Predictive support recovery with TV-Elastic Net penalty and logistic regression: an application to structural MRI
This work addresses the challenge of obtaining spatially coherent predictive patterns in brain disease diagnosis using MRI, though it is incremental as it builds on existing penalty methods with a new optimization approach.
The authors tackled the problem of irregular or scattered predictive patterns in neuroimaging classification by proposing an optimization framework that combines l1, l2, and Total Variation (TV) penalties, applied to structural MRI data from the ADNI dataset. The result showed that the TV penalty did not improve prediction accuracy but provided a major breakthrough in support recovery of predictive brain regions.
The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide irregular (l2 penalty) or scattered (l1 penalty) predictive pattern with a very limited relevance. A penalty like Total Variation (TV) that exploits the natural 3D structure of the images can increase the spatial coherence of the weight map. However, TV penalization leads to non-smooth optimization problems that are hard to minimize. We propose an optimization framework that minimizes any combination of l1, l2, and TV penalties while preserving the exact l1 penalty. This algorithm uses Nesterov's smoothing technique to approximate the TV penalty with a smooth function such that the loss and the penalties are minimized with an exact accelerated proximal gradient algorithm. We propose an original continuation algorithm that uses successively smaller values of the smoothing parameter to reach a prescribed precision while achieving the best possible convergence rate. This algorithm can be used with other losses or penalties. The algorithm is applied on a classification problem on the ADNI dataset. We observe that the TV penalty does not necessarily improve the prediction but provides a major breakthrough in terms of support recovery of the predictive brain regions.