Structured Variable Selection with Sparsity-Inducing Norms
The Journal of Machine Learning Research
Optimization with Sparsity-Inducing Penalties
Foundations and Trends® in Machine Learning
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Inverse inference, or "brain reading", is a recent paradigm for analyzing functional magnetic resonance imaging (fMRI) data, based on pattern recognition tools. By predicting some cognitive variables related to brain activation maps, this approach aims at decoding brain activity. Inverse inference takes into account the multivariate information between voxels and is currently the only way to assess how precisely some cognitive information is encoded by the activity of neural populations within the whole brain. However, it relies on a prediction function that is plagued by the curse of dimensionality, as we have far more features than samples, i.e., more voxels than fMRI volumes. To address this problem, different methods have been proposed. Among them are univariate feature selection, feature agglomeration and regularization techniques. In this paper, we consider a hierarchical structured regularization. Specifically, the penalization we use is constructed from a tree that is obtained by spatially constrained agglomerative clustering. This approach encodes the spatial prior information in the regularization process, which makes the overall prediction procedure more robust to inter-subject variability. We test our algorithm on a real data acquired for studying the mental representation of objects, and we show that the proposed algorithm yields better prediction accuracy than reference methods.