:

1) PREP pipeline

2) remove mastoids & PREP-interpolated chans for rank reduction

3) 1hz hi-pass

4) epoch no baseline correction

5) epoch rejection (ch means deviation, variance, max amplitude dif > 2.5 SDs)

Not sure what else I can do to clean the data to make the eigenvalues positive.

I'm using Biosemi 128ch which is known for dynamic range issues, but I run everything in double. Not sure if demeaning each channel would help since it's already hi-passed.

Also, not sure if it matters, but AMICA seems to do dimension reduction despite me removing channels to make up for 'robust' reference rank reduction.

For the subjects that do run on AMICA, the ICs seem a lot cleaner than Infomax, which makes me want to stick to AMICA.

1 : data =  -2.3969683647155762 -2.910743236541748
getting the mean ...
mean =  -7.73083349593588626E-2 -8.98852135101791128E-2 -0.17064473790401868
subtracting the mean ...
getting the sphering matrix ...
cnt =  706560
doing eig nx =  128  lwork =  163840
minimum eigenvalues =  -4.02618476752492072E-14 0.59534647773064309 0.66105027982216646
maximum eigenvalues =  3718.0696499000956 2980.9762500746847 1012.6027880321443
num eigs kept =  127
numeigs =  127

Good subject log example:

1 : data =  3.1855385303497314 5.7855358123779297
getting the mean ...
mean =  -0.38155908557715745 -0.27761248863920301 -0.3608881566308772
subtracting the mean ...
getting the sphering matrix ...
cnt =  703488
doing eig nx =  130  lwork =  169000
minimum eigenvalues =  1.35676859295476523E-13 0.80288149429025613 1.1256218532296671
maximum eigenvalues =  9749.2425686202987 1277.5793884179475 700.98046655297128
num eigs kept =  129
numeigs =  129

Many many thanks for the continued help!

–Kevin

--

Kevin Alastair M. Tan

Lab Manager/Research Assistant

Department of Psychology & Center for the Neural Basis of Cognition

Carnegie Mellon University

Baker Hall 434 <https://www.google.com/maps/place/40%C2%B026%2729.5%22N+79%C2%B056%2744.0%22W/@40.4414869,-79.9455701,61m/data=!3m1!1e3!4m2!3m1!1s0x0:0x0>  | kevintan at cmu.edu | tarrlab.org/kevintan <http://tarrlabwiki.cnbc.cmu.edu/index.php/KevinTan>

On Fri, Aug 21, 2015 at 7:36 PM, Makoto Miyakoshi <mmiyakoshi at ucsd.edu> wrote:

Dear Kevin and Jason,

In the Figure 1 of the following paper, you can see an example of the shift of log likelihood of AMICA model along with iteration.

Rissling AJ, Miyakoshi M, Sugar CA, Braff DL, Makeig S, Light GA. (2014). Cortical substrates and functional correlates of auditory deviance processing deficits in schizophrenia. Neuroimage Clin. Oct 01; 6 424-437

You can see that after 700 iterations there is no 'jump' any more, which may correspond to what Jason says reaching to the 'noise floor'. In the beta version (?) of AMICA we use here in SCCN, it has a convergence criterion and usually stops at around 1000 iterations (smallest I saw was around 700, maximum 1500).

Kevin, your questions are always very interesting and I learn a lot from them. Thank you Jason for your answers and sharing knowledge.

Makoto

On Mon, Aug 17, 2015 at 4:35 PM, Jason Palmer <japalmer29 at gmail.com> wrote:

Hi Kevin,

The Infomax wchange is actually the weight change TIMES the lrate, which is going to 1e-7. So the actual final wchange for extended infomax is 1e7 * wchange.

For Amica, if the nd weight change gets down to the 10^-5 magnitude, that is usually about the best you can expect with the large number of parameters being estimated and the finite computer precision. How small it can get depends on the number of samples you have compared to the number of channels. More channels = more parameters (nchan^2) = relatively little data = “noisier” convergence. More data = better determined optimum = less noisy convergence = smaller nd. For 64 channels with 100,000 samples, an nd of 10^-5 sounds appropriate.

However you can change “maxiter” from the default 2000, using the ‘maxiter’ keyword. This LL should continue to increase and the nd decrease (or at least not increase) beyond 2000 iterations, but not significantly. There should be a weight change “noise floor” reached, where the LL continues to increase by less and less, with possible reductions in lrate, and the nd hovers around the “noise floor”.

Best,

Jason

From: Kevin Tan [mailto:kevintan at cmu.edu]
Sent: Monday, August 17, 2015 4:21 PM
To: japalmer at ucsd.edu; EEGLAB List
Subject: Re: AMICA lrate gets stuck

Hi Jason,

Thanks so much for the detailed response, really helps clarify what drives the lrate changes between the two implementations.

However, for the same dataset processed the same way, AMICA yields higher wchange at last iteration (0.0000464763) versus extended Infomax (0.000000).

What are some reasons for this discrepancy, and what can I do improve it? Or is weight change between the two implementations not comparable? The entire AMICA log is linked in original post if that helps.

Thanks again,

Kevin

--

Kevin Alastair M. Tan

Lab Manager/Research Assistant

Department of Psychology & Center for the Neural Basis of Cognition

Carnegie Mellon University

Baker Hall 434 <https://www.google.com/maps/place/40%C2%B026%2729.5%22N+79%C2%B056%2744.0%22W/@40.4414869,-79.9455701,61m/data=!3m1!1e3!4m2!3m1!1s0x0:0x0>  | kevintan at cmu.edu | tarrlab.org/kevintan <http://tarrlabwiki.cnbc.cmu.edu/index.php/KevinTan>

On Mon, Aug 17, 2015 at 7:06 PM, Jason Palmer <japalmer29 at gmail.com> wrote:

Hi Kevin,

The Amica lrate is not supposed to decrease. The algorithm is a more typical gradient descent / Newton optimization algorithm, as opposed to the Infomax implementation in runica.m, which uses a type of simulated annealing, deciding whether to reduce the learning rate based on the angle between recent update directions. The idea there is that this angle will be small when the algorithm is near an optimum, as though it is “heading right for it”, so the lrate gets reduced if the algorithm is moving “erratically” with a large angle between consecutive directions, and doesn’t get reduced if the estimate is “moving smoothly”. In practice, this annealing method usually ends up in fact reducing the learning rate continuously until it reaches the preset minimum, which usually happens at around 500 iterations (500 reductions). I.e. the angle is never actually small, so the stopping condition is essentially a maximum number of iterations, with the updates being of smaller and smaller magnitude due to the lrate decreasing.

Amica only reduces the lrate if the likelihood decreases. In theory, with a reasonable optimum, an optimization algorithm should be able to converge without reducing the learning rate. The convergence is measured by the weight change (the nd in the amica output) independently of the lrate. That is, the weight change should theoretically decrease to zero with a constant (sufficiently small) lrate—the higher the better since higher lrate means faster convergence. A potential issue with the runica Infomax is early convergence if you are starting far from the optimum. Fortunately the optimum is usually not far from the “sphering” starting point, so 500 iterations is usually enough to converge (even with decreasing lrate).

So in Amica, the convergence is judged by the “nd”, not the lrate. The lrate should be ideally be 0.5 or 1.0, and the LL should be increasing, and the nd should be decreasing to zero.

Best,

Jason

From: Kevin Tan [mailto:kevintan at cmu.edu]
Sent: Monday, August 17, 2015 2:31 PM
To: jason at sccn.ucsd.edu; EEGLAB List
Subject: AMICA lrate gets stuck

Hi Dr. Palmer & EEGLAB list,

I'm trying out AMICA for artifact rejection and DIPFIT. In my tests, the lrate consistently gets stuck at 0.5, stopping only due to max iteration limit. This does not happen with extended Infomax.

This happens whether I use the cluster (128 threads) or a normal PC (4 threads). I run AMICA 'locally' as it's called within a matlab script already run via PBS, not sure if that makes a difference.

Here's the AMICA test stream:

- PREP pipeline

- Remove PREP-interpolated channels

- Remove 1 additional channel for rank consistency

- 1hz FIR hi-pass

- Epoch -500 to 1000ms no baseline correction

- Epoch rejection

- AMICA (using EEG(:,:) -- is it ok to concatenate epochs like this?)

Here's the output log (using the cluster):

https://cmu.box.com/s/t7j3shmwjj1wj8to80au8mdm6b5676rh

Many thanks,

Kevin

--

Kevin Alastair M. Tan

Lab Manager/Research Assistant

Department of Psychology & Center for the Neural Basis of Cognition

Carnegie Mellon University

Baker Hall 434 <https://www.google.com/maps/place/40%C2%B026%2729.5%22N+79%C2%B056%2744.0%22W/@40.4414869,-79.9455701,61m/data=!3m1!1e3!4m2!3m1!1s0x0:0x0>  | kevintan at cmu.edu | tarrlab.org/kevintan <http://tarrlabwiki.cnbc.cmu.edu/index.php/KevinTan>

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--

Makoto Miyakoshi
Swartz Center for Computational Neuroscience
Institute for Neural Computation, University of California San Diego

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