In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity.
For standard Lasso theory to hold though, the regularization parameter should be proportional to the noise level, which is generally unknown in practice.
A remedy is to consider estimators, such as the Concomitant Lasso, which jointly optimize over the regression coefficients and the noise level.
However, when data from different sources are pooled to increase sample size, or when dealing with multimodal data, noise levels differ and new dedicated estimators are needed.
We provide new statistical and computational solutions to perform heteroscedastic regression, with an emphasis on functional brain imaging with magneto- and electroencephalographic (M/EEG) signals.
When instantiated to de-correlated noise, our framework leads to an efficient algorithm.Experiments demonstrate improved prediction and support identification with correct estimation of noise levels. Results on multimodal neuroimaging problems with M/EEG data are also reported.
This is joint work with M. Massias and A. Gramfort.