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Bug 2717 - create a FAQ about cfg.lambda
| Status | ASSIGNED |
| Reported | 2014-10-02 13:37:00 +0200 |
| Modified | 2014-12-04 15:32:42 +0100 |
| Product: | FieldTrip |
| Component: | documentation |
| Version: | unspecified |
| Hardware: | PC |
| Operating System: | Mac OS |
| Importance: | P5 normal |
| Assigned to: | Jim Herring |
| URL: | |
| Tags: | |
| Depends on: | |
| Blocks: | |
| See also: | http://bugzilla.fcdonders.nl/show_bug.cgi?id=2016 |
Jim Herring - 2014-10-02 13:37:53 +0200
cfg.lambda can be an important parameter in getting clean results from beamformer analyses. However, to non-engineers (like me) it is often unclear what it does (conceptually and computationally). Therefore, we should create a FAQ that explains this.
Jim Herring - 2014-10-02 13:59:50 +0200
From wikipedia: Regularization, in mathematics and statistics and particularly in the fields of machine learning and inverse problems, refers to a process of introducing additional information in order to solve an ill-posed problem or to prevent overfitting. This information is usually of the form of a penalty for complexity, such as restrictions for smoothness or bounds on the vector space norm.
Jim Herring - 2014-10-02 14:32:43 +0200
Some notes: When beamforming we are trying to solve an ill-posed problem; there are multiple possible solutions to calculate a spatial filter. Furthermore, our data is usually noisy. We still try to solve our inverse problem. To account for the amount of noise in the data we can use what is called a regularization paramater, lambda in our case. The amount of regularization, i.e. the size of lambda, depends on the noise level. However, there is always a trade-off. The larger your regularization parameter, the less you trust your data and the more noise you assume to be present in the data. The consequence is that your estimation is more blurry. The smaller your amount of regularization is, the better you assume your data to be (i.e. lower noise level) the unstable the result can be under noisy conditions. The trick is to find the right amount of regularization that fits the noise level in your data. In a way the regularization parameter reflects how much you trust your data. Practically, in DICS beamforming you specify lambda as a percentage. Behind the scenes this percentage is translated into the specified percentage of the average cross-correlaton within channels. This result is then added to the cross-spectral density matrix before inversion.
Robert Oostenveld - 2014-10-02 19:22:51 +0200
*** Bug 2016 has been marked as a duplicate of this bug. ***
Jim Herring - 2014-10-02 22:00:37 +0200
I found a very helpful comment from Michael Wibral that explains the effect of lambda in a nutshell on the discussion list: Quoting Michael Wibral
Johanna - 2014-11-21 11:41:37 +0100
I look forward to having this FAQ to point others to! :-) One idea I'd add to this, is useful to me. In the ideal world of sufficient data, then lambda=0 and one gets the 'true' beamformer result. In the opposite extreme of not trusting your data at all (and/or insufficient amount), then you could set lambda='100%' which means that you are effectively ignoring the data (by turning the data covariance matrix into indentity matrix times a constnat) and you end up with a min-norm result.
Robert Oostenveld - 2014-12-04 14:32:57 +0100
(In reply to Johanna from comment #5) Lambda*eye(cnhan) is added to the data covariance matrix, i.e. it is not (1-lambda)*cov + lamda*eye to achieve minnorm, lambda would have to approach infinity.