[Mne_analysis] Tuning Lambda^2 in High Noise Systems

Alexandre Gramfort alexandre.gramfort at inria.fr
Wed Feb 12 08:23:04 EST 2020
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hi Taylor,

sorry for the late reply.

Tuning lambda (or generally hyperparameters) in inverse problems is a
known challenge.
The MNE recommendation has shown to be a sensible default but surely
would be optimized
for certain studies / systems. Various strategies exist to do this:
cross-validation, "Bayesian
Ridge", L-Curve etc.

do not hesitate to share your experimental findings here.

Alex



On Thu, Jan 16, 2020 at 12:39 AM Taylor Williams
<williams.taylor at gmail.com> wrote:
>
>         External Email - Use Caution
>
> Hi All,
>
>
> I have some questions about good choices for the regularization parameter lambda^2 in high noise systems. I’m using MNE-Python to run simulations of theoretical high-density solid-state MEG arrays that operate with much higher sensor noise than low-Tc SQUID sensors. These arrays contain a small number of sensors with SNRs > 1, but the average SNR is usually << 1.
>
>
> I’ve been analyzing dipole localization error (DLE) and spatial dispersion (SD) on a resolution matrix with sensor noise injected in the middle (M @ N @ G, for M: inverse operator matrix, G: forward operator matrix, N: sensor noise matrix). I’m using MNE-Python to create my inverse and forward matrix.
>
>
> For a given system at a given sensor noise level, my measurements of DLE and SD are predictably quite sensitive to choice of lambda^2. It seems that the recommended choice of lambda^2 = 1/avg_snr (where avg_snr is the average power snr of the system) is not close to the best choice for lambda^2 found through tuning.
>
>
> As I sweep lambda^2 values, there is a clear minimum in the SD function that coincides with a knee of the curve for DLE. This seems like the right value to choose for optimal overall system performance. Most often, the tuned lambda^2 ends up being one or more orders of magnitude higher than the recommended value, with the scale factor increasing with more noise in the system.
>
>
> Does using a large lambda^2 value lead to simulation results that are valid, or is this a numerical exercise that introduces some bias that I don’t yet understand? Does it make sense that the tuned value for lambda^2 would be much larger than 1/avg_snr for high noise systems, or is this likely indicating a bug somewhere?
>
>
> Thanks,
>
> Taylor Williams
>
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